A car of mass 1000 kg is moving with a velocity of 20 m/s. It applies brakes and comes to a stop in 5 seconds. What is the average force exerted by the brakes?

Correct Option: A. Solution: The change in momentum $\Delta p$ is $1000 \times 20 = 20000 \text{ kg m/s}$. The average force $F$ is given by $F = \frac{\Delta p}{\Delta t} = \frac{20000}{5} = 4000 \text{ N}$.

Laws of Motion

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Summary

Summary of Laws of Motion

Aristotle's Fallacy: A force is not necessary to keep a body in uniform motion; it is needed to counteract friction.
Law of Inertia: A body remains at rest or in uniform motion unless acted upon by an external force.
Newton's First Law: If the external force on a body is zero, its acceleration is zero.
Momentum (p): Defined as the product of mass (m) and velocity (v):

$p = mv$
Newton's Second Law: The rate of change of momentum is proportional to the applied force, expressed as:

$F = rac{dp}{dt}$

where F is the net external force and a is the acceleration.
- SI unit of force: 1 N = 1 kg m s⁻².
- The second law is a vector equation applicable to particles and systems of particles.
Impulse: The product of force and time, equal to the change in momentum. Useful for large forces acting over short times.
Newton's Third Law: For every action, there is an equal and opposite reaction.
Common Forces in Mechanics: Includes gravitational force, tension, friction, normal force, etc.
Static Friction: A self-adjusting force, up to its limit, defined as:

$f_s ext{ (static friction)} ext{ where } f_s ext{ ≤ } ext{µ}_s N$
Kinetic Friction: Defined as:

$f_k = ext{µ}_k N$
Centripetal Force: Not a separate force but the name for the force providing inward radial acceleration in circular motion.

Learning Objectives

Understand the concept of inertia and its implications in motion.
Explain Newton's three laws of motion and their applications.
Calculate momentum and understand its significance in mechanics.
Apply Newton's second law to solve problems involving force and acceleration.
Analyze the concept of impulse and its relationship to momentum.
Differentiate between static and kinetic friction and their applications in real-world scenarios.
Utilize free-body diagrams to visualize forces acting on a system.
Solve problems involving tension in strings and forces in circular motion.

Detailed Notes

Chapter Notes on Laws of Motion

4.1 Introduction

4.2 Aristotle's Fallacy

Aristotle's view that a force is necessary to keep a body in uniform motion is incorrect. A force is necessary to counteract friction.

4.3 The Law of Inertia

Galileo's observations led to the law of inertia, which states that a body remains at rest or in uniform motion unless acted upon by an external force.
Newton's First Law of Motion: If the external force on a body is zero, its acceleration is zero.

4.4 Newton's First Law of Motion

Rephrased: Everybody continues in its state of rest or uniform motion unless compelled by an external force.

4.5 Newton's Second Law of Motion

Definition: The rate of change of momentum is proportional to the applied force and occurs in the direction of the force.
Formula: F = ma, where F is the net external force and a is acceleration.
SI Unit of Force: 1 N = 1 kg m s⁻².
Key Points:
- Consistent with the First Law (F = 0 implies a = 0).
- Applicable to particles and systems of particles.
- Local law: acceleration at a point does not depend on the history of motion.

4.6 Newton's Third Law of Motion

Statement: To every action, there is always an equal and opposite reaction.
Important Notes:
- Action and reaction forces act on different bodies.
- They occur simultaneously, not sequentially.

4.7 Conservation of Momentum

Momentum (p) is defined as the product of mass (m) and velocity (v): p = mv.

4.8 Equilibrium of a Particle

In equilibrium, the sum of forces acting on a particle is zero.

4.9 Common Forces in Mechanics

Types of forces include:
- Gravitational force
- Tension
- Friction
- Normal force

4.10 Circular Motion

Centripetal force is not a separate force but the name for the net force causing circular motion.

4.11 Solving Problems in Mechanics

Drawing free-body diagrams is essential for visualizing forces acting on a system.

Summary

Aristotle's view on force and motion is incorrect.
Galileo's law of inertia is foundational to Newton's First Law.
Momentum is defined as p = mv.
Newton's Second Law relates force, mass, and acceleration.
Impulse is the product of force and time, equating to change in momentum.
Newton's Third Law emphasizes action-reaction pairs.

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Misunderstanding Newton's Laws: Many students confuse the terms 'action' and 'reaction' in Newton's third law, thinking that action precedes reaction. Remember, they act simultaneously on different bodies.
Static Friction Misapplication: Do not assume that static friction always equals µₛ N. It is a self-adjusting force and only reaches its maximum value when necessary.
Forces in Equilibrium: The equation mg = R is only valid when the body is in equilibrium. In non-equilibrium situations, these forces can differ.
Centripetal Force Confusion: Centripetal force is not a separate force; it is the net force causing circular motion, such as tension or gravity.
Impulse Calculation Errors: When calculating impulse, ensure you understand that it is the change in momentum and can be calculated even if the forces during contact are unknown.

Exam Tips

Draw Free-Body Diagrams: This practice helps clarify the forces acting on a system and is essential for solving mechanics problems.
Understand the Context of Forces: Familiarize yourself with different types of forces (e.g., tension, friction, normal force) and their contexts to avoid confusion.
Practice with Real-World Examples: Relate problems to everyday situations to better grasp concepts like inertia, momentum, and forces.
Review Key Definitions and Formulas: Make sure you can define and apply key terms like impulse, momentum, and Newton's laws accurately.
Check Units Consistency: Always ensure that your units are consistent, especially when applying formulas in mechanics.

Practice & Assessment

Multiple Choice Questions

The stone moves radially outwards.

The stone flies off tangentially.

The stone flies off at an angle with the tangent.

The stone remains in circular motion.

Correct Answer: B

Solution:

When the string breaks, the stone flies off tangentially due to inertia.

A new type of force specific to circular motion.

The force that acts perpendicular to the direction of motion.

Any material force like tension or gravity that acts towards the center.

The force that acts in the direction of motion.

Correct Answer: C

Solution:

Centripetal force is not a new type of force; it is provided by material forces like tension, gravity, etc., that act towards the center of the circular path.

1 m/s

2 m/s

3 m/s

0 m/s

Correct Answer: B

Solution:

In a perfectly elastic collision, both momentum and kinetic energy are conserved. Using the conservation of momentum:

0.2 \times 3 + 0.3 \times 0 = 0.2 \times v_1 + 0.3 \times v_2

. Using conservation of kinetic energy:

\frac{1}{2} \times 0.2 \times 3^2 = \frac{1}{2} \times 0.2 \times v_1^2 + \frac{1}{2} \times 0.3 \times v_2^2

. Solving these equations,

v_1 = 2 \text{ m/s}

20 m/s

30 m/s

40 m/s

50 m/s

Correct Answer: C

Solution:

The initial momentum of the object is

p_i = mv = 15 \times 10 = 150 \, \text{kg m/s}

. The force applied is

F = 30 \, \text{N}

, and the time duration is

t = 5 \, \text{s}

. The change in momentum (impulse) is

\Delta p = Ft = 30 \times 5 = 150 \, \text{kg m/s}

. The final momentum is

p_f = p_i + \Delta p = 150 + 150 = 300 \, \text{kg m/s}

. Therefore, the final velocity is

v_f = \frac{p_f}{m} = \frac{300}{15} = 20 \, \text{m/s}

For every action, there is an equal and opposite reaction.

A force is necessary to keep a body in uniform motion.

The rate of change of momentum is proportional to the applied force.

Momentum is the product of mass and velocity.

Correct Answer: A

Solution:

Newton's third law states that for every action, there is an equal and opposite reaction.

Static friction is always greater than kinetic friction.

Kinetic friction is always greater than static friction.

Static friction does not depend on the area of contact.

Kinetic friction depends on the speed of the moving object.

Correct Answer: A

Solution:

Static friction is generally greater than kinetic friction because it needs to overcome the initial interlocking between surfaces.

1.5 m/s

2 m/s

3 m/s

4 m/s

Correct Answer: C

Solution:

By conservation of momentum, the total momentum before and after must be zero. If one skater moves with 3 m/s, the other must move with 3 m/s in the opposite direction to conserve momentum:

50 \times 3 + 50 \times v = 0

, thus

v = -3 \text{ m/s}

8 N

7.84 N

9.8 N

10 N

Correct Answer: B

Solution:

The maximum static friction force

f_s

is given by

f_s = \mu_s N

, where

N = mg = 2 \times 9.8 = 19.6 \text{ N}

. Thus,

f_s = 0.4 \times 19.6 = 7.84 \text{ N}

. This is the minimum force required to overcome static friction and start moving the block.

14 Ns

18 Ns

22 Ns

26 Ns

Correct Answer: C

Solution:

Impulse is the integral of force over time:

I = \int_0^2 (3t^2 + 2t + 1) \, dt = [t^3 + t^2 + t]_0^2 = (8 + 4 + 2) - (0) = 14 \text{ Ns}

The body moves in the direction of the force.

An equal and opposite force acts on a different body.

The body accelerates indefinitely.

The force is absorbed by the body.

Correct Answer: B

Solution:

Newton's third law states that for every action, there is an equal and opposite reaction, meaning forces act in pairs on different bodies.

1.96 m/s²

2.45 m/s²

3.27 m/s²

4.90 m/s²

Correct Answer: B

Solution:

The acceleration

a

can be found using the formula

a = \frac{(m_2 - m_1)g}{m_1 + m_2} = \frac{(12 - 8) \times 9.8}{12 + 8} = 2.45 \text{ m/s}^2

1 m/s²

2 m/s²

3 m/s²

4 m/s²

Correct Answer: C

Solution:

The total mass of the system is 15 kg. Using Newton's second law,

F = ma

, the acceleration

a = \frac{F}{m} = \frac{30}{15} = 2 \text{ m/s}^2

Newton

Joule

Watt

Pascal

Correct Answer: A

Solution:

The SI unit of force is the newton, which is equivalent to 1 kg m s⁻².

9.5 m

11.5 m

12.5 m

14.5 m

Correct Answer: B

Solution:

Using the equation

v^2 = u^2 - 2gh

, where

v = 0

at the maximum height,

u = 15 \text{ m/s}

, and

g = 9.8 \text{ m/s}^2

, we solve for

h

0 = 15^2 - 2 \cdot 9.8 \cdot h \Rightarrow h = \frac{225}{19.6} \approx 11.5 \text{ m}

It states that force is the product of mass and velocity.

It states that the rate of change of momentum is proportional to the applied force.

It states that every action has an equal and opposite reaction.

It states that a body at rest will remain at rest unless acted upon by an external force.

Correct Answer: B

Solution:

Newton's second law of motion states that the rate of change of momentum of a body is proportional to the applied force and occurs in the direction of the force.

It requires a force to maintain its motion.

It continues in motion without any force.

It comes to rest without a force.

It accelerates without a force.

Correct Answer: A

Solution:

Aristotle's fallacy states that a force is necessary to keep a body in uniform motion, which is incorrect as per modern physics.

5 seconds

10 seconds

15 seconds

20 seconds

Correct Answer: B

Solution:

Using Newton's second law,

a = \frac{F}{m} = \frac{1000}{500} = 2 \text{ m/s}^2

. Using

v = u + at

, where

u = 0

v = 20

, we solve for

t

20 = 0 + 2t \Rightarrow t = 10 \text{ seconds}

1 m/s²

2 m/s²

3 m/s²

4 m/s²

Correct Answer: B

Solution:

The total mass of the system is

m = 5 + 10 = 15 \, \text{kg}

. The force applied is

F = 30 \, \text{N}

. The acceleration

a

is given by

a = \frac{F}{m} = \frac{30}{15} = 2 \, \text{m/s}^2

The force of gravity acting on a falling apple.

The force of a bat hitting a ball and the ball hitting the bat.

The force of friction slowing down a sliding box.

The tension in a rope holding a hanging weight.

Correct Answer: B

Solution:

According to Newton's third law, the force of a bat on a ball and the force of the ball on the bat are equal and opposite, forming an action-reaction pair.

5 m/s²

10 m/s²

2 m/s²

20 m/s²

Correct Answer: A

Solution:

According to Newton's second law, acceleration is given by

a = \frac{F}{m}

. Therefore,

a = \frac{10\, \text{N}}{2\, \text{kg}} = 5\, \text{m/s}^2

2 Ns

0 Ns

-2 Ns

-1 Ns

Correct Answer: C

Solution:

Impulse is the change in momentum. The impulse due to gravity is

\Delta p = m \cdot \Delta v = 0.2 \cdot (-10) = -2 \text{ Ns}

The products move in the same direction.

The products move in opposite directions.

The products remain stationary.

The products move randomly.

Correct Answer: B

Solution:

According to the conservation of momentum, if a nucleus disintegrates at rest, the two smaller nuclei must move in opposite directions to conserve momentum.

14 m/s

20 m/s

10 m/s

9.8 m/s

Correct Answer: A

Solution:

Using the equation of motion

v^2 = u^2 + 2gh

, where

u = 0

g = 9.8 \text{ m/s}^2

, and

h = 10 \text{ m}

. Thus,

v^2 = 0 + 2 \times 9.8 \times 10 = 196

. Therefore,

v = \sqrt{196} = 14 \text{ m/s}

20 N

15 N

25 N

10 N

Correct Answer: A

Solution:

The maximum static frictional force is given by

f_s = \mu_s N

, where

\mu_s = 0.4

and

N = mg = 5 \times 9.8 = 49 \text{ N}

. Thus,

f_s = 0.4 \times 49 = 19.6 \text{ N}

. The maximum horizontal force that can be applied without moving the block is approximately

20 \text{ N}

20 m/s

5 m/s

10 m/s

15 m/s

Correct Answer: A

Solution:

Using Newton's second law, we have

F = ma

. Here,

F = 50 \text{ N}

and

m = 10 \text{ kg}

, so

a = \frac{F}{m} = \frac{50}{10} = 5 \text{ m/s}^2

. The final velocity

v

can be calculated using

v = u + at

, where

u = 0

a = 5 \text{ m/s}^2

, and

t = 4 \text{ s}

. Thus,

v = 0 + 5 \times 4 = 20 \text{ m/s}

Tension in the string

Gravitational force

Frictional force

Air resistance

Correct Answer: A

Solution:

In circular motion, the tension in the string provides the necessary centripetal force to keep the stone moving in a circle.

It remains at rest or moves with constant velocity.

It accelerates.

It changes direction.

It comes to a stop.

Correct Answer: A

Solution:

Newton's first law states that a body remains at rest or in uniform motion unless acted upon by an external force.

Impulse is the rate of change of momentum.

Impulse is the product of momentum and time.

Impulse is equal to the change in momentum.

Impulse is the force required to maintain momentum.

Correct Answer: C

Solution:

Impulse is defined as the product of force and time, which equals the change in momentum.

Force

Impulse

Momentum

Acceleration

Correct Answer: C

Solution:

Momentum is defined as the product of mass and velocity of a body, represented as

p = mv

1 m/s

2 m/s

-1 m/s

-2 m/s

Correct Answer: D

Solution:

Using the conservation of momentum and the fact that kinetic energy is conserved in elastic collisions, we have the equations:

m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2

and

\frac{1}{2}m_1u_1^2 + \frac{1}{2}m_2u_2^2 = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2

. Solving these with

m_1 = 0.2 \text{ kg}

u_1 = 3 \text{ m/s}

m_2 = 0.3 \text{ kg}

, and

u_2 = 0

, we find

v_1 = -2 \text{ m/s}

7 Ns

9.8 Ns

14 Ns

19.6 Ns

Correct Answer: D

Solution:

The speed just before impact is

v = \sqrt{2gh} = \sqrt{2 \cdot 9.8 \cdot 10} = 14 \text{ m/s}

. The change in velocity is

\Delta v = 14 - (-14) = 28 \text{ m/s}

. Impulse

J = m \cdot \Delta v = 0.5 \cdot 28 = 14 \text{ Ns}

It opposes impending relative motion.

It is always greater than kinetic friction.

It is independent of the area of contact.

It acts only when there is motion.

Correct Answer: D

Solution:

Static friction acts to prevent motion and only opposes impending motion, not actual motion.

5000 N

6000 N

7000 N

8000 N

Correct Answer: B

Solution:

Using the equation

F = ma

, where

m = 1200 \text{ kg}

and

a = \frac{\Delta v}{\Delta t} = \frac{0 - 25}{6} = -4.17 \text{ m/s}^2

. Therefore,

F = 1200 \times (-4.17) = -5000 \text{ N}

. The magnitude of the force is

6000 \text{ N}

The stone moves radially outwards.

The stone flies off tangentially from the instant the string breaks.

The stone flies off at an angle with the tangent.

The stone moves in a spiral path.

Correct Answer: B

Solution:

When the string breaks, the stone will continue to move in the direction it was moving at the instant of the break, which is tangentially to the circular path.

0 kg m/s

1 kg m/s

2 kg m/s

4 kg m/s

Correct Answer: C

Solution:

The total momentum before the collision is

0.5 \times 4 + 0 = 2 \text{ kg m/s}

. By conservation of momentum, the total momentum after the collision is also 2 kg m/s.

Force is inversely proportional to acceleration.

Force is directly proportional to acceleration.

Force is independent of acceleration.

Force is equal to mass times velocity.

Correct Answer: B

Solution:

Newton's second law states that the rate of change of momentum of a body is proportional to the applied force, which is directly proportional to the acceleration.

5 m/s²

8.66 m/s²

4.33 m/s²

10 m/s²

Correct Answer: C

Solution:

The horizontal component of the force is

F_x = 10 \cos(30°) = 10 \times \frac{\sqrt{3}}{2} = 8.66 \text{ N}

. The acceleration is given by

a = \frac{F_x}{m} = \frac{8.66}{2} = 4.33 \text{ m/s}^2

26 m/s

20 m/s

18 m/s

16 m/s

Correct Answer: A

Solution:

Using the equation of motion,

v = u + at

, where initial velocity

u = 10 \text{ m/s}

, acceleration

a = \frac{F}{m} = \frac{15}{5} = 3 \text{ m/s}^2

, and time

t = 4 \text{ s}

. Thus, final velocity

v = 10 + 3 \times 4 = 22 \text{ m/s}

25 N

39.5 N

50 N

75 N

Correct Answer: B

Solution:

The tension in the string is calculated using the formula for centripetal force:

T = m \cdot \omega^2 \cdot r

, where

\omega = \frac{2\pi \cdot 40}{60}

rad/s.

0.3 Ns

0.6 Ns

0.1 Ns

0.5 Ns

Correct Answer: B

Solution:

Impulse is the change in momentum. The change in velocity is 12 m/s (from 6 m/s to -6 m/s), so impulse = mass × change in velocity = 0.05 kg × 12 m/s = 0.6 Ns.

5 N

10 N

20 N

25 N

Correct Answer: B

Solution:

The centripetal force

F_c

is given by

F_c = \frac{mv^2}{r}

. Substituting the values,

F_c = \frac{0.2 \times 5^2}{0.5} = 10 \text{ N}

1 m/s

2 m/s

3 m/s

4 m/s

Correct Answer: C

Solution:

In an elastic collision, both momentum and kinetic energy are conserved. Using conservation of momentum:

0.1 \times 5 + 0.2 \times 0 = 0.1 \times v_1 + 0.2 \times v_2

. Using conservation of kinetic energy:

\frac{1}{2} \times 0.1 \times 5^2 = \frac{1}{2} \times 0.1 \times v_1^2 + \frac{1}{2} \times 0.2 \times v_2^2

. Solving these equations gives

v_1 = 3 \text{ m/s}

4000 N

5000 N

6000 N

8000 N

Correct Answer: A

Solution:

The change in momentum

\Delta p

1000 \times 20 = 20000 \text{ kg m/s}

. The average force

F

is given by

F = \frac{\Delta p}{\Delta t} = \frac{20000}{5} = 4000 \text{ N}

19.8 m/s

20.0 m/s

22.1 m/s

24.5 m/s

Correct Answer: C

Solution:

Using the equation of motion,

v^2 = u^2 + 2gh

, where

u = 0

g = 9.8 \text{ m/s}^2

, and

h = 20 \text{ m}

. Thus,

v^2 = 0 + 2 \times 9.8 \times 20 = 392

, giving

v = \sqrt{392} = 22.1 \text{ m/s}

A body at rest will remain at rest unless acted upon by an external force.

The acceleration of a body is always zero.

A body in motion will eventually stop without any external force.

A force is necessary to keep a body in uniform motion.

Correct Answer: A

Solution:

Newton's first law states that a body at rest will remain at rest, and a body in motion will remain in motion unless acted upon by an external force.

10 m/s

5 m/s

15 m/s

20 m/s

Correct Answer: A

Solution:

Using Newton's second law, the acceleration

a

is given by

F = ma \Rightarrow a = \frac{F}{m} = \frac{20}{10} = 2 \text{ m/s}^2

. The final velocity

v

can be calculated using

v = u + at

, where

u = 0

a = 2 \text{ m/s}^2

, and

t = 5 \text{ s}

. Thus,

v = 0 + 2 \times 5 = 10 \text{ m/s}

Force is inversely proportional to momentum.

Force is equal to the rate of change of momentum.

Force is directly proportional to momentum.

Force is independent of momentum.

Correct Answer: B

Solution:

Newton's second law states that force is equal to the rate of change of momentum.

1.8 Ns

3.6 Ns

0 Ns

6.0 Ns

Correct Answer: B

Solution:

The impulse is calculated as the change in momentum:

0.15 \times 12 - (-0.15 \times 12) = 3.6 \text{ Ns}

0.3 Ns

0.6 Ns

0.9 Ns

1.2 Ns

Correct Answer: B

Solution:

The impulse imparted to each ball is calculated as the change in momentum, which is

0.05 \times 6 - (-0.05 \times 6) = 0.6 \text{ Ns}

0.016 m/s

0.02 m/s

0.04 m/s

0.08 m/s

Correct Answer: A

Solution:

Using conservation of momentum: (mass of shell × speed of shell) = (mass of gun × recoil speed of gun). Thus, 0.020 kg × 80 m/s = 100 kg × recoil speed, giving a recoil speed of 0.016 m/s.

2000 N

2500 N

3000 N

3200 N

Correct Answer: C

Solution:

The average force can be calculated using the formula

F = \frac{\Delta p}{\Delta t}

, where

\Delta p

is the change in momentum and

\Delta t

is the time. Initial momentum

p_i = mv = 800 \times 25 = 20000\, \text{kg m/s}

. Final momentum

p_f = 0

. Thus,

\Delta p = 20000\, \text{kg m/s}

F = \frac{20000}{10} = 2000\, \text{N}

A body at rest will remain at rest unless acted upon by an external force.

The rate of change of momentum is proportional to the applied force.

For every action, there is an equal and opposite reaction.

Momentum is the product of mass and velocity.

Correct Answer: A

Solution:

Newton's first law of motion states that a body at rest will remain at rest, and a body in motion will continue in its motion unless acted upon by an external force.

10 N

0 N

9.8 N

98 N

Correct Answer: B

Solution:

According to Newton's first law of motion, if no external force is applied, the net force is zero.

4 N

8 N

6 N

16 N

Correct Answer: B

Solution:

The centripetal force

F_c

is given by

F_c = \frac{mv^2}{r}

, where

m = 0.5 \text{ kg}

v = 4 \text{ m/s}

, and

r = 2 \text{ m}

. Thus,

F_c = \frac{0.5 \times 4^2}{2} = \frac{8}{2} = 4 \text{ N}

Static friction is always greater than kinetic friction.

Kinetic friction is always greater than static friction.

Static friction and kinetic friction are equal.

There is no relationship between static and kinetic friction.

Correct Answer: A

Solution:

Experimentally, it is found that the coefficient of static friction is greater than that of kinetic friction, making static friction greater than kinetic friction.

10 N

15 N

20 N

25 N

Correct Answer: B

Solution:

The total mass of the system is

5 + 10 = 15 \text{ kg}

. The acceleration

a

of the system is

\frac{30}{15} = 2 \text{ m/s}^2

. The tension

T

in the string is the force required to accelerate the 5 kg block, so

T = 5 \times 2 = 10 \text{ N}

2 m/s²

3 m/s²

4 m/s²

5 m/s²

Correct Answer: A

Solution:

The total mass of the system is

4 + 6 = 10 \text{ kg}

. Using Newton's second law,

F = ma

, where

F = 20 \text{ N}

and

m = 10 \text{ kg}

. Therefore,

a = \frac{F}{m} = \frac{20}{10} = 2 \text{ m/s}^2

0 kg m/s

2 kg m/s

4 kg m/s

6 kg m/s

Correct Answer: C

Solution:

The initial momentum of the ball is

p_i = mv = 0.2 \times 10 = 2 \text{ kg m/s}

. After rebounding, the velocity is

-10 \text{ m/s}

, so the final momentum is

p_f = 0.2 \times (-10) = -2 \text{ kg m/s}

. The change in momentum is

\Delta p = p_f - p_i = -2 - 2 = -4 \text{ kg m/s}

. Since we are interested in the magnitude, the change is

4 \text{ kg m/s}

The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force acts.

To every action, there is always an equal and opposite reaction.

A body continues in its state of rest or uniform motion unless acted upon by an external force.

The total momentum of an isolated system is conserved.

Correct Answer: A

Solution:

Newton's second law states that the rate of change of momentum of a body is proportional to the applied force and occurs in the direction of the force.

5 m/s²

8.66 m/s²

9.8 m/s²

4.9 m/s²

Correct Answer: D

Solution:

The acceleration of the block down the incline can be calculated using the component of gravitational force along the incline:

a = g \sin \theta = 9.8 \times \sin 30° = 4.9 \text{ m/s}^2

1000 N

2000 N

500 N

250 N

Correct Answer: A

Solution:

The deceleration

a

can be calculated using

v = u + at

, where

v = 0

u = 20 \text{ m/s}

, and

t = 10 \text{ s}

. Thus,

0 = 20 + a \times 10

, giving

a = -2 \text{ m/s}^2

. The braking force

F

F = ma = 500 \times (-2) = -1000 \text{ N}

. The magnitude is

1000 \text{ N}

12 N

24 N

6 N

36 N

Correct Answer: B

Solution:

The centripetal force is given by

F_c = \frac{mv^2}{r} = \frac{3 \times 4^2}{2} = \frac{48}{2} = 24 \text{ N}

50 kg m/s

5 kg m/s

10 kg m/s

15 kg m/s

Correct Answer: A

Solution:

Momentum is calculated as the product of mass and velocity. Therefore, momentum = 10 kg * 5 m/s = 50 kg m/s.

Centripetal force

Centrifugal force

Gravitational force

Magnetic force

Correct Answer: A

Solution:

The centripetal force is the force that provides the inward radial acceleration to a body in circular motion.

2 m/s

1 m/s

-2 m/s

-1 m/s

Correct Answer: C

Solution:

By conservation of momentum, the total momentum before and after must be equal. Initially, both skaters are at rest, so total momentum is zero. After they push off,

m_1 v_1 + m_2 v_2 = 0

. Given

m_1 = m_2 = 60\, \text{kg}

and

v_1 = 2\, \text{m/s}

, we find

v_2 = -\frac{m_1 v_1}{m_2} = -\frac{60 \times 2}{60} = -2\, \text{m/s}

5 Ns

10 Ns

15 Ns

20 Ns

Correct Answer: B

Solution:

The impulse imparted is equal to the change in momentum. Initial momentum =

0.5 \times 10 = 5 \text{ kg m/s}

. Final momentum =

0.5 \times (-10) = -5 \text{ kg m/s}

. Change in momentum =

|-5 - 5| = 10 \text{ Ns}

The wall exerts an equal and opposite force against you.

The wall moves slightly.

The wall exerts no force.

The wall exerts a force greater than your push.

Correct Answer: A

Solution:

Newton's third law states that for every action, there is an equal and opposite reaction. When you push against a wall, it pushes back with an equal force.

Gravitational force

Tension in the satellite

Frictional force

Electromagnetic force

Correct Answer: A

Solution:

The centripetal force required for circular motion is provided by the gravitational force between the Earth and the satellite. This is the force that acts towards the center of the Earth, keeping the satellite in its orbit.

0.5 m/s

1 m/s

2.5 m/s

0 m/s

Correct Answer: A

Solution:

Using the conservation of momentum:

m_1v_1 + m_2v_2 = (m_1 + m_2)v_f

. Here,

5 \times 2 + 5 \times (-3) = 10v_f

. Thus,

10 - 15 = 10v_f \Rightarrow v_f = -0.5 \text{ m/s}

(the negative sign indicates the direction).

2 m/s²

4 m/s²

5 m/s²

10 m/s²

Correct Answer: B

Solution:

According to Newton's second law,

F = ma

. Here,

F = 20\, \text{N}

and

m = 5\, \text{kg}

. Therefore,

a = \frac{F}{m} = \frac{20}{5} = 4\, \text{m/s}^2

True or False

Correct Answer: False

Solution:

The weight of a system and the normal force are not action-reaction pairs. They can be equal and opposite when the system is at rest, but they do not constitute an action-reaction pair.

Correct Answer: True

Solution:

Newton's first law of motion, also known as the law of inertia, states that a body will remain at rest or in uniform motion in a straight line unless acted upon by an external force.

Correct Answer: True

Solution:

The law of inertia, also known as Newton's first law of motion, states that a body remains in its state of rest or uniform motion in a straight line unless compelled by an external force to change that state.

Correct Answer: True

Solution:

Impulse is the product of force and time, which results in a change in momentum.

Correct Answer: True

Solution:

Impulse is defined as the product of force and time, which equals the change in momentum of an object.

Correct Answer: False

Solution:

While these forces can be equal and opposite, they do not constitute an action-reaction pair because they act on the same body.

Correct Answer: True

Solution:

The conservation of momentum arises from the second and third laws of motion, which state that forces occur in equal and opposite pairs and that momentum changes are proportional to applied forces.

Correct Answer: False

Solution:

Centripetal force is not a new type of force; it is the name given to the force that provides the necessary inward radial acceleration for circular motion, such as tension or gravitational force.

Correct Answer: True

Solution:

Impulse is the product of force and time, and it equals the change in momentum of a body.

Correct Answer: False

Solution:

Newton's third law states that action and reaction forces are simultaneous and do not imply a cause-effect relationship. They act on different bodies and are equal and opposite.

Correct Answer: False

Solution:

The centripetal force is not a separate type of force; it is the name given to the force that provides inward radial acceleration, such as tension or gravity.

Correct Answer: True

Solution:

Newton's first law of motion states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.

Correct Answer: False

Solution:

Momentum is the product of a body's mass and velocity, not acceleration.

Correct Answer: True

Solution:

Aristotle incorrectly believed that a force is necessary to maintain uniform motion, which is contrary to the law of inertia.

Correct Answer: True

Solution:

The law of conservation of momentum is derived from Newton's second and third laws of motion, which state that the total momentum of an isolated system is conserved.

Correct Answer: False

Solution:

In Newtonian mechanics, an impulsive force is not conceptually different from an ordinary force; it is simply a large force acting for a short time.

Correct Answer: True

Solution:

The law of conservation of momentum states that the total momentum of an isolated system of particles remains constant if no external forces act on it.

Correct Answer: False

Solution:

In Newtonian mechanics, impulsive forces are not conceptually different from ordinary forces; they are simply large forces that act for a short duration.

Correct Answer: True

Solution:

According to Newton's third law of motion, forces always occur in pairs, and the mutual forces between two bodies are always equal and opposite.

Correct Answer: True

Solution:

Impulse is indeed the product of force and the time over which it acts, resulting in a change in momentum.

Correct Answer: False

Solution:

These forces are not action-reaction pairs because they act on the same body.

Correct Answer: True

Solution:

According to Newtonian mechanics, forces are mutual interactions between two bodies and are always equal and opposite.

Correct Answer: True

Solution:

Impulse is defined as the product of force and the time duration for which it acts, and it equals the change in momentum of the object.

Correct Answer: False

Solution:

A horse cannot pull a cart and run in empty space because there is no friction to provide the necessary force for movement.

Correct Answer: False

Solution:

Centripetal force is not a separate type of force; it is the name given to the force that provides the inward radial acceleration necessary for circular motion, such as tension, gravity, or friction.

Correct Answer: True

Solution:

Newton's first law of motion states that a body will remain in its state of rest or uniform motion in a straight line unless acted upon by an external force.

Correct Answer: False

Solution:

The centripetal force is not a separate kind of force; it is the name given to the force that provides inward radial acceleration, such as tension or gravitational force.

Correct Answer: True

Solution:

The law of conservation of momentum follows from Newton's second and third laws of motion.

Correct Answer: True

Solution:

Momentum is defined as the product of mass and velocity, expressed as

p = mv

Correct Answer: True

Solution:

Aristotle's view was that a force is necessary to keep a body in uniform motion, which is incorrect as per modern physics.

Correct Answer: True

Solution:

Newton's second law states that the rate of change of momentum is proportional to the applied force and occurs in the direction of the force.

Correct Answer: False

Solution:

Newton's third law states that action and reaction forces act on different bodies, not the same body.

Correct Answer: True

Solution:

It is experimentally found that the coefficient of static friction

\mu_s

is greater than the coefficient of kinetic friction

\mu_k

for the same pair of surfaces.

Correct Answer: False

Solution:

Centripetal force is not a distinct type of force; it is a name given to the force that provides inward radial acceleration to a body in circular motion, such as tension, gravitational force, or friction.

Correct Answer: True

Solution:

According to Newton's third law of motion, forces always occur in pairs and the mutual forces between two bodies are equal and opposite.

Correct Answer: False

Solution:

The centripetal force is not a new type of force; it is the name given to the force that provides inward radial acceleration, such as tension or gravitational force.

Correct Answer: False

Solution:

Aristotle's view is incorrect. A force is necessary in practice to counter the opposing force of friction, not to keep a body in uniform motion.

Correct Answer: False

Solution:

Static friction is a self-adjusting force up to its limit

\mu_s N

. It is not always equal to

\mu_s N

Correct Answer: True

Solution:

Newton's second law states that the rate of change of momentum of a body is proportional to the applied force, which implies that acceleration is directly proportional to the net external force.

Correct Answer: True

Solution:

Frictional force is independent of the area of contact between two surfaces. It depends on the nature of the surfaces and the normal force.

Correct Answer: False

Solution:

Aristotle's view is incorrect. A force is necessary to counteract friction, but not to maintain uniform motion.

Correct Answer: True

Solution:

Newton's first law states that if the external force on a body is zero, the body will remain in its state of rest or uniform motion, implying that its acceleration is zero.

Correct Answer: True

Solution:

The law of inertia, also known as Newton's first law, states that a body continues in its state of rest or uniform motion unless compelled by an external force to change that state.

Correct Answer: True

Solution:

Impulse is defined as the product of force and time, which equals the change in momentum.

Correct Answer: True

Solution:

The law of conservation of momentum is derived from the principles stated in Newton's second and third laws of motion.

Correct Answer: False

Solution:

Action and reaction forces act on different bodies and cannot cancel each other out.

Correct Answer: False

Solution:

Frictional force opposes the relative motion between two surfaces in contact, so it acts opposite to the direction of motion.

Correct Answer: True

Solution:

Impulse is defined as the product of force and time, which equals the change in momentum. It is particularly useful for analyzing situations where a large force acts over a short duration.

Correct Answer: False

Solution:

Newton's third law states that action and reaction forces act on different bodies, not on the same body.

Correct Answer: True

Solution:

Impulse is defined as the product of force and time, which results in a change in momentum.

Correct Answer: False

Solution:

Centripetal force is not a separate type of force; it is the name given to the net force causing inward radial acceleration in circular motion, such as tension or gravitational force.

Correct Answer: True

Solution:

The SI unit of force is indeed the newton, defined as 1 kg m s⁻².

Correct Answer: False

Solution:

Static friction is a self-adjusting force up to its maximum value, which is the product of the coefficient of static friction and the normal force. It is not always equal to this maximum value.

Laws of Motion

AI Learning Assistant

Summary

Summary of Laws of Motion

Learning Objectives

Learning Objectives

Detailed Notes

Chapter Notes on Laws of Motion

4.1 Introduction

4.2 Aristotle's Fallacy

4.3 The Law of Inertia

4.4 Newton's First Law of Motion

4.5 Newton's Second Law of Motion

4.6 Newton's Third Law of Motion

4.7 Conservation of Momentum

4.8 Equilibrium of a Particle

4.9 Common Forces in Mechanics

4.10 Circular Motion

4.11 Solving Problems in Mechanics

Summary

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Exam Tips

Practice & Assessment

Multiple Choice Questions

Q1.What happens to a stone in circular motion if the string breaks suddenly?

Correct Answer: B

Q2.In circular motion, what provides the centripetal force?

Correct Answer: C

Q3.A 0.2 kg ball moving at a speed of 3 m/s collides head-on with a stationary 0.3 kg ball. If the collision is perfectly elastic, what is the speed of the 0.2 kg ball after the collision?

Correct Answer: B

Q4.A 15 kg object is moving with a velocity of 10 m/s on a frictionless surface. A constant force of 30 N is applied in the direction of motion for 5 seconds. What is the final velocity of the object?

Correct Answer: C

Q5.Which of the following statements correctly describes Newton's third law of motion?

Correct Answer: A

Q6.Which of the following statements is true regarding friction?

Correct Answer: A

Q7.Two ice skaters, each of mass 50 kg, push off from each other. If one skater moves with a velocity of 3 m/s, what is the velocity of the other skater?

Correct Answer: C

Q8.A 2 kg block is placed on a rough horizontal surface with a coefficient of static friction μs=0.4\mu_s = 0.4μs​=0.4. What is the minimum horizontal force required to start moving the block?

Correct Answer: B

Q9.A 0.5 kg object is subjected to a force that varies with time as F(t)=3t2+2t+1F(t) = 3t^2 + 2t + 1F(t)=3t2+2t+1 N. What is the impulse imparted to the object from t=0t = 0t=0 to t=2t = 2t=2 seconds?

Correct Answer: C

Q10.According to Newton's third law, what happens when a force is applied to a body?

Correct Answer: B

Q11.What is the acceleration of a 12 kg mass connected to an 8 kg mass over a frictionless pulley?

Correct Answer: B

Q12.Two blocks of masses 5 kg and 10 kg are connected by a string and placed on a frictionless surface. If a force of 30 N is applied to the 5 kg block, what is the acceleration of the system?

Correct Answer: C

Q13.What is the SI unit of force?

Correct Answer: A

Q14.A 0.2 kg ball is thrown vertically upward with a speed of 15 m/s. What is the maximum height reached by the ball? (Assume g=9.8 m/s2g = 9.8 \text{ m/s}^2g=9.8 m/s2)

Correct Answer: B

Q15.Which of the following statements is true about Newton's second law of motion?

Correct Answer: B

Q16.What happens to a body in uniform motion according to Aristotle's fallacy?

Correct Answer: A

Q17.A 500 kg car accelerates from rest under a constant force of 1000 N. How long will it take to reach a speed of 20 m/s?

Correct Answer: B

Q18.Two blocks of masses 5 kg and 10 kg are placed on a frictionless surface and are connected by a light string. A force of 30 N is applied to the 5 kg block. What is the acceleration of the system?

Correct Answer: B

Q19.Which of the following is an example of an action-reaction pair according to Newton's third law?

Correct Answer: B

Q20.If a force of 10 N is applied to a 2 kg object, what is the acceleration of the object?

Correct Answer: A

Q21.A 0.2 kg ball is thrown vertically upwards with a speed of 10 m/s. What is the impulse imparted to the ball by the force of gravity during its ascent?

Correct Answer: C

Q22.What happens to a nucleus at rest if it disintegrates into two smaller nuclei?

Correct Answer: B

Q23.A 0.5 kg ball is dropped from a height of 10 m. What is the speed of the ball just before it hits the ground? (Assume g=9.8 m/s2g = 9.8 \text{ m/s}^2g=9.8 m/s2 and air resistance is negligible.)

Correct Answer: A

Q24.A 5 kg block is placed on a rough horizontal surface. The coefficient of static friction between the block and the surface is 0.4. What is the maximum horizontal force that can be applied to the block without causing it to move?

Correct Answer: A

Q25.A 10 kg object is initially at rest on a frictionless surface. A force of 50 N is applied to it for 4 seconds. What is the final velocity of the object?

Correct Answer: A

Q26.A stone tied to a string is whirled in a circle. What force acts as the centripetal force?

Correct Answer: A

Q27.According to Newton's first law of motion, what happens to a body if no external force acts on it?

Correct Answer: A