Force and Laws of Motion

Learning Objectives

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Learning Objectives

  • Understand the concept of force and its effects on motion.
  • Explain the relationship between force, mass, and acceleration (Newton's Second Law).
  • Describe the principle of inertia and its implications in everyday scenarios.
  • Analyze the effects of unbalanced forces on the motion of objects.
  • Illustrate the action-reaction forces as per Newton's Third Law.
  • Apply the laws of motion to practical examples and experiments.

Revision Notes & Summary

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Chapter 8: Force and Laws of Motion

Introduction

  • Motion of an object can be uniform or non-uniform.
  • Force is required to change the state of motion of an object.

Concept of Force

  • Force can be described as a push, hit, or pull.
  • Effects of force include:
    • Changing the magnitude of velocity (speeding up or slowing down).
    • Changing the direction of motion.
    • Changing the shape and size of objects.

Newton's Laws of Motion

First Law of Motion

  • An object remains at rest or in uniform motion unless acted upon by an unbalanced force.
  • Inertia: The natural tendency of objects to resist changes in their state of motion.
    • Example: A person falls backward when a bus suddenly starts moving.

Second Law of Motion

  • The rate of change of momentum is proportional to the applied unbalanced force.
  • Formula: F = ma (Force = mass × acceleration)

Third Law of Motion

  • For every action, there is an equal and opposite reaction.
  • Example: When a sailor jumps forward from a boat, the boat moves backward.

Activities to Illustrate Concepts

  • Activity 8.1: Using carom coins to demonstrate inertia.
  • Activity 8.4: Children on carts throwing a sandbag to observe different accelerations.

Important Diagrams

Diagram 8.1

  • Description: Pushing, pulling, or hitting objects changes their state of motion.

Diagram 8.2

  • Description: Illustrates a person jumping from a boat to a dock, demonstrating action and reaction forces.

Diagram 8.6

  • Description: Shows a carom coin being hit and the inertia of the remaining coins.

Diagram 8.9

  • Description: Velocity-time graph of a ball showing uniform deceleration.

Summary of Key Points

  • Force is essential for changing motion.
  • Newton's laws explain the relationship between force and motion.
  • Inertia is a key concept in understanding motion.

Exam Tips & Common Mistakes

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Common Mistakes and Exam Tips

Common Pitfalls

  • Misunderstanding Inertia: Students often confuse inertia with mass. Remember, inertia is the tendency of an object to resist changes in its state of motion, while mass is a measure of that inertia.
  • Forgetting the Direction of Forces: When analyzing problems involving forces, students may neglect to consider the direction of the forces acting on an object, which can lead to incorrect conclusions about motion.
  • Confusing Newton's Laws: It is common to mix up the first and second laws of motion. Ensure you understand that the first law deals with inertia and the second law relates to the relationship between force, mass, and acceleration.

Exam Tips

  • Draw Diagrams: When faced with problems involving forces and motion, sketching diagrams can help visualize the situation and clarify the forces at play.
  • Use Units Consistently: Always check that you are using the correct units for mass (kg), force (N), and acceleration (m/s²) to avoid calculation errors.
  • Practice with Real-Life Examples: Relate concepts to everyday experiences, such as how seatbelts work (inertia) or how pushing a stationary object requires force, to reinforce understanding.
  • Review Key Formulas: Familiarize yourself with important equations, such as F = ma (force equals mass times acceleration) and the concept of momentum, to ensure you can apply them correctly in exam scenarios.
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Practice Test – MCQs, True/False

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Multiple Choice Questions

A.

3 kg m/s

B.

1.5 kg m/s

C.

2 kg m/s

D.

0.5 kg m/s
Correct Answer: A

Solution:

The change in momentum is given by the formula: Δp=m(vfvi)\Delta p = m(v_f - v_i), where m=0.2 kgm = 0.2 \text{ kg}, vf=5 m/sv_f = -5 \text{ m/s}, and vi=10 m/sv_i = 10 \text{ m/s}. Thus, Δp=0.2(510)=0.2(15)=3 kg m/s\Delta p = 0.2(-5 - 10) = 0.2(-15) = -3 \text{ kg m/s}. The magnitude is 3 kg m/s.

A.

3 kg m/s

B.

1.5 kg m/s

C.

2 kg m/s

D.

0.5 kg m/s
Correct Answer: A

Solution:

Change in momentum is given by Δp=m(vfvi)\Delta p = m(v_f - v_i). Here, m=0.2 kgm = 0.2 \text{ kg}, vf=5 m/sv_f = -5 \text{ m/s}, and vi=10 m/sv_i = 10 \text{ m/s}. Thus, Δp=0.2(510)=3 kg m/s\Delta p = 0.2(-5 - 10) = -3 \text{ kg m/s}. The magnitude is 3 kg m/s.

A.

Due to the force of gravity.

B.

Due to the inertia of the leaves.

C.

Due to the wind resistance.

D.

Due to the friction between leaves and air.
Correct Answer: B

Solution:

The leaves tend to remain in their state of rest due to inertia, and when the branch is shaken, they detach.

A.

3 J

B.

6 J

C.

15 J

D.

30 J
Correct Answer: B

Solution:

The potential energy stored in a compressed spring is given by PE=12kx2PE = \frac{1}{2} k x^2, where kk is the spring constant and xx is the compression. Substituting the given values, PE=12×150×(0.2)2=6 JPE = \frac{1}{2} \times 150 \times (0.2)^2 = 6 \text{ J}.

A.

1200 N

B.

2400 N

C.

3000 N

D.

6000 N
Correct Answer: B

Solution:

The average force exerted can be calculated using the formula F=ΔpΔtF = \frac{\Delta p}{\Delta t}, where Δp\Delta p is the change in momentum and Δt\Delta t is the time. The initial momentum pi=mv=0.02×300=6 kg m/sp_i = mv = 0.02 \times 300 = 6 \text{ kg m/s}, and the final momentum pf=0p_f = 0. Thus, Δp=60=6 kg m/s\Delta p = 6 - 0 = 6 \text{ kg m/s}. Therefore, F=60.05=120 NF = \frac{6}{0.05} = 120 \text{ N}.

A.

5 m/s

B.

15 m/s

C.

10 m/s

D.

20 m/s
Correct Answer: B

Solution:

The change in velocity is the final velocity minus the initial velocity. Since the ball changes direction, the change is 5 m/s - (-10 m/s) = 15 m/s.

A.

2 m/s²

B.

5 m/s²

C.

10 m/s²

D.

20 m/s²
Correct Answer: B

Solution:

Using Newton's second law, F=maF = ma, where F=10 NF = 10 \text{ N} and m=2 kgm = 2 \text{ kg}. Thus, a=Fm=102=5 m/s2a = \frac{F}{m} = \frac{10}{2} = 5 \text{ m/s}^2.

A.

0.2 m

B.

0.1 m

C.

0.4 m

D.

0.3 m
Correct Answer: B

Solution:

The compression distance of the spring can be calculated using Hooke's Law, F=kxF = kx, where FF is the force applied, kk is the spring constant, and xx is the compression distance. Rearranging for xx, we have x=Fk=50250=0.2 mx = \frac{F}{k} = \frac{50}{250} = 0.2 \text{ m}.

A.

6 N to the right

B.

14 N to the right

C.

6 N to the left

D.

4 N to the right
Correct Answer: A

Solution:

The net force is calculated by subtracting the frictional force from the applied force: Fnet=10 N4 N=6 NF_{net} = 10 \text{ N} - 4 \text{ N} = 6 \text{ N}. Since the applied force is greater, the net force is 6 N to the right.

A.

0.75 m/s

B.

1.5 m/s

C.

0.5 m/s

D.

1 m/s
Correct Answer: A

Solution:

Using the conservation of momentum, the initial momentum is zero. After firing, the momentum of the bullet and gun must be equal and opposite. Thus, mbvb=mgvgm_b v_b = m_g v_g, where mb=0.01 kgm_b = 0.01 \text{ kg}, vb=150 m/sv_b = 150 \text{ m/s}, mg=2 kgm_g = 2 \text{ kg}. Solving for vgv_g, we have vg=mbvbmg=0.01×1502=0.75 m/sv_g = \frac{m_b v_b}{m_g} = \frac{0.01 \times 150}{2} = 0.75 \text{ m/s}.

A.

Forward

B.

Backward

C.

Upward

D.

Downward
Correct Answer: B

Solution:

The recoil force on the gun is in the opposite direction to the force propelling the bullet, which is backward.

A.

The boat moves towards the dock.

B.

The boat remains stationary.

C.

The boat moves away from the dock.

D.

The boat sinks.
Correct Answer: C

Solution:

According to Newton's Third Law of Motion, the action of jumping forward causes a reaction that moves the boat backward.

A.

1000 J

B.

2000 J

C.

5000 J

D.

10000 J
Correct Answer: C

Solution:

The work done on the object is equal to the change in kinetic energy, given by W=ΔKE=12mv212mu2W = \Delta KE = \frac{1}{2} m v^2 - \frac{1}{2} m u^2, where u=0u = 0 (initial velocity). Thus, W=12×100×102=5000 JW = \frac{1}{2} \times 100 \times 10^2 = 5000 \text{ J}.

A.

Law of conservation of energy

B.

Law of inertia

C.

Newton's Third Law of Motion

D.

Law of conservation of momentum
Correct Answer: B

Solution:

The principle demonstrated is the law of inertia, where the coin tends to remain in its state of rest and falls directly into the cup when the card is flicked away.

A.

0 N

B.

100 N

C.

200 N

D.

400 N
Correct Answer: C

Solution:

Since the cabinet is moving at a constant velocity, the net force is zero. Therefore, the friction force must equal the applied force, which is 200 N.

A.

A balanced force

B.

An unbalanced force

C.

No force

D.

A gravitational force
Correct Answer: B

Solution:

Newton's First Law of Motion states that an object will remain at rest or in uniform motion unless acted upon by an unbalanced force.

A.

The boat moves towards the dock.

B.

The boat remains stationary.

C.

The boat moves away from the dock.

D.

The boat sinks.
Correct Answer: C

Solution:

According to Newton's Third Law, for every action, there is an equal and opposite reaction. When the person jumps towards the dock, the boat moves in the opposite direction, away from the dock.

A.

1 m/s

B.

2 m/s

C.

3 m/s

D.

4 m/s
Correct Answer: A

Solution:

Using conservation of momentum: m1v1=m2v2m_1v_1 = m_2v_2, where m1=0.01 kgm_1 = 0.01 \text{ kg}, v1=200 m/sv_1 = 200 \text{ m/s}, m2=2 kgm_2 = 2 \text{ kg}. Solving for v2v_2 gives v2=0.01×2002=1 m/sv_2 = \frac{0.01 \times 200}{2} = 1 \text{ m/s}.

A.

Because it is moving faster.

B.

Because it has more mass.

C.

Because it is longer.

D.

Because it is on tracks.
Correct Answer: B

Solution:

Inertia is directly related to mass. A train has more mass than a small cart, thus it has more inertia.

A.

1 m/s

B.

1.5 m/s

C.

0.5 m/s

D.

2 m/s
Correct Answer: C

Solution:

According to the conservation of momentum, the total momentum before and after the jump must be equal. Let the velocity of the boat be vbv_b. Initial momentum is 0 because both are at rest. Final momentum is 60×3+120×(vb)=060 \times 3 + 120 \times (-v_b) = 0. Solving for vbv_b, we get vb=0.5v_b = 0.5 m/s.

A.

Both carts will move towards each other.

B.

Both carts will move away from each other.

C.

The carts will remain stationary.

D.

Only one cart will move.
Correct Answer: B

Solution:

When the bag is thrown, the action of throwing causes a reaction that moves the carts away from each other due to conservation of momentum.

A.

1.5 kg m/s

B.

3 kg m/s

C.

0.5 kg m/s

D.

2 kg m/s
Correct Answer: A

Solution:

Initial momentum = 0.2×10=20.2 \times 10 = 2 kg m/s. Final momentum = 0.2×(5)=10.2 \times (-5) = -1 kg m/s. Change in momentum = 2(1)=3|2 - (-1)| = 3 kg m/s.

A.

A rubber ball and a stone of the same size

B.

A bicycle and a train

C.

A five-rupees coin and a one-rupee coin

D.

A feather and a metal ball of the same size
Correct Answer: B

Solution:

Inertia is the resistance of an object to change its state of motion, and it is directly related to the mass of the object. A train has more mass than a bicycle, thus it has more inertia.

A.

Due to gravity

B.

Due to inertia

C.

Due to friction

D.

Due to air resistance
Correct Answer: B

Solution:

According to the law of inertia, an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. When the bus stops, your body tends to continue moving forward.

A.

A car accelerating from rest.

B.

A ball rolling on a frictionless surface maintaining its velocity.

C.

A rocket launching into space.

D.

A spring being compressed by a force.
Correct Answer: B

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. A ball rolling on a frictionless surface maintaining its velocity perfectly illustrates this law, as it continues its motion without any external forces acting on it.

A.

4.9 m/s²

B.

9.8 m/s²

C.

5.0 m/s²

D.

8.5 m/s²
Correct Answer: A

Solution:

The acceleration aa is given by a=gsinθa = g \sin \theta, where g=9.8 m/s2g = 9.8 \text{ m/s}^2 and θ=30\theta = 30^\circ. Thus, a=9.8×sin30=4.9 m/s2a = 9.8 \times \sin 30^\circ = 4.9 \text{ m/s}^2.

A.

The coin moves with the card.

B.

The coin falls straight down.

C.

The coin remains in place.

D.

The coin flies upwards.
Correct Answer: B

Solution:

Due to inertia, the coin tends to remain in its state of rest and falls straight down into the cup when the card is flicked away.

A.

The block will accelerate towards Y.

B.

The block will move with constant velocity towards Y.

C.

The block will not move.

D.

The block will move towards X.
Correct Answer: B

Solution:

If the applied force is equal to the frictional force, the net force on the block is zero. According to Newton's First Law, the block will move with a constant velocity towards Y.

A.

6000 N

B.

3000 N

C.

1500 N

D.

7500 N
Correct Answer: A

Solution:

The change in velocity Δv=020=20 m/s\Delta v = 0 - 20 = -20 \text{ m/s}. Using the formula for force, F=maF = m \cdot a, where a=ΔvΔt=205=4 m/s2a = \frac{\Delta v}{\Delta t} = \frac{-20}{5} = -4 \text{ m/s}^2. Thus, F=1500×(4)=6000 NF = 1500 \times (-4) = -6000 \text{ N}. The magnitude is 6000 N.

A.

0.75 m/s

B.

0.5 m/s

C.

0.25 m/s

D.

1 m/s
Correct Answer: C

Solution:

Using conservation of momentum, the total initial momentum is zero. Let vv be the velocity of the first cart. The equation is: 30v+30×0.5=030v + 30 \times 0.5 = 0. Solving for vv, we get v=0.5×0.5=0.25 m/sv = -0.5 \times 0.5 = -0.25 \text{ m/s}. The magnitude is 0.25 m/s.

A.

The boat moves towards the dock.

B.

The boat remains stationary.

C.

The boat moves away from the dock.

D.

The boat sinks.
Correct Answer: C

Solution:

According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. As the person jumps towards the dock, the boat experiences an equal and opposite force, causing it to move away from the dock.

A.

It stops at the bottom of the incline.

B.

It rolls up to the same height from which it was released.

C.

It rolls indefinitely without stopping.

D.

It rolls back to its starting point.
Correct Answer: B

Solution:

According to Galileo's observations, a marble will roll up to the same height it was released from if the inclines are equal.

A.

50 N

B.

30 N

C.

20 N

D.

40 N
Correct Answer: A

Solution:

The acceleration aa can be calculated using the formula a=vfvit=856=0.5 m/s2a = \frac{v_f - v_i}{t} = \frac{8 - 5}{6} = 0.5 \text{ m/s}^2. The force FF is then given by F=ma=100×0.5=50 NF = ma = 100 \times 0.5 = 50 \text{ N}.

A.

2400 N

B.

4800 N

C.

6000 N

D.

7200 N
Correct Answer: B

Solution:

Initial momentum pi=1200×20=24000 kg m/sp_i = 1200 \times 20 = 24000 \text{ kg m/s}. Final momentum pf=0p_f = 0. Change in momentum Δp=24000 kg m/s\Delta p = -24000 \text{ kg m/s}. Force F=ΔpΔt=240005=4800 NF = \frac{\Delta p}{\Delta t} = \frac{-24000}{5} = -4800 \text{ N}. Magnitude is 4800 N.

A.

Both carts will move towards each other.

B.

Both carts will move away from each other.

C.

The carts will remain stationary.

D.

Only the cart of the person throwing the bag will move.
Correct Answer: B

Solution:

When one person throws a bag to the other, both will experience forces due to the action and reaction principle. As a result, both carts will move away from each other.

A.

(mv)2(mv)^2

B.

mv2mv^2

C.

12mv2\frac{1}{2} mv^2

D.

mvmv
Correct Answer: D

Solution:

Momentum is calculated as the product of mass and velocity, which is mvmv.

A.

Conservation of mass

B.

Newton's First Law of Motion

C.

Conservation of momentum

D.

Newton's Second Law of Motion
Correct Answer: C

Solution:

The movement of the carts illustrates the conservation of momentum. As the sandbag is thrown, the momentum is transferred, causing the carts to move in opposite directions.

A.

500 N

B.

1000 N

C.

1500 N

D.

2000 N
Correct Answer: A

Solution:

The force exerted can be calculated using the formula: F=ΔpΔtF = \frac{\Delta p}{\Delta t}, where Δp=mΔv\Delta p = m \cdot \Delta v. Here, m=0.01 kgm = 0.01 \text{ kg}, Δv=150 m/s\Delta v = 150 \text{ m/s}, and Δt=0.03 s\Delta t = 0.03 \text{ s}. Thus, F=0.01×1500.03=500 NF = \frac{0.01 \times 150}{0.03} = 500 \text{ N}.

A.

The forces cancel each other out.

B.

The truck has too much inertia.

C.

The person is not applying enough force.

D.

The truck is on a frictionless surface.
Correct Answer: B

Solution:

The truck does not move because it has a large mass, and thus a large inertia, which resists changes in its state of motion.

A.

It remains the same

B.

It is halved

C.

It is doubled

D.

It is quadrupled
Correct Answer: C

Solution:

Momentum is directly proportional to velocity. If the velocity is doubled, the momentum is also doubled.

A.

10 N

B.

20 N

C.

30 N

D.

40 N
Correct Answer: B

Solution:

The force can be calculated using Newton's second law, F=maF = ma. First, calculate the acceleration using a=vfvit=624=1 m/s2a = \frac{v_f - v_i}{t} = \frac{6 - 2}{4} = 1 \text{ m/s}^2. Then, F=10×1=10 NF = 10 \times 1 = 10 \text{ N}.

A.

1.67 m/s

B.

2 m/s

C.

3 m/s

D.

5 m/s
Correct Answer: A

Solution:

Using conservation of momentum, the total momentum before collision is equal to the total momentum after collision. m1v1+m2v2=(m1+m2)vm_1v_1 + m_2v_2 = (m_1 + m_2)v. Thus, 1×10+5×0=(1+5)v1 \times 10 + 5 \times 0 = (1 + 5)v, solving gives v=1.67 m/sv = 1.67 \text{ m/s}.

A.

Conservation of energy

B.

Newton's First Law of Motion

C.

Newton's Third Law of Motion

D.

Conservation of mass
Correct Answer: C

Solution:

The action of throwing the bag causes an equal and opposite reaction, demonstrating Newton's Third Law of Motion.

A.

250 N/m

B.

200 N/m

C.

300 N/m

D.

150 N/m
Correct Answer: A

Solution:

Using Hooke's Law, F=kxF = kx, where F=50 NF = 50 \text{ N} and x=0.2 mx = 0.2 \text{ m}. Solving for kk gives k=Fx=500.2=250 N/mk = \frac{F}{x} = \frac{50}{0.2} = 250 \text{ N/m}.

A.

The boat moves towards the dock.

B.

The boat remains stationary.

C.

The boat moves away from the dock.

D.

The boat sinks.
Correct Answer: C

Solution:

According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. As the person jumps towards the dock, the boat moves in the opposite direction, away from the dock.

A.

1 kg m/s

B.

2 kg m/s

C.

3 kg m/s

D.

5 kg m/s
Correct Answer: C

Solution:

Initial momentum pi=0.2×15=3 kg m/sp_i = 0.2 \times 15 = 3 \text{ kg m/s}. Final momentum pf=0.2×(10)=2 kg m/sp_f = 0.2 \times (-10) = -2 \text{ kg m/s}. Change in momentum Δp=pfpi=23=5 kg m/s\Delta p = p_f - p_i = -2 - 3 = -5 \text{ kg m/s}. Magnitude is 5 kg m/s.

A.

0.2 m/s

B.

0.4 m/s

C.

0.5 m/s

D.

1 m/s
Correct Answer: A

Solution:

Using conservation of momentum, initial momentum is zero. After throwing, 50×v1+5×2=050 \times v_1 + 5 \times 2 = 0. Solving gives v1=0.2 m/sv_1 = -0.2 \text{ m/s}. The other cart moves with the same speed in the opposite direction.

A.

1 J

B.

2 J

C.

0.5 J

D.

10 J
Correct Answer: A

Solution:

The potential energy stored in a spring is given by PE=12kx2PE = \frac{1}{2} k x^2, where kk is the spring constant and xx is the compression. PE=12×200×(0.1)2=1PE = \frac{1}{2} \times 200 \times (0.1)^2 = 1 J.

A.

The block continues to move at a constant velocity.

B.

The block comes to a stop immediately.

C.

The block accelerates indefinitely.

D.

The block moves in the opposite direction.
Correct Answer: A

Solution:

According to Newton's First Law, an object in motion will stay in motion with the same velocity unless acted upon by an unbalanced force.

A.

The coin moves with the card.

B.

The coin remains on the card.

C.

The coin falls into the glass tumbler.

D.

The coin flies off in the opposite direction.
Correct Answer: C

Solution:

Due to inertia, the coin remains in its state of rest and falls vertically into the glass when the card is flicked away.

A.

5 m/s

B.

6.25 m/s

C.

7.5 m/s

D.

8 m/s
Correct Answer: B

Solution:

Using the conservation of momentum, the total momentum before collision equals the total momentum after collision. m1v1+m2v2=(m1+m2)vm_1v_1 + m_2v_2 = (m_1 + m_2)v. Here, m1=5 kgm_1 = 5 \text{ kg}, v1=10 m/sv_1 = 10 \text{ m/s}, m2=3 kgm_2 = 3 \text{ kg}, v2=0v_2 = 0. Thus, 5×10+3×0=(5+3)v5 \times 10 + 3 \times 0 = (5 + 3)v. Solving for vv, v=508=6.25 m/sv = \frac{50}{8} = 6.25 \text{ m/s}.

A.

Inertia is the tendency of an object to resist a change in its state of motion.

B.

Inertia is the force that acts on an object to change its motion.

C.

Inertia is the energy required to move an object.

D.

Inertia is the speed at which an object moves.
Correct Answer: A

Solution:

Inertia is the natural tendency of an object to resist a change in its state of motion or rest.

A.

The truck

B.

The car

C.

Both have the same inertia

D.

Inertia is not related to mass
Correct Answer: A

Solution:

Inertia is directly related to mass. The truck, being more massive, has more inertia.

A.

Due to the friction between the car and the road.

B.

Because of the inertia of the passengers.

C.

Because the car accelerates.

D.

Due to the gravitational pull.
Correct Answer: B

Solution:

The tendency of passengers to continue in their straight-line motion while the car turns is due to inertia.

A.

50 N

B.

500 N

C.

750 N

D.

1500 N
Correct Answer: B

Solution:

The force exerted can be calculated using the formula F=ΔpΔtF = \frac{\Delta p}{\Delta t}, where Δp\Delta p is the change in momentum. The initial momentum is mv=0.01×150=1.5 kg m/smv = 0.01 \times 150 = 1.5 \text{ kg m/s} and the final momentum is 0. Thus, Δp=1.5 kg m/s\Delta p = 1.5 \text{ kg m/s}. The force is F=1.50.03=50 NF = \frac{1.5}{0.03} = 50 \text{ N}.

A.

It will stop immediately.

B.

It will continue moving to the right.

C.

It will move to the left.

D.

It will move in a circular path.
Correct Answer: B

Solution:

According to Newton's First Law of Motion, the block will continue moving in the same direction unless acted upon by another force.

A.

400 N

B.

800 N

C.

1000 N

D.

2000 N
Correct Answer: B

Solution:

The change in momentum Δp=m(vfvi)=0.01×(0200)=2 kg m/s\Delta p = m(v_f - v_i) = 0.01 \times (0 - 200) = -2 \text{ kg m/s}. The force is F=ΔpΔt=20.05=40 NF = \frac{\Delta p}{\Delta t} = \frac{-2}{0.05} = -40 \text{ N}. The magnitude is 800 N.

True or False

Correct Answer: False

Solution:

According to Galileo's observations and Newton's First Law of Motion, an object in uniform motion on a frictionless surface does not require a force to maintain its motion.

Correct Answer: True

Solution:

When a hockey ball is struck by a stick, the force applied changes the velocity of the ball, thereby changing its momentum.

Correct Answer: True

Solution:

When the sandbag is thrown, both individuals experience an equal and opposite force due to the action-reaction principle described by Newton's Third Law of Motion.

Correct Answer: True

Solution:

Inertia is the resistance of any physical object to any change in its velocity. The mass of an object is a quantitative measure of its inertia.

Correct Answer: False

Solution:

According to Newton's First Law of Motion, an object in motion will remain in motion at a constant velocity unless acted upon by an unbalanced force. On a frictionless surface, no force is needed to maintain constant velocity.

Correct Answer: False

Solution:

According to Newton's First Law of Motion, a stationary object will remain at rest unless acted upon by an unbalanced force. No force is needed to keep it at rest.

Correct Answer: False

Solution:

A stationary truck does not move because the force applied is not sufficient to overcome the static friction and inertia of the truck. The forces do not cancel out; rather, the applied force is less than the force of static friction.

Correct Answer: False

Solution:

A stationary object does not require a force to remain at rest. It will stay at rest unless acted upon by an unbalanced force, as stated by the first law of motion.

Correct Answer: True

Solution:

This is an application of Newton's Third Law of Motion. When the bullet is propelled forward, the gun experiences an equal and opposite recoil force.

Correct Answer: True

Solution:

A force is required to change the direction of an object's motion, as it involves altering the object's velocity vector.

Correct Answer: True

Solution:

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. When a person jumps forward from a boat, they exert a force on the boat, causing it to move backward.

Correct Answer: False

Solution:

The change in momentum of an object is dependent on both the magnitude and direction of the force applied. The direction of the force determines the direction of the change in momentum.

Correct Answer: False

Solution:

On a frictionless inclined plane, a marble will continue to move indefinitely without coming to rest, as there is no unbalanced force acting to stop it.

Correct Answer: True

Solution:

Inertia is the resistance of an object to change its state of motion, and it is directly proportional to the mass of the object.

Correct Answer: True

Solution:

Inertia is the tendency of an object to resist changes in its state of motion, and it is directly proportional to the object's mass. More massive objects have greater inertia.

Correct Answer: True

Solution:

Newton's Third Law states that for every action, there is an equal and opposite reaction. When the person jumps towards the dock, the boat moves in the opposite direction due to the reaction force.

Correct Answer: False

Solution:

Inertia is directly related to the mass of an object. More massive objects have greater inertia and resist changes in their state of motion more than less massive objects.

Correct Answer: True

Solution:

When a gun is fired, the bullet is propelled forward by an explosive force, while the gun experiences a recoil force in the opposite direction, illustrating Newton's Third Law of Motion.

Correct Answer: True

Solution:

According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. When the person jumps forward, they exert a force on the boat in the backward direction, causing the boat to move backward.

Correct Answer: False

Solution:

The truck does not move because the force exerted by the person is not sufficient to overcome the static friction and the inertia of the truck, not because the forces cancel each other.

Correct Answer: True

Solution:

This is an example of Newton's Third Law of Motion. When the bullet is propelled forward by the explosive force, the gun experiences an equal and opposite recoil force.

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Force and Laws of Motion

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