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Class 11 Science (PCM)

Physics Part 1

Work, Energy and Power

Work, Energy and Power

Action PlanNotesQuestionsMock-Test
Study Action Plan (Sorted by Difficulty)
Elastic and Inelastic Collisions
Accuracy: 45%
Total Attempted20
Total Correct9
Total Incorrect11
Difficulty Level:
High
Collisions in Two Dimensions
Accuracy: 50%
Total Attempted24
Total Correct12
Total Incorrect12
Difficulty Level:
Medium
Scalar Product of Vectors
Accuracy: 50%
Total Attempted14
Total Correct7
Total Incorrect7
Difficulty Level:
Medium
Collisions in One Dimension
Accuracy: 53%
Total Attempted15
Total Correct8
Total Incorrect7
Difficulty Level:
Medium
Conservative Forces and Potential Energy
Accuracy: 57%
Total Attempted14
Total Correct8
Total Incorrect6
Difficulty Level:
Medium
Work Done by Constant Force
Accuracy: 60%
Total Attempted5
Total Correct3
Total Incorrect2
Difficulty Level:
Medium
Potential Energy of a Spring
Accuracy: 64%
Total Attempted14
Total Correct9
Total Incorrect5
Difficulty Level:
Medium
Conservation of Mechanical Energy
Accuracy: 67%
Total Attempted18
Total Correct12
Total Incorrect6
Difficulty Level:
Medium
Work-Energy Theorem
Accuracy: 70%
Total Attempted10
Total Correct7
Total Incorrect3
Difficulty Level:
Medium
Work Done by Variable Force
Accuracy: 71%
Total Attempted21
Total Correct15
Total Incorrect6
Difficulty Level:
Medium
Kinetic Energy
Accuracy: 82%
Total Attempted17
Total Correct14
Total Incorrect3
Difficulty Level:
Low
Non-Conservative Forces and Energy Loss
Accuracy: 83%
Total Attempted6
Total Correct5
Total Incorrect1
Difficulty Level:
Low
Power and Its Calculation
Accuracy: 92%
Total Attempted13
Total Correct12
Total Incorrect1
Difficulty Level:
Low

Learning Objectives

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Learning Objectives

  • Understand the Work-Energy Theorem and its application in calculating the change in kinetic energy as equivalent to the work done by net forces.
  • Calculate the scalar product of vectors and apply it to solve problems involving vector quantities in physics.
  • Analyze conservative forces and derive potential energy functions, understanding the path independence of work done by these forces.
  • Apply the principle of conservation of mechanical energy in systems where only conservative forces are acting, ensuring the total mechanical energy remains constant.
  • Differentiate between elastic and inelastic collisions, focusing on the conservation of momentum and kinetic energy in elastic collisions.
  • Integrate variable forces over displacement to determine the work done, using calculus to handle non-constant forces.
  • Compute the potential energy stored in a spring using Hooke's Law and relate it to the displacement from equilibrium.
  • Calculate power as the rate of work done or energy transfer, utilizing the relationship between force and velocity.
  • Solve problems involving two-dimensional collisions by conserving momentum in both x and y components.
  • Evaluate the work done by constant forces, considering the angle between force and displacement, and apply this to scenarios involving friction, gravity, and normal forces.
  • Determine kinetic energy changes using the formula K=12mv2K = \frac{1}{2}mv^2 and relate it to speed and mass.
  • Examine the effects of non-conservative forces like friction on energy loss and modify energy conservation equations accordingly.
  • Analyze one-dimensional collisions for head-on elastic and inelastic interactions, using final velocity formulas and considering special mass cases.

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Revision Notes & Summary

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Chapter Notes

Work-Energy Theorem

  • Definition: The change in kinetic energy of a body is equal to the work done by the net force on the body.
  • Formula: Kf−Ki=WnetK_f - K_i = W_{net}

Scalar Product of Vectors

  • Definition: The scalar or dot product of two vectors A\mathbf{A} and B\mathbf{B} is a scalar quantity.
  • Formula: A⋅B=ABcos⁡Θ\mathbf{A} \cdot \mathbf{B} = AB \cos \Theta
    • Θ\Theta is the angle between A\mathbf{A} and B\mathbf{B}.

Conservative Forces and Potential Energy

  • Conservative Force: A force is conservative if the work done by it is path-independent and can be derived from a potential energy function V(x)V(x).
  • Relation: F(x)=−dVdxF(x) = -\frac{dV}{dx}

Conservation of Mechanical Energy

  • Principle: The total mechanical energy of a system remains constant if only conservative forces act on it.
  • Formula: E=K+VE = K + V

Elastic and Inelastic Collisions

  • Elastic Collisions: Both momentum and kinetic energy are conserved.
  • Inelastic Collisions: Only momentum is conserved.

Work Done by Variable Force

  • Formula: W=∫F(x) dxW = \int F(x) \, dx

Potential Energy of a Spring

  • Formula: V(x)=12kx2V(x) = \frac{1}{2} kx^2
    • kk is the spring constant.
    • xx is the displacement from equilibrium.

Power and Its Calculation

  • Definition: Power is the rate at which work is done or energy is transferred.
  • Formula: P=F⋅vP = \mathbf{F} \cdot \mathbf{v}

Collisions in Two Dimensions

  • Momentum Conservation: Applies to both x and y components.
  • Analysis: Requires vector analysis to solve for final velocities and angles.

Work Done by Constant Force

  • Formula: W=Fdcos⁡θW = Fd \cos \theta
    • Work can be positive, negative, or zero depending on the angle θ\theta.

Kinetic Energy

  • Formula: K=12mv2K = \frac{1}{2}mv^2
    • Scalar nature, related to speed.

Non-Conservative Forces and Energy Loss

  • Relation: Ef−Ei=WncE_f - E_i = W_{nc}
    • WncW_{nc} is the work done by non-conservative forces.

Collisions in One Dimension

  • Head-on Elastic Collisions: Both momentum and kinetic energy are conserved.
  • Completely Inelastic Collisions: Objects stick together, only momentum is conserved.
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Practice Test – MCQs, True/False

Top

Multiple Choice Questions

A.

0 degrees

B.

37 degrees

C.

53 degrees

D.

90 degrees
Correct Answer: D

Solution:

When two equal masses undergo a glancing elastic collision with one at rest, they move at right angles to each other after the collision.

Chapter Concept:

Collisions in Two Dimensions

A.

2gh\sqrt{2gh}

B.

ghgh

C.

gh2\frac{gh}{2}

D.

12gh\frac{1}{2}gh
Correct Answer: A

Solution:

Using conservation of mechanical energy, the potential energy at the top is converted to kinetic energy at the bottom: mgh=12mv2mgh = \frac{1}{2}mv^2, solving for vv gives v=2ghv = \sqrt{2gh}.

Chapter Concept:

Conservative Forces and Potential Energy

A.

0°

B.

45°

C.

90°

D.

180°
Correct Answer: C

Solution:

In an elastic collision between two equal masses, the two masses move at right angles to each other after the collision.

Chapter Concept:

Collisions in Two Dimensions

A.

12kx2\frac{1}{2}kx^2

B.

kxkx

C.

12kx\frac{1}{2}kx

D.

k2x2k^2x^2
Correct Answer: A

Solution:

The potential energy stored in a spring is given by V(x)=12kx2V(x) = \frac{1}{2}kx^2, where kk is the spring constant and xx is the displacement from equilibrium.

Chapter Concept:

Conservative Forces and Potential Energy

A.

5 m/s

B.

10 m/s

C.

9.9 m/s

D.

14 m/s
Correct Answer: B

Solution:

Using the conservation of energy, the potential energy at the top is converted to kinetic energy at the bottom: mgh=12mv2mgh = \frac{1}{2} mv^2. Solving for vv, v=2gh=2×9.8×5=10 m/sv = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} = 10 \, \text{m/s}.

Chapter Concept:

Work Done by Variable Force

A.

0.25 J0.25 \text{ J}

B.

0.5 J0.5 \text{ J}

C.

1.0 J1.0 \text{ J}

D.

1.5 J1.5 \text{ J}
Correct Answer: B

Solution:

The work done by the retarding force is W=∫0.12.01−0.5/x dx=−0.5ln⁡(20.1)≈−1.5 JW = \int_{0.1}^{2.01} -0.5/x \, dx = -0.5 \ln(20.1) \approx -1.5 \text{ J}. The initial kinetic energy is Ki=0.5×1×22=2 JK_i = 0.5 \times 1 \times 2^2 = 2 \text{ J}. Thus, the final kinetic energy Kf=Ki+W=2−1.5=0.5 JK_f = K_i + W = 2 - 1.5 = 0.5 \text{ J}.

Chapter Concept:

Work-Energy Theorem

A.

Work done is zero if the displacement is zero.

B.

Work done is always positive.

C.

Work done is independent of the angle between force and displacement.

D.

Work done is maximum when force is perpendicular to displacement.
Correct Answer: A

Solution:

Work done by a force is defined as W=Fdcos⁡θW = Fd \cos \theta. If the displacement dd is zero, then the work done is zero regardless of the force applied.

Chapter Concept:

Work Done by Constant Force

A.

1/9

B.

2/3

C.

8/9

D.

1/2
Correct Answer: C

Solution:

For an elastic collision between a neutron and a deuterium nucleus, f2=89f_2 = \frac{8}{9} of the neutron's kinetic energy is transferred to the deuterium nucleus.

Chapter Concept:

Collisions in Two Dimensions

A.

The total mechanical energy of a system remains constant if only non-conservative forces act on it.

B.

The total mechanical energy of a system remains constant if only conservative forces act on it.

C.

The total mechanical energy of a system increases if only conservative forces act on it.

D.

The total mechanical energy of a system decreases if only conservative forces act on it.
Correct Answer: B

Solution:

The principle of conservation of mechanical energy states that the total mechanical energy of a system remains constant if only conservative forces act on it.

Chapter Concept:

Conservation of Mechanical Energy

A.

ABAB

B.

00

C.

A2+B2A^2 + B^2

D.

A2−B2A^2 - B^2
Correct Answer: B

Solution:

The scalar product A⋅B=ABcos⁡Θ\mathbf{A} \cdot \mathbf{B} = AB \cos \Theta. When A\mathbf{A} and B\mathbf{B} are perpendicular, Θ=90∘\Theta = 90^\circ, so cos⁡90∘=0\cos 90^\circ = 0. Therefore, A⋅B=0\mathbf{A} \cdot \mathbf{B} = 0.

Chapter Concept:

Scalar Product of Vectors

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Work, Energy and Power

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True or False

Correct Answer: True

Solution:

In an elastic collision, both momentum and kinetic energy are conserved. For two-dimensional collisions, this applies to all directions in the plane of collision.

Chapter Concept :

Collisions in Two Dimensions

Correct Answer: True

Solution:

The formula V(x)=12kx2V(x) = \frac{1}{2} kx^2 correctly represents the potential energy stored in a spring, where kk is the spring constant and xx is the displacement from its equilibrium position.

Chapter Concept :

Potential Energy of a Spring

Correct Answer: True

Solution:

In two-dimensional collisions, momentum conservation applies to both x and y components, requiring vector analysis.

Chapter Concept :

Collisions in Two Dimensions

Correct Answer: True

Solution:

In elastic collisions, both momentum and kinetic energy are conserved, as stated in the provided text.

Chapter Concept :

Elastic and Inelastic Collisions

Correct Answer: True

Solution:

According to the principle of conservation of mechanical energy, the total mechanical energy (sum of kinetic and potential energies) remains constant in a system where only conservative forces are acting.

Chapter Concept :

Conservation of Mechanical Energy

Correct Answer: False

Solution:

Non-conservative forces such as friction cause dissipation of energy as heat, which means the total mechanical energy is not conserved.

Chapter Concept :

Conservation of Mechanical Energy

Correct Answer: True

Solution:

The work-energy theorem relates the change in kinetic energy of a body to the work done by the net force acting on it. This is mathematically expressed as Kf−Ki=WnetK_f - K_i = W_{net}, where KfK_f and KiK_i are the final and initial kinetic energies, respectively, and WnetW_{net} is the work done by the net force.

Chapter Concept :

Work-Energy Theorem

Correct Answer: True

Solution:

If the force and displacement are perpendicular, the angle θ\theta between them is 90∘90^\circ, making cos⁡θ=0\cos \theta = 0. Hence, the work done W=Fdcos⁡θ=0W = Fd \cos \theta = 0.

Chapter Concept :

Work Done by Constant Force

Correct Answer: True

Solution:

For a conservative force, the work done around any closed path is zero. This is because the work done only depends on the initial and final positions, not on the path taken, leading to a net work of zero for closed paths.

Chapter Concept :

Conservative Forces and Potential Energy

Correct Answer: False

Solution:

Kinetic energy is a scalar quantity, as it is defined by the equation K=12mv2K = \frac{1}{2}mv^2, which involves only magnitudes and no direction.

Chapter Concept :

Kinetic Energy

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