Physics Chapter on Work and Energy

Questions and Answers

What is the work done by the forces during a displacement from x = 0 to x = d, if the coefficient of restitution is e?

$\frac{e R}{2}$

$\frac{e^2 R}{mk 2d^2}$

$\frac{e^3 R}{mk d^2}$ (correct)

$\frac{m d^3 k^3}{2}$

If a particle of mass m moving horizontally at 6 m/s collides elastically with another particle, which of the following statements is true regarding their velocities after collision?

Both particles will have equal speeds.

Identification of velocities requires additional information. (correct)

One particle will always move faster than the other.

The velocities depend on the masses of the particles involved.

After an elastic collision, if one particle has a velocity of $3\hat{i} - 2\hat{j}$ m/s, what must the other particle's velocity be?

$\hat{i} + 3\hat{j}$

$2\hat{i} + 3\hat{j}$

$\hat{i} + \hat{j}$

$2\hat{i} - \hat{j}$ (correct)

What is the formula for power delivered to a body undergoing one-dimensional motion with constant acceleration, starting from rest?

$t^2$ Signup and view all the answers

In an elastic collision scenario, if the masses are equal and one is at rest before the collision, what can be inferred about their velocities after the collision?

The initially at rest particle moves with the same speed. Signup and view all the answers

Which formula accurately describes the relationship between velocity and distance for a particle influenced by a vertical restitution coefficient?

$v = Kx$ Signup and view all the answers

If the coefficient of restitution is 'e', how does it influence the horizontal range after a collision?

It keeps the range consistent. Signup and view all the answers

Consider a scenario where two particles collide and one is stationary. What primarily determines the post-collision speeds of these particles?

The initial velocities and directions of both particles. Signup and view all the answers

What is the outcome of an elastic collision between two equal mass particles where one is initially at rest?

The moving particle transfers all motion to the stationary particle. Signup and view all the answers

What does the coefficient of restitution, 'e', quantify in regards to elasticity in a collision?

The ratio of relative speeds of separation to approach. Signup and view all the answers

Study Notes

Work and Energy Concepts

Work done (WI, WII, WIII) is related to different paths taken by an object under conservative forces.
Work done is independent of the path when no non-conservative forces are present.
If WI, WII, and WIII are work done along paths I, II, and III respectively, valid relationships include WI = WII = WIII.

Force vs Displacement

The net work done by a force is represented by the area under the force vs displacement graph.
Displacement from x = 0 to x = 16 m results in a specific calculated net work, dependent on the graph's area.

Chain and Work Done

A chain of mass 2 kg with 1/3 of its length hanging (4 m total) exerts a gravitational force affecting the work done as it is pulled back to the table.

Kinetic Energy and Momentum Relationships

A 50% decrease in momentum results in a 75% decrease in kinetic energy due to the relationship between momentum (p = mv) and kinetic energy (KE = 1/2 mv²).
Elastic collisions conserve momentum and kinetic energy, and for equal masses, the velocities after collision are interchanged.

Particle Motion and Energy

If a particle moves through a force field with a defined potential (U = k(x + y)), the work done is calculated based on the change in potential energy.
The work done can also be determined through the force applied and the distance moved in that force's direction.

Air Resistance

Work done against air resistance can be calculated from the initial and final speeds of an object (20 m/s to 10 m/s).

Power Calculation

The power at the maximum height of a projectile is affected by its potential energy (P = mgh) and can be equated to other derived functions based on angle and speed.

Elastic Collision Outcomes

In a perfectly elastic collision, both momentum and kinetic energy are conserved, leading to predictable outcomes in post-collision velocities.

Motion Fundamentals

The relationship between power, velocity, and time can be analyzed when a body undergoes constant acceleration, showing a proportional relationship to time, either directly or squared.

Description

This quiz focuses on the concept of work done along different paths in the context of conservative forces, based on NCERT guidelines. Explore the principles of energy conservation and the implications of non-conservative forces in various physical scenarios.