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?
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?
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?
What is the formula for power delivered to a body undergoing one-dimensional motion with constant acceleration, starting from rest?
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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?
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Which formula accurately describes the relationship between velocity and distance for a particle influenced by a vertical restitution coefficient?
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If the coefficient of restitution is 'e', how does it influence the horizontal range after a collision?
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Consider a scenario where two particles collide and one is stationary. What primarily determines the post-collision speeds of these particles?
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What is the outcome of an elastic collision between two equal mass particles where one is initially at rest?
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What does the coefficient of restitution, 'e', quantify in regards to elasticity in a collision?
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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.
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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.