Review problem. A 60.0 -kg person running at an initial speed of 4.00 m / s jumps onto a 120 -kg

step 1 We have 60 kilograms times 4 meter per second equals 120 kilogram plus 60 kilogram times v final

Review problem. A 60.0 -kg person running at an initial...

Review problem. A 60.0 -kg person running at an initial speed of 4.00 $\mathrm{m} / \mathrm{s}$ jumps onto a 120 -kg cart initially at rest (Figure P9.55). The person slides on the cart's top surface and finally comes to rest relative to the cart. The coefficient of kinetic friction between the person and the cart is 0.400 Friction between the cart and ground can be neglected. (a) Find the final velocity of the person and cart relative to the ground. (b) Find the friction force acting on the person while he is sliding across the top surface of the cart. ( $\mathrm{How}$ long does the friction force act on the person? (d) Find the change in momentum of the person and the change in momentum of the cart. (e) Determine the displacement of the person relative to the ground while he is sliding on the cart. (f) Determine the displacement of the cart relative to the ground while the person is sliding. (g) Find the change in kinetic energy of the person. (h) Find the change in kinetic energy of the cart. (i) Explain why the answers to $(\mathrm{g})$ and (h) differ. (What kind of collision is this, and what accounts for the loss of mechanical energy?)

Review problem. A 60.0 -kg person running at an initial speed of 4.00 $\mathrm{m} / \mathrm{s}$ jumps onto a 120 -kg cart initially at rest (Figure P9.55). The person slides on the cart's top surface
and finally comes to rest relative to the cart. The coefficient of kinetic friction between the person and the cart is 0.400 Friction between the cart and ground can be neglected. (a) Find the final velocity of the person and cart relative to the ground. (b) Find the friction force acting on the person while he is sliding across the top surface of the cart. ( $\mathrm{How}$ long does the friction force act on the person? (d) Find the change in momentum of the person and the change in momentum of the cart. (e) Determine the displacement of the person relative to the ground while he is sliding on the cart.
(f) Determine the displacement of the cart relative to the ground while the person is sliding. (g) Find the change in kinetic energy of the person. (h) Find the change in kinetic energy of the cart. (i) Explain why the answers to $(\mathrm{g})$ and (h) differ. (What kind of collision is this, and what accounts
for the loss of mechanical energy?)

Key Concepts

Inelastic Collisions

In an inelastic collision, while momentum is conserved, kinetic energy is not conserved because some of it is transformed into other forms of energy, such as heat or deformation energy. This concept explains why there is an apparent loss in kinetic energy in systems where objects stick together or undergo frictional interactions during the collision.

Relative Motion

Relative motion addresses the analysis of an object's movement from different reference frames. It is important for understanding how distances and velocities are measured differently when, for example, an object moves on top of another moving object. This concept helps in determining individual displacements and velocities relative to a chosen frame, such as the ground, during interactions.

Coefficient of Kinetic Friction

This is a dimensionless constant that measures the ratio of the force of friction between two sliding surfaces to the normal force pressing them together. It is crucial for calculating the frictional force acting on objects in motion and for determining the deceleration or work done by the friction force, especially when one object is sliding relative to another.

Conservation of Momentum

This principle states that in a closed system with no net external forces, the total momentum remains constant before and after an event such as a collision. In problems involving collisions, particularly when friction with the ground is negligible, conservation of momentum is used to determine final velocities after interaction, regardless of changes in kinetic energy.

Work Done by Friction

Work done by friction involves energy being removed from the system, often converting mechanical kinetic energy into thermal energy. In scenarios where objects slide and friction acts over a distance, calculating the work done by friction is essential to understanding the decrease in mechanical energy, even when momentum is conserved.

Transcript

Please give Ace some feedback