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A student investigates the motion of a cart rolling down an incline and colliding with another cart at the bottom. The following data were collected: Part A – Motion Down the Incline The cart (mass = 0.40 kg) is released from rest at different heights. The velocity at the bottom is measured and the data is recorded as shown in the table below. Height (m) Velocity at Bottom (m/s) 0.15 1.6 0.25 2.2 0.35 2.7 Questions: Use the principle of conservation of energy to explain why the velocity increases with height. Compare the measured velocities to the theoretical prediction v=2ghv = \sqrt{2gh}​. Do they agree reasonably well? Part B – Collision at the Bottom After rolling down, the 0.40 kg cart collides head-on with a stationary cart of mass 0.60 kg. After the collision, the two carts stick together and move off with a velocity of 1.0 m/s. Questions: 3. Identify the type of collision (elastic, inelastic, or perfectly inelastic). Justify your answer. 4. Using momentum conservation, show how the final velocity of 1.0 m/s supports the data. 5. Is kinetic energy conserved in this collision? Explain briefly.

Two carts collide on a frictionless track. Cart A (`ma` kg) moves at `v1` m/s and collides with Cart B (`mb` kg) at rest. After the collision, Cart A stops. What is the velocity of Cart B? Give your answer in m/s and round to two decimal places

A `ma` kg block moving at `vi` m/s collides and sticks to a `m2` kg block at rest. What is their final velocity after the collision? Round your answer to two decimal places.

A `f` N horizontal force pushes a `m` kg box across a frictionless floor. What is the box’s acceleration? Provide your answer in m/s2 and round to two decimal points.

A `m` kg box is pulled with a net force of `f` N. What is the acceleration of the box? Provide your answer in m/s2, round to two decimal places.

A `m1` kg car moving at `v1` m/s collides inelastically with a `m2` kg car moving at `v2` m/s in the same direction. What is their velocity after sticking together? Round your answer to two decimal places.

A car of mass `m` kg accelerates at `a` m/s². What net force acts on the car? Provide your answer in Newtons (N).

In a perfectly inelastic collision, two objects stick together after impact. Which is always true?

A soccer ball is kicked and continues rolling across a smooth field until friction slows it down. Which force causes the ball to eventually stop?

A figure skater is spinning with her arms extended. Her rotational inertia in this position is 2.0 kg·m2. She then pulls her arms close to her body, reducing her rotational inertia to 1.2 kg·m2. If her final angular velocity is 3.0 rev/s, what was her initial angular velocity when her arms were extended?