Question

A 105 g granite cube slides down a 40 ∘ frictionless ramp. At the bottom, just as it exits onto a horizontal table, it collides with a 260 g steel cube at rest. Assume an elastic collision. How high above the table should the granite cube be released to give the steel cube a speed of 190 cm/s ?

Answer 1

The granite cube should be released from a height of approximately 69.3 centimeters above the table to give the steel cube a speed of 190 cm/s.

Explanation.

Initially, determine the potential energy of the granite cube at the release point using ( PE = mgh ). Then, equate this potential energy to the kinetic energy of the steel cube just after the collision. Apply conservation of momentum and kinetic energy to solve for the final velocity of the steel cube. Using the equation
`\( KE = (1)/(2)mv^2 \),`relate the velocity to the height from which the granite cube was released. Solving for
`\( h \)`yields the required height.

In this scenario, the potential energy at the release point of the granite cube converts into kinetic energy of the steel cube after the collision. By equating these energies and applying conservation laws for momentum and kinetic energy in an elastic collision, the relationship between the height of release and the resulting velocity of the steel cube is established.

This calculation ensures that the kinetic energy gained by the steel cube is equivalent to the potential energy lost by the granite cube, leading to the determination of the required initial height for the granite cube to impart the desired speed to the steel cube upon collision.""