Question

question 8 (1 point)
a lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. they both slide up the same frictionless hill. which rises to a greater height?
the heavy object, because it has greater kinetic energy.
the lightweight object, because it weighs less.
they both slide to the same height.
cannot be determined from the information given

Explanation:

We use the principle of conservation of mechanical energy (kinetic energy \( KE \) converts to gravitational potential energy \( PE \)). The formula for kinetic energy is \( KE = \frac{1}{2}mv^2 \), and for gravitational potential energy is \( PE = mgh \). At the start, both objects have the same speed \( v \), but different masses \( m_1 \) (light) and \( m_2 \) (heavy). When they slide up the hill, all kinetic energy converts to potential energy, so \( \frac{1}{2}mv^2 = mgh \). Simplifying, \( h=\frac{v^2}{2g} \), which is independent of mass. So both reach the same height.

Answer:

They both slide to the same height.