Lesson: Conservation of Energy

A particle of mass 281 g was projected at 37 cm/s up the line of greatest slope of a smooth plane inclined to the horizontal at an angle whose sine is . Determine the change in the particle’s gravitational potential energy from the moment it was projected until its speed became 29 cm/s.

A body was projected up a rough inclined plane from its bottom. Its initial kinetic energy was 242 joules. The body continued moving until it reached its maximum height and then slid back down to the bottom. When it reached the bottom, its kinetic energy was 186 joules. Find the work done against friction during the ascent and the gain in gravitational potential energy when the body was at its maximum height.

A sphere started moving down a rough inclined plane of length 50 m. When it reached the bottom of the plane, it had descended 15 m vertically and it continued moving along a horizontal plane of the same resistance. Given that of the gravitational potential energy was lost as a result of the work done against the resistance of the plane, find the speed of the sphere at the bottom of the inclined plane and the distance covered by the sphere along the horizontal plane. Consider the acceleration due to gravity to be 9.8 m/s².