The height above the ground of a child on a swing varies from 0.5 m at the lowest point to 2.0 m at the highest point. The maximum speed of the child is
A) about 5.4 m/s.
B) about 7.7 m/s.
C) about 29.4 m/s.
D) dependent on the child's mass.

Question

Quizplus · Accepted Answer

The maximum speed of the child on the swing can be found using the principle of conservation of mechanical energy. At the highest point, all the energy is potential, and at the lowest point, it is converted into kinetic energy. The difference in height (2.0 m - 0.5 m = 1.5 m) can be used with the formula for gravitational potential energy (mgh) and kinetic energy (1/2 mv^2) to solve for v, the speed. The mass of the child cancels out, showing that the speed is not dependent on the child's mass. Using g = 9.8 m/s^2, the calculation yields a maximum speed of about 5.4 m/s.

The Height Above the Ground of a Child on a Swing