Question

A pendulum has 15-J of potential energy at the top of its swing. a) What is its kinetic energy at the bottom of its swing? b) At another time the pendulum has 8-J of potential energy. What is its kinetic energy? c)For the pendulum in “b”, what will its kinetic energy be if it loses 2-J to heat?

Answer 1

Given data:

* The potential energy of the pendulum at the swing is U = 15 J.

Solution:

(a). At the top of the swing, the pendulum is in the rest state, thus, the kinetic energy of the pendulum at the top of the swing is,

$K=0\text{ J}$

The net energy of the system at the top of the swing is,

$\begin{gathered} E=K+U \\ E=0+15 \\ E=15\text{ J} \end{gathered}$

According to the law of conservation of energy, the net energy at the bottom of the swing is the same as the net energy at the top of the swing.

As the value of height at the bottom of the swing is zero, thus, the potential energy of the pendulum at the bottom of the swing is,

$U_1=0\text{ J}$

Thus, the kinetic energy at the bottom of the swing is,

$\begin{gathered} E=U_1+K_1 \\ 15=0+K_1 \\ K_1=15\text{ J} \end{gathered}$

Thus, the kinetic energy at the bottom of the swing is 15 J.

(b). If the potential energy of the pendulum is,

$U_2=8\text{ J}$

The kinetic energy of the pendulum is,

$\begin{gathered} E=U_2+K_2 \\ 15=8+K_2 \\ K_2=15-8_{} \\ K_2=7\text{ J} \end{gathered}$

Thus, the kinetic energy of the pendulum in the given case is 7 J.

(c). If the loss of 2 J energy takes place, then the kinetic energy in the case b is,

$\begin{gathered} K_3=K_2-2 \\ K_3=7-2 \\ K_3=5\text{ J} \end{gathered}$

Thus, the kinetic energy of the pendulum in the given case is 5 J.