Question

A 2.0 kg pendulum has an initial total energy of 20 J. Calculate the energy lost as heat if the pendulum is 0.10 m high and is traveling at 4.0 m/s.
A) 2.0J
B) 18J
C) 14J
D)16J

Answer 1

The correct answer is (A) 2.0 J

Total energy of the pendulum is the sum of its kinetic and potential energy. At the instant of time, when the pendulum is at a height h and has a speed v, Its energy is given by,

$E=mgh+\frac{1}{2} mv^2$

Substitute 2.0 kg for m, the mass of the pendulum, 9.81 m/s² for g, the acceleration due to gravity, 0.10 m for h and 4.0 m/s for v.

$E=mgh+\frac{1}{2} mv^2\\ =(2.0kg)(9.81m/s^2)(0.10 m)+\frac{1}{2}(2.0kg)(4.0m/s)^2\\ =17.962J$

The pendulum has an initial energy of 20 J. the energy lost is given by,

$\Delta E=(20J)-(17.962J)\\ =2.038J=2.0J$

Thus, the energy lost by the pendulum is (A) 2.0 J