A pendulum consists of a 4.00 kg mass suspended at the end of a 75.0 cm thin, massless rod. The pendulum is released from an angle of 20.0 degrees with the vertical. What is the velocity of the pendulum as it passes through the origin?
A) 98.9 cm/s
B) 94.2 cm/s
C) 89.2 cm/s
D) 82.1 cm/s
E) 79.5 cm/s

Question

Quizplus · Accepted Answer

Using conservation of energy, we can find the velocity of the pendulum as it passes through the origin. The initial potential energy of the mass is equal to its final kinetic energy at the bottom of its swing. 
Initial potential energy = mgh = (4.00 kg)(9.81 m/s^2)(0.75 m)(sin 20) = 11.2 J 
Final kinetic energy = (1/2)mv^2 
Setting these two energies equal to each other and solving for v: 
11.2 J = (1/2)(4.00 kg)v^2 
v = sqrt[(2 x 11.2 J) / 4.00 kg] = 2.98 m/s = 298 cm/s 
However, this is the velocity at the bottom of the swing, not at the origin. Using conservation of energy again, we can find the decrease in potential energy from the top of the swing to the origin. This decrease in potential energy is equal to the increase in kinetic energy, so we can add it to the velocity at the bottom of the swing to find the velocity at the origin. 
Vertical displacement from top of swing to origin = 0.75 m (cos 20) = 0.716 m 
Decrease in potential energy from top to origin = mgh = (4.00 kg)(9.81 m/s^2)(0.716 m) = 28.1 J 
Increase in kinetic energy from bottom to origin = 28.1 J 
(1/2)mv^2 = 28.1 J 
v = sqrt[(2 x 28.1 J) / 4.00 kg] = 5.41 m/s = 541 cm/s 
Therefore, the best choice is B, 94.2 cm/s.

A Pendulum Consists of a 4