Question

A pendulum has kinetic energy of 1.6 J at the bottom of its swing. If the mass of the bob on the end of the pendulum is 3.1 kg, what height does the pendulum reach?

A) 1.0 m
B) 1.5 m
C) 2.0 m
D) 2.5 m

Answer 1

Using the conservation of mechanical energy, the potential energy at the peak of the pendulum's swing (which is equal to the initial kinetic energy) was calculated, yielding a height of approximately 0.0523 meters.

However, this result does not match any of the provided options, suggesting there may be an error in the question.

Step-by-step explanation:

To determine the height that the pendulum reaches, we can use the conservation of mechanical energy principle. The kinetic energy (KE) at the bottom of the swing will be equal to the potential energy (PE) at the highest point of the swing.

To find the height (h), we use the formula for gravitational potential energy:
PE = mgh
Where:
m is the mass of the pendulum bob (3.1 kg),
g is the acceleration due to gravity (9.8 m/s2), and
h is the height in meters.

We know that the kinetic energy (KE) at the bottom is 1.6 J and that KE equals PE at the highest point, so:
1.6 J = (3.1 kg)(9.8 m/s2)h

Now we solve for h:
h = 1.6 J / (3.1 kg × 9.8 m/s2)
h ≈ 0.0523 m

Since the options given are all in whole meters, there may be a mistake as none of the options match the calculated height of approximately 0.0523 m.