Question

Mike attaches a 3.00 kg lead ball to a string to make a pendulum of length 10.0 meters. Let us call the position at which the lead ball hangs down vertically and is at rest the equilibrium position. Mike then pulls the lead ball to the side so that its center is raised to a vertical height of 0.0409 meters above its equilibrium position, and he gives the lead ball (pendulum bob) a push. Thus Mike gives the pendulum bob an initial kinetic energy of 2.00 J as he releases it. Assume there is no air resistance or friction. Choose the reference level for potential energy at the bottom of the pendulum's swing (the equilibrium position). How long does the pendulum take to complete one cycle, i.e. what is the pendulum's period?

a.12.7 seconds
b.10.2 seconds
c.8.75 seconds
d.3.35 seconds
e.none of the items

Answer 1

The period of a pendulum with a length of 10.0 meters is approximately 6.34 seconds, which is not listed among the options provided. The correct answer is 'e. none of the items'.

Step-by-step explanation:

To calculate the pendulum's period, we will use the formula for the period (T) of a simple pendulum:

T = 2π√(l/g)

where:

• l = length of the pendulum (10.0 meters)
• g = acceleration due to gravity (9.81 m/s2)

Plugging these values into the formula, we get:

T = 2π√(10.0 m / 9.81 m/s2)

T ≈ 6.28√(1.019) seconds

T ≈ 6.28 × 1.009 s

T ≈ 6.34 seconds

Therefore, the period for one complete cycle is about 6.34 seconds, which does not match any of the options (a) through (e). Thus, the correct answer is 'e. none of the items'.