Question

A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.500 s for a 0.0150-kg mass?

a) 0.048 N/m
b) 0.192 N/m
c) 0.384 N/m
d) 1.536 N/m

Answer 1

The force constant needed to produce a period of 0.500 s for a 0.0150-kg mass in a bouncing clock is 0.192 N/m.

Step-by-step explanation:

To determine the force constant needed to produce a period of 0.500 s for a 0.0150-kg mass in a bouncing clock, we can use the formula for the period of a mass-spring system:

T = 2π√(m/k)

where T is the period, m is the mass, and k is the force constant. Rearranging the formula, we have:
k = (4π²m)/T²

Substituting the given values, we get:
k = (4π² * 0.0150 kg) / (0.500 s)²

Calculating the values, we find that the force constant is approximately 0.192 N/m.