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

Answer 1

Answer:

the force constant  k = 2.369 N/m

Explanation:

Given that:

A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair.

with period T = 0.500 s and a mass of 0.0150 kg, Then the force constant can be calculated by using the formula:

$\mathtt{T = 2 \pi \ \sqrt{\dfrac{m}{k} }}$

where;

T = time period

m = mass

k = force constant.

By making k the subject of the formula; we have:

$\mathtt{T^2 = 4 \pi^2 (\dfrac{m}{k})}$

$\mathtt{k =\dfrac{4 \pi ^2 \ m}{T^2}}$

replacing our given values , we have:

$\mathtt{k =\dfrac{4 (3.142) ^2 \ \times 0.0150 }{0.5^2}}$

$\mathtt{k =\dfrac{39.49 \ \times 0.0150 }{0.25}}$

$\mathtt{k =\dfrac{0.59235 }{0.25}}$

k = 2.369 N/m