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:
[tex]\mathtt{T = 2 \pi \ \sqrt{\dfrac{m}{k} }}[/tex]
where;
T = time period
m = mass
k = force constant.
By making k the subject of the formula; we have:
[tex]\mathtt{T^2 = 4 \pi^2 (\dfrac{m}{k})}[/tex]
[tex]\mathtt{k =\dfrac{4 \pi ^2 \ m}{T^2}}[/tex]
replacing our given values , we have:
[tex]\mathtt{k =\dfrac{4 (3.142) ^2 \ \times 0.0150 }{0.5^2}}[/tex]
[tex]\mathtt{k =\dfrac{39.49 \ \times 0.0150 }{0.25}}[/tex]
[tex]\mathtt{k =\dfrac{0.59235 }{0.25}}[/tex]
k = 2.369 N/m
According to the information available in the question, the force constant is 2.37N/m.
Using the relation;
T = 2π√m/k
T = period = 0.500 s
m = mass in kilograms = 0.0150-kg
k = spring constant = ?
Making k the subject of the formula;
k = 4π^2m/T^2
k = 4 × (3.142)^2 × 0.0150/(0.500 )^2
k = 2.37N/m
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