A.) Four people sit in a car. Their masses are 45 kg, 52 kg, 67 kg and 61 kg. Th

Question

A.) Four people sit in a car. Their masses are 45 kg, 52 kg, 67 kg and 61 kg. The car’s mass is 1020 kg. When the car drives over a bump, its springs cause an oscillation with a frequency of 2 Hz. What would the frequency be if only the 45 kg person was present?

B.) A 50 kg hoop with a radius of 2 m is rotating at a constant angular velocity of 10 rad/s. A spray can is used to evenly paint a thin layer on the hoop. The paint was sprayed over a time of 10 s, where the speed reduced to 9 rad/s. What was the paint spray rate in kgs?

Explanation / Answer

(A)

Basic equation
k= F/x
F/x = m w^2 ( w is the angular velocity = 2 pi() f or 2Pi()/T)
so if the spring constant k is the same then
w^2 is proportional to 1/m
or w is proportional to sqrt(1/m)

this means that w2/w1 = sqrt(m1/m2)
w2 = w1 * sqrt(m1/m2)

As w and f are proportional then it is just as true that
f2 = f1*sqrt(m1/m2)

now m1 = 1020 +45+52+67+61 = 1245Kg
and m2 = 1020+45 = 1065kg

so f2= 2Hz * sqrt(1245/1065)
= 2.16 Hz

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