You have a two-wheel trailer that you pull behind your ATV. Two children with a

Question

You have a two-wheel trailer that you pull behind your ATV. Two children with a combined mass of 84.2 kg hop on board for a ride through the woods and the springs (one for each wheel) each compress by 5.97 cm. When you pull the trailer over a tree root in the trail, it oscillates with a period of 1.74 s. Determine the following.

(a) force constant of the springs

How is the force constant of a spring related to the force the spring exerts when it is stretched or compressed?___________ N/m

(b) mass of the trailer__________ kg

(c) frequency of the oscillation_________ Hz

(d) time it takes for the trailer to bounce up and down 10 times_______ s

Explanation / Answer

(a) force constant of the springs
k = F/x
k = 84.2(9.81) / 0.0597
k = 13835.88 N/m

This is the combined spring constant for both springs. Each spring individually would have a spring constant of half that value or 6917.92 N/m

(b) mass of the trailer
T = 1.74 s
f = 1/T = 0.5747 Hz
f = /2
= 2f = 3.61 rad/s
² = k/m
m = k / ² = 13835.88 / 3.62² = 1061.07 kg

so trailer mass is
m = 1061.07 - 84.2 = 976.88 kg

(c) frequency of the oscillation
already found at 1/T
= 0.5747 Hz

(d) time it takes for the trailer to bounce up and down 10 times

t = 10T = 17.4 s

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