(29) please help fix the two areas marked wrong (with red x) You have a two-whee

Question

(29) please help fix the two areas marked wrong (with red x)

You have a two-wheel trailer that you pull behind your ATV. Two children with a combined mass of 66.2 kg hop on board for a ride through the woods and the springs (one for each wheel) each compress by 5.37 cm. When you pull the trailer over a tree root in the trail, it oscillates with a period of 1.49 s. Determine the following (a) force constant of the springs 6040.6 N/m (b) mass of the trailer 273.8 How is the period of osc ation for an oscillating mass related to the force constant of the spring and the mass suspended by the spring? kg (c) frequency of the oscillation 0.67 Hz (d) time it takes for the trailer to bounce up and down 10 times 14.9

Explanation / Answer

A)(a)mg = kx

k' = mg/x = 66.2 x 9.8/0.0537 = 12081.2 N/m

this is combines for two springs, so for one

k ' =k'/2 = 6040.6 N/m

Hence, k = 6040.6 N/m

(b)Let m be the mass.

T = 1.49 s

f = 1/T = 1/1.49 = 0.671 Hz

w = 2 pi f = 2 x 3.14 x 0.671 = 4.21 rad/s

w = sqrt (k/m)

w^2 = k/m =>m = k/w^2

m' = k'/w^2 = 12081.2/4.21^2 = 681.23 kg

m = m' - 66.2 = 615.03 kg

Hence, m = 615.03 kg

c)f = 1/t = 1/1.49

f = 0.67 Hz

d)T = 10t

T = 10 x 1.49 = 14.9 s

Hence, T = 14.9 s

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