1994 Paper 2 Q10

Year: 1994
Paper: 2
Question Number: 10

Course: UFM Mechanics
Section: Work, energy and Power 2

Difficulty: 1600.0 Banger: 1486.7
work energy power elastic rope Hooke's law SHM simple harmonic motion collision towing differential equation second order

Problem

A truck is towing a trailer of mass \(m\) across level ground by means of an elastic rope of natural length \(l\) whose modulus of elasticity is \(\lambda.\) At first the rope is slack and the trailer stationary. The truck then accelerates until the rope becomes taut and thereafter the truck travels in a straight line at a constant speed \(u\). Assuming that the effect of friction on the trailer is negligible, show that the trailer will collide with the truck at a time \[ \pi\left(\frac{lm}{\lambda}\right)^{\frac{1}{2}}+\frac{l}{u} \] after the rope first becomes taut.

No solution available for this problem.

Rating Information

Difficulty Rating: 1600.0

Difficulty Comparisons: 0

Banger Rating: 1486.7

Banger Comparisons: 1

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Problem source
A truck is towing a trailer of mass $m$ across level ground by means of an elastic rope of natural length $l$ whose modulus of elasticity is $\lambda.$ At first the rope is slack and the trailer stationary.
The truck then accelerates until the rope becomes taut and thereafter the truck travels in a straight line at a constant speed $u$. Assuming that the effect of friction on the trailer is negligible, show that the trailer will collide with the truck at a time 
\[
\pi\left(\frac{lm}{\lambda}\right)^{\frac{1}{2}}+\frac{l}{u}
\]
after the rope first becomes taut.
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