A $4700\,\text{kg}$ truck carrying a $900\,\text{kg}$ crate is traveling at $25\,\text{m/s}$ to the right along a straight, level highway, as shown above. The truck driver then applies the brakes, and as it slows down, the truck travels $55\,\text{m}$ in the next $3.0\,\text{s}$. The crate does not slide on the back of the truck.

Question

A $4700\,\text{kg}$ truck carrying a $900\,\text{kg}$ crate is traveling at $25\,\text{m/s}$ to the right along a straight, level highway, as shown above. The truck driver then applies the brakes, and as it slows down, the truck travels $55\,\text{m}$ in the next $3.0\,\text{s}$. The crate does not slide on the back of the truck.(a) Draw and label all the forces acting on the crate during braking.
, (b) Calculate the magnitude of the acceleration of the truck, as it is constant.
, (c) Calculate the minimum coefficient of friction between the crate and the truck that prevents the crate from sliding. Indicate whether this friction is static or kinetic.
, (d) Now assume the bed of the truck is frictionless, but there is a spring of spring constant $9200\,\text{N/m}$ attaching the crate to the truck. If the truck and crate have the same acceleration, calculate the extension of the spring as the truck accelerates from rest to $25\,\text{m/s}$ in $10\,\text{s}$.
, (e) Now the truck is moving at a constant speed of $25\,\text{m/s}$ and the crate is in equilibrium. Indicate whether the extension of the spring is greater than, less than, or the same as in part (d) when the truck was accelerating. Explain your reasoning.
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Rachel · Accepted Answer

$4.4\,\text{m/s}^2$
$\mu_{\min}=0.45,\,\text{static}$
$0.24\,\text{m}$
$\text{less than}$

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