20 A truck carries a crate which can slide. Suppose the truck and crate are traveling to the right at an initial velocity of v0 and the distance between the front of the crate and the front of the trailer is d0. The brakes are applied and the truck decele

PROBLEM STATEMENT:

A truck carries a crate which can slide. Suppose the truck and crate are traveling to the right at an initial velocity of v₀ and the distance between the front of the crate and the front of the trailer is d₀. The brakes are applied and the truck decelerates with constantacceleration and stops in time t_s.

a.) Express the truck’s acceleration a_T < 0 in terms of velocity and stopping time.

MY ANSWER: From the equation of motion:

v = v₀+at

0=v₀-at_s

a=v₀/t_s

I’m pretty sure this is correct.

b.) Assume the truck brakes hard enough that the crate slides to the right relative to the truck. The coefficient of friction (static and dynamic) is mu. Write the equations of motion for the crate, then express the relative acceleration of the crate with respect to the truck, a_c/t before and after the truck stops. Express it in terms of the given quantities v₀, t_s, mu, and g.

This is the part I am not so sure about. I’m not exactly sure how to approach this part.

 

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