Question

A pickup truck is carrying a toolbox, but the rear gate of the truck is missing, so the box will slide out if it is set moving. The coefficients of kinetic and static friction between the box and the bed of the truck are 0.250 and 0.500, respectively. Starting from rest, what is the shortest time this truck could accelerate uniformly to 36.0m/s (≈ 80.5mph ) without causing the box to slide?

Answer 1

t=7.33 s

Step-by-step explanation:

According to Newton's second law:

`\sum F=m*a`

because we don't want the box to slide, the acceleration has to be zero.

`\sum F=-F_(friction)+F_(truck)=0\\F_(truck)=F_(friction)\\F_(friction)=\µ*m*g=0.500*9.81*m\\F_(friction)=4.91*m`

we know that:

`F=m*a\\4.91m=m*a\\a=4.91m/s^2`

Now having the acceleration, we can use the following formula.

`v_f=a*t\\t=(36.0m/s)/(4.91m/s^2)\\\\t=7.33s`