Question

A 200 kg wood crate sits in the back of a truck. The coefficients of friction between the crate and the truck are ????s = 0.9 and ????k = 0.5. The truck starts off up a 20° slope. What is the maximum acceleration the truck can have without the crate slipping out the back?

Answer 1

Answer:

Maximum acceleration of the truck is 5.25 m/s^2

Explanation:

To find the maximum acceleration the truck first we need to calculate friction between truck and wood. Because of wood is not moving, coefficient of c_{s} need to be used for it. Then the formula will be:

$F_{s}=c_{s}*200*9.8*cos(20)\\F_{s}=0.9*200*9.8*0.94\\F_{s}=1657.62$

1657.62 Newton is the friction.

So force against friction need to be at most 1657.62 N. Then equation will be:

$F_{s}=F_{a}+F_{m}\\1657.62=200*9.8*sin(20)+200*a*cos(20)\\1657.62=670.36+187.94*a\\987.26=187.94*a\\a=5.25$

Maximum acceleration of the truck need to be 5.25 m/s^2