A heavy crate (mass $m$) is placed inside the flatbed of a truck but not tied down

Question

A heavy crate (mass m) is placed inside the flatbed of a truck but not tied down. As the truck pulls away from a stop sign the crate remains in place and does not slide on the truck bed. What force causes the acceleration of the crate?

a) weight force

b) a static friction force

c) normal force

d) ma force

e) no force needed

I think that the answer is b) static friction force.. But I also need to explain how I came to that answer.. All I can think is that the static friction force is what would cause the acceleration of the crate because when the static friction force is increased in this case it would acellerate the crate to the right?

so essentially the Static Friction Force $\int f_s$ keeps the crate from moving, so essentially the crate will accelerate as the truck accelerates?

Answer 1

I think that you have a pretty good qualitative understanding of whats going on. The box will not move as long as the static frictional force on the box is sufficient to overcome the acceleration of the truck. This condition will be given by:

$f_s > m_Ba_T$

where

$f_s = \mu_s m_Bg$