The crate will not slip as long as it has the same acceleration as the truck. Therefore, a net force must act on the crate to accelerate it, and the static frictional force
contributes to this net force. Since the crate tends to slip backward, the static frictional force is directed forward, up the hill. As the acceleration of the truck increases,
must also increase to produce a corresponding increase in the acceleration of the crate. However, the static frictional force can increase only until its maximum value
is reached, at which point the crate and truck have the maximum acceleration
. If the acceleration increases even more, the crate will slip. To find
, we will employ Newton's second law, the definition of weight, and the relationship between the maximum static frictional force and the normal force.