A crate is resting on the back of a truck and has a coefficient of of friction of 0.45. What is the maximum acceleration that the truck can undergo before the crate starts to slide off the back of the truck.

To determine the maximum acceleration at which the crate will not slide off the back of the truck, we need to consider the forces acting on the crate.

The force due to gravity is acting vertically downward and can be calculated using the equation F_gravity = m * g, where m is the mass of the crate and g is the acceleration due to gravity (approximately 9.8 m/s^2).

The maximum force of static friction that can be exerted between the crate and the truck bed can be calculated using the equation F_friction = μ * N, where μ is the coefficient of friction and N is the normal force exerted on the crate by the truck bed. Since the crate is resting on the truck bed, the normal force is equal to the force due to gravity (N = m * g).

To prevent the crate from sliding, the force of static friction must be equal to or greater than the force due to gravity. So we set up the following inequality:

F_friction ≥ F_gravity

Substituting the respective equations:

μ * N ≥ m * g

Substituting for N:

μ * (m * g) ≥ m * g

Dividing both sides of the inequality by m * g:

μ ≥ 1

Since the coefficient of friction is given as 0.45, which is less than 1, this means that the maximum acceleration that the truck can undergo before the crate starts to slide off the back of the truck is 0 m/s^2. In other words, the truck must not accelerate at all in order to keep the crate from sliding off.