A man tries to push a crate of 8kg across a rough surface. The static friction coefficient is 0.6 and the kinetic friction coefficient is 0.4. Calculate the friction force exerted on the crate if: a) a horizontal force of 45 N is exerted on the crate and b) a horizontal force of 60 N is exerted on the crate

Maybe This will help out:

Friction and weight are common experiences and taken for granted, but were not always understood. Aristotle believed that objects that contained the "element," earth, fell because Earth was at the center of the universe, and that was the natural order of things. We now know that weight, which is the force of gravity between objects, not only makes apples fall from trees, but keeps the Moon circling the Earth, and the Earth circling the sun. Without gravity to hold them in orbit, they would continue to move in a straight line until interfered with.

Aristotle also believed (and some students still believe) that the natural state of an object is to be at rest. That is, he believed unless a force was pushing an object, the object will slow down to a stop. This view overlooks friction, the force that resists the movement of surfaces sliding against each other. Friction causes most objects we see to come to rest. Unlike Aristotle, we know that there is nothing pushing planets along their orbit: since there is no friction to slow down planets, they will continue to move until interfered with.

Ff = mu Fn = mu mg = .6*8*9.8

So 45 won't do it, but 60 will.
Once it's moving
Ff = mu mg = .4*8*9.8
F - Ff = ma, solve for a

To calculate the friction force exerted on the crate, we need to consider the maximum static friction force and the kinetic friction force.

a) When a horizontal force of 45 N is exerted on the crate:
First, we need to determine the maximum static friction force (F_max_static). The formula to calculate it is:

F_max_static = coefficient of static friction x normal force

The normal force (N) is equal to the weight of the crate, given by the formula:

N = mass x gravitational acceleration

The gravitational acceleration (g) is approximately 9.8 m/s².

So, N = 8 kg x 9.8 m/s² = 78.4 N

Now, we can calculate F_max_static:

F_max_static = 0.6 x 78.4 N = 47.04 N

Since the applied force of 45 N is less than the maximum static friction force, the crate remains stationary and the friction force experienced by the crate is equal to the applied force. Therefore, the friction force exerted on the crate is 45 N.

b) When a horizontal force of 60 N is exerted on the crate:
Since the applied force of 60 N is greater than the maximum static friction force, the crate will start moving, and the friction force will change to kinetic friction.

The kinetic friction force (F_kinetic) is given by the formula:

F_kinetic = coefficient of kinetic friction x normal force

Using the same normal force value as before (N = 78.4 N) and the coefficient of kinetic friction (0.4), we can calculate F_kinetic:

F_kinetic = 0.4 x 78.4 N = 31.36 N

Therefore, when a force of 60 N is exerted on the crate, the friction force exerted on the crate will be 31.36 N (the kinetic friction force).

Note: The values obtained in this explanation assume the surface is level and there are no other significant forces acting on the crate.