A crate of mass 100kg is at rest on a horizontal floor. The coefficient of static friction between the crate and the floor is 0.4, and the coefficient of kinetic friction is 0.3. A horizontal force, F, or magnitude 350N is applied to the crate. Which of the following is true?

A. The crate accelerates horizontally at 0.5m/s^2
B. The crate slides across the floor at .5m/s
C. The crate does not move.

Please give the correct answer and an explanation why it is correct.

M*g = 100 * 9.8 = 980 N. = Wt. of crate = Normal force(Fn).

Fs = us*Fn = 0.4 * 980 = 392 N. = Force of static friction.

The crate does not move, because the applied force is less than the fore of static friction(Fs).

C. The crate does not move.

The coefficient of static friction is 0.4, which means that the maximum force of static friction that can be exerted by the floor on the crate is μ_s * m * g = 0.4 * 100 kg * 9.8 m/s^2 = 392 N.

The applied force of 350 N is less than the maximum force of static friction, so the crate remains at rest because the static friction is able to counteract and balance out the applied force.

Option A is incorrect because the crate does not accelerate; it remains at rest.

Option B is incorrect because there is no motion involved. The crate does not slide across the floor.

Therefore, C. The crate does not move is the correct answer.

The correct answer is C. The crate does not move.

Explanation:
The maximum static friction force is given by the equation F_s = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force. The normal force is equal to the weight of the crate, which is mass times the acceleration due to gravity (N = mg).

In this case, the maximum static friction force F_s_max = 0.4 * 100kg * 9.8m/s^2 = 392N.

Since the applied force F (350N) is less than the maximum static friction force, the crate will not move. The static friction force counteracts the applied force, preventing any horizontal acceleration. Therefore, option C is correct, and the crate does not move.

The correct answer is C. The crate does not move.

To understand why, let's consider the forces acting on the crate.

- There is a gravitational force acting downwards, which can be calculated using the formula F = mg, where m is the mass of the crate and g is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, F = (100 kg)(9.8 m/s^2) = 980 N.

- There is also a normal force exerted by the floor on the crate, equal in magnitude and opposite in direction to the gravitational force. So, the normal force is 980 N.

- Finally, there is the force of static friction between the crate and the floor. The maximum static friction force can be calculated using the formula F_friction = mu_s * N, where mu_s is the coefficient of static friction (0.4 in this case) and N is the normal force. So, the maximum static friction force is (0.4)(980 N) = 392 N.

Now, when the horizontal force F is applied to the crate, it needs to overcome the force of static friction to start moving. In this case, the applied force F = 350 N is less than the maximum static friction force (392 N). Therefore, the crate does not have enough force to overcome the static friction and does not move.

The acceleration and velocity options are not true because the crate is at rest and does not experience any acceleration or velocity.