A crate of mass 50.0 kg rests on a flat surface, and there is a coefficient of static friction of 0.200 between the crate and the surface. A person pushed on the crate with a force of 5.00 N at an angle of 25.0 degrees below the horizontal. Will the crate move? If it does move what acceleration will the crate have?

the frictional force (which must be overcome) is __ m * g * 0.200

To determine whether the crate will move, we need to compare the force of friction with the force applied by the person. If the force of friction is greater than the applied force, the crate will not move. If the applied force is greater than the force of friction, the crate will start to move.

Let's break down the forces acting on the crate:

1. Force applied horizontally: F_applied = 5.00 N (given in the question)
2. Angle of the applied force below the horizontal: θ = 25.0 degrees (given)
3. Force of gravity acting vertically downward: F_gravity = m * g, where m is the mass of the crate (50.0 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
4. Normal force by the flat surface: F_normal = F_gravity (since the crate is not moving vertically)
5. Force of static friction: F_friction = μ * F_normal, where μ is the coefficient of static friction (0.200)

Now, let's calculate the forces involved:

1. Resolve the applied force into horizontal and vertical components:
F_applied_horizontal = F_applied * cos(θ)
F_applied_vertical = F_applied * sin(θ)

2. Calculate the force of static friction:
F_friction = μ * F_normal = μ * F_gravity

3. Compare the horizontal components of the applied force and the force of friction:
If F_applied_horizontal > F_friction, the crate will start moving.
If F_applied_horizontal ≤ F_friction, the crate will not move.

To calculate the acceleration when the crate moves, we need to use Newton's second law of motion: F_net = m * a, where F_net is the net force acting on the crate, m is the mass of the crate, and a is the acceleration.

4. Calculate the net force acting in the horizontal direction (F_net_horizontal):
F_net_horizontal = F_applied_horizontal - F_friction

5. If the crate starts moving (F_applied_horizontal > F_friction):
The net force in the horizontal direction equals the force of kinetic friction: F_net_horizontal = F_friction_kinetic
Therefore, F_friction_kinetic = m * a

Now we have all the necessary information to solve the problem. Let's substitute the given values and calculate the results.