A 1200 N force is exerted on a 700 kg crate to move it across a loading dock. If the coefficient of friction is .50 what is the crates acceleration?

To determine the crate's acceleration, we need to consider the forces acting on it and apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

First, let's identify the forces acting on the crate:
1. The applied force of 1200 N, which is exerted to move the crate.
2. The force of friction opposing the motion, which depends on the coefficient of friction and the normal force.
3. The weight of the crate, which is the force due to gravity and is equal to the mass of the crate multiplied by the acceleration due to gravity (9.8 m/s²).

Now, let's calculate the net force:
1. The force of friction is found by multiplying the coefficient of friction (0.50) by the normal force. The normal force is equal to the weight of the crate, which is the mass of the crate multiplied by the acceleration due to gravity: F_friction = coefficient of friction * (mass of the crate * acceleration due to gravity).
2. The net force is the difference between the applied force and the force of friction: Net force = Applied force - Force of friction.

Finally, we can determine the crate's acceleration:
Using Newton's second law of motion, we can rearrange the formula to solve for acceleration: Net force = mass * acceleration. Rearranging the equation, we have: Acceleration = Net force / mass.

By plugging in the values and solving the equation, we can determine the crate's acceleration.