A warehouse employee used a cable to pull a 125 kg crate across the floor. the angle between the cable and the floor was 25°. The magnitude of the pulling force was 185 N. The coefficient of kinetic friction between the crate and the floor was 0.27.

A)What was the weight of the crate?

B)What was the magnitude of the normal force of the floor on the crate?

C)What was the magnitude of the friction force between the floor and the crate?

D)What was the x-component of the applied force?

E)What is the magnitude of Fx-Ff?

F)What is the acceleration of the crate?

A) To find the weight of the crate, we'll use the formula:

Weight = mass * acceleration due to gravity

Given that the mass of the crate is 125 kg, we can calculate the weight:

Weight = 125 kg * 9.8 m/s^2

B) The normal force, denoted by N, is the force exerted perpendicular to the surface of an object resting on a surface. In this case, the normal force is equal to the weight of the crate since it's not accelerating vertically.

So, the magnitude of the normal force is the weight of the crate, which we calculated in part A.

C) The frictional force can be determined using the formula:

Frictional force = coefficient of friction * normal force

Given that the coefficient of kinetic friction is 0.27, and we found the magnitude of the normal force in part B, we can calculate:

Frictional force = 0.27 * (weight of the crate)

D) The x-component of the applied force can be found using the formula:

Applied force (x-component) = Magnitude of the pulling force * cos(angle)

Given that the magnitude of the pulling force is 185 N, and the angle between the cable and the floor is 25°, we can calculate:

Applied force (x-component) = 185 N * cos(25°)

E) The magnitude of Fx - Ff can be calculated by subtracting the magnitude of the friction force from the x-component of the applied force.

Magnitude of Fx - Ff = Applied force (x-component) - Frictional force

F) The acceleration of the crate can be found using Newton's second law of motion:

Force = mass * acceleration

In this case, the net force acting on the crate is (Applied force (x-component) - Frictional force). So, we can rearrange the formula as:

(Applied force (x-component) - Frictional force) = mass * acceleration

Given the mass of the crate is 125 kg, and we know the net force acting on the crate from part E, we can solve for the acceleration.

To answer these questions, we need to first understand the forces acting on the crate.

A) The weight of the crate can be calculated using the formula: Weight = mass × gravitational acceleration. In this case, the mass is given as 125 kg. The gravitational acceleration is approximately 9.8 m/s².

B) The normal force of the floor on the crate is equal in magnitude but opposite in direction to the weight of the crate. So, the normal force will also be 125 kg × 9.8 m/s².

C) The magnitude of the friction force between the floor and the crate can be calculated using the formula: Friction force = coefficient of friction × normal force. Here, the coefficient of kinetic friction is given as 0.27, and the normal force can be determined from part B.

D) The x-component of the applied force is given as 185 N. Keep in mind that this force is not the same as the magnitude of the pulling force. The pulling force can be resolved into horizontal and vertical components, and its horizontal component is the x-component we are looking for.

E) To calculate the magnitude of Fx - Ff, we need to subtract the magnitude of the friction force (as calculated in part C) from the x-component of the applied force (as calculated in part D).

F) The acceleration of the crate can be determined by dividing the net force acting on it by its mass. The net force is the difference between the x-component of the applied force and the friction force (calculated in part E). The mass of the crate is given as 125 kg.

By following these steps and using the given values, you can calculate the answers to the questions.