A 23.1 kg block is dragged over a rough, horizontal surface by a constant force of 95.0 N acting at an angle of angle 29.3 ° above the horizontal. The block is displaced 5.50 m, and the coefficient of kinetic friction is 0.341. Find the magnitude of the work done by the normal force. Answer in units of J

To find the magnitude of the work done by the normal force, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

The work done by a force can be calculated using the formula:

Work = Force * Distance * cos(theta)

Where:
- Force is the magnitude of the force applied to the object
- Distance is the displacement of the object along the direction of the force
- theta is the angle between the force and the displacement vector

In this case, the force applied to the block is 95.0 N at an angle of θ = 29.3° above the horizontal, and the block is displaced a distance of 5.50 m. So, we can calculate the work done by the applied force as:

Work = 95.0 N * 5.50 m * cos(29.3°)

Next, we need to consider the work done by the friction force. The coefficient of kinetic friction is given as 0.341. The work done by the friction force can be calculated using the formula:

Work = Force of friction * Distance

The force of friction can be calculated using the formula:

Force of friction = coefficient of friction * normal force

Here, we need to find the normal force. In this case, the block is on a rough horizontal surface, and the normal force is equal to the weight (mg) of the block, where m is the mass of the block and g is the acceleration due to gravity (9.8 m/s^2).

So, the normal force is given by:

Normal force = (mass of the block) * (acceleration due to gravity)

In this case, the mass of the block is 23.1 kg, so the normal force is:

Normal force = 23.1 kg * 9.8 m/s^2

Finally, we can calculate the work done by the friction force using:

Work = (coefficient of friction) * (normal force) * Distance

Substituting the given values, we can calculate the work done by the friction force.

The magnitude of the work done by the normal force is the sum of the work done by the applied force and the work done by the friction force. So, to find the answer, we need to add the work done by the applied force:

Work done by the normal force = (work done by the applied force) + (work done by the friction force)

zero