A 15.2 kg block dragged over rough horizontal surface by constant force of 124N acting at an angle of 34.9 degrees above the horizontal. The block is displaced 37.8m. The coefficient of kinetic friction is .171. Acceleration is 9.8 m/s^2.

Find the work done by the 124N force.
Find the magnitude of the work done by the force of friction.
Find the work done by the normal force.

124

To find the work done by a force, you can use the formula:

Work = Force x Distance x Cosine(theta)

Where:
- Work is the work done by the force (measured in joules),
- Force is the magnitude of the force (measured in newtons),
- Distance is the displacement of the object (measured in meters),
- Theta is the angle between the force and displacement (measured in degrees).

1. Work done by the 124N force:
Given: Force = 124N, Distance = 37.8m, Theta = 34.9 degrees

Using the formula, we can calculate:

Work = 124N x 37.8m x Cos(34.9 degrees)
= 124N x 37.8m x 0.819 (cosine of 34.9 degrees)
≈ 3839 J

Therefore, the work done by the 124N force is approximately 3839 joules.

2. Magnitude of the work done by the force of friction:
The work done by the force of friction can be determined using the formula mentioned above, but with the force of friction instead of the applied force.

The force of friction can be calculated using the equation:

Force of friction = coefficient of friction x Normal force

Given: coefficient of friction = 0.171, Normal force = mass x acceleration (according to Newton's second law)

We are also given the mass of the block (15.2 kg) and the acceleration (9.8 m/s^2).

Normal force = 15.2 kg x 9.8 m/s^2
= 149.6 N

Force of friction = 0.171 x 149.6 N
= 25.56 N

Now, to find the work done by the force of friction:

Work = Force of friction x Distance x Cos(theta)

Given: Force of friction = 25.56 N, Distance = 37.8m, Theta = 180 degrees (opposite direction of motion)

Work = 25.56N x 37.8m x Cos(180 degrees)
= 25.56N x 37.8m x (-1) (Cosine of 180 degrees is -1)
≈ -967 J

The negative sign indicates that the work done by the force of friction is in the opposite direction of the displacement.

Therefore, the magnitude of the work done by the force of friction is approximately 967 joules.

3. Work done by the normal force:
The work done by the normal force is equal to zero since the normal force is perpendicular to the displacement and, therefore, does not contribute to the work.