A 17.9 kg block is dragged over a rough, horizontal

surface by a constant force of 119 N
acting at an angle of 30◦
above the horizontal.
The block is displaced 40.7 m, and the
coefficient of kinetic friction is 0.111.
what is the final speed

see other post.

To find the final speed of the block, we need to consider the work done by the force of friction and the work done by the applied force.

1. Calculate the work done by the force of friction:
Friction force = coefficient of kinetic friction * normal force
The normal force is equal to the weight of the block, which is given by: weight = mass * acceleration due to gravity.

mass = 17.9 kg
acceleration due to gravity = 9.8 m/s^2

Therefore, weight = 17.9 kg * 9.8 m/s^2

Next, calculate the normal force using the weight.

Now, calculate the work done by the friction force using the formula:
Work = force * displacement * cos(theta)
In this case, the displacement is the same as the displacement of the block, which is given as 40.7 m. theta refers to the angle between the force and the displacement, which is 180 degrees, as the force and displacement are in opposite directions.

work_friction = friction force * 40.7 m * cos(180 degrees)

2. Calculate the work done by the applied force:
The work done by the applied force is given by the formula:
Work = force * displacement * cos(theta)
In this case, the force is given as 119 N, the displacement is 40.7 m, and the angle theta is 30 degrees.

work_applied = 119 N * 40.7 m * cos(30 degrees)

3. Calculate the net work done:
The net work done is the sum of the work done by the friction force and the work done by the applied force.

net work = work_applied - work_friction

4. Use the work-energy theorem to find the final speed:
The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. Therefore, we can equate the net work done to the change in kinetic energy to find the final speed.

net work = change in kinetic energy
change in kinetic energy = (1/2) * mass * (final speed)^2 - (1/2) * mass * (initial speed)^2

Since the block starts from rest, the initial speed is 0.

So, we can write the equation as:
net work = (1/2) * mass * (final speed)^2

Rearranging the equation, we get:
(final speed)^2 = (2 * net work) / mass

Finally, calculate the final speed by taking the square root of both sides of the equation.

final speed = sqrt((2 * net work) / mass)

Plug in the calculated values and solve for the final speed.