A rope is used to pull a 5.19 kg block at constant speed 3.38 m along a horizontal floor. The force on the block from the rope is 3.23 N and directed 20.0° above the horizontal. What are (a) the work done by the rope's force, (b) the increase in thermal energy of the block-floor system, and (c) the coefficient of kinetic friction between the block and floor?

weight = m g = 5.19 (9.81)

normal force = 5.19(9.81) - 3.23 sin 20

pull force = 3.23 cos 20

work done per second = power = 3.23 cos 20 (3.38) Watts. Without time can not get energy.

power wasted to heat = all of it above

3.23 cos 20 = mu (normal force above)

To find the answers to these questions, we can use the following formulas:

(a) The work done by a force is given by the formula: Work = Force * Distance * cos(theta), where theta is the angle between the force and the displacement.

(b) The increase in thermal energy is equal to the work done against friction, which can be calculated using: Work against friction = Force of friction * Distance.

(c) The coefficient of kinetic friction can be found using: Force of friction = coefficient of kinetic friction * Normal force, where the normal force is equal to the weight of the block.

Let's calculate the answers step by step:

(a) First, we need to find the distance traveled by the block. The force applied by the rope is in the horizontal direction, so it does not contribute to the vertical displacement. Therefore, we only need to consider the horizontal component of the force.

Horizontal Force = Force * cos(theta)
= 3.23 N * cos(20.0°)
= 3.23 N * 0.9397
= 3.04 N (approximately to two decimal places)

We know that Work = Force * Distance * cos(theta). Since the object is moving at a constant speed, the work done by the rope's force is equal in magnitude but opposite in direction to the work done against friction. Therefore, the work done by the rope's force is zero.

(b) The increase in thermal energy of the block-floor system is equal to the work done against friction. To find the work against friction, we need to calculate the force of friction first.

We can use the formula: Force of friction = coefficient of kinetic friction * Normal force.

The normal force is equal to the weight of the block, which can be calculated as: Normal force = mass * gravitational acceleration.

Normal force = 5.19 kg * 9.8 m/s^2
= 50.842 N (approximately to three decimal places)

Now, we can calculate the force of friction. Since the block is moving at a constant speed, the force of friction is equal in magnitude but opposite in direction to the horizontal force applied by the rope.

Force of friction = 3.04 N (approximately to two decimal places)

Finally, we can calculate the work done against friction using the formula: Work against friction = Force of friction * Distance.

(c) The coefficient of kinetic friction can be found using the formula: Force of friction = coefficient of kinetic friction * Normal force.

Substituting the known values, we have: 3.04 N = coefficient of kinetic friction * 50.842 N.

Simplifying, we find: coefficient of kinetic friction = 3.04 N / 50.842 N.

Calculating this division, we find the coefficient of kinetic friction to be approximately 0.06 (to two decimal places).

To summarize:
(a) The work done by the rope's force is zero.
(b) The increase in thermal energy of the block-floor system is equal to the work done against friction.
(c) The coefficient of kinetic friction between the block and floor is approximately 0.06.