A rope is used to pull a 2.54 kg block at constant speed 4.48 m along a horizontal floor. The force on the block from the rope is 5.87 N and directed 29.8° 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?

Wb = mg = 2.54kg * 9.8N/kg = 24.89N. =

Weight of block.

Fb = 4.89N @ 0deg.
Fp = 24.89sin(0) = 0 = Force parallel to floor.
Fv = 24.89cos(0) = 24.89N. = Force perpendicular to floor.

a. W = Fap*cos29.8 * d,
W = 5.87cos29.8 * 4.48 = 5.1J.

c. Fn = Fap*cos29.8 - Fp - Ff = 0,
5.87cos29.6 - 0 - Ff = 0,
Ff = 5.87cos29.8 = 5.09N. = Force of friction.

u = Ff / Fv = 5.09 / 24.89 = 0.205.

Correction:

u = Ff / (Fv-Fap*sin29.8),
u = 5.09 / (24.89-5.87sin29.8) = 0.23.

To find the answers to these questions, we'll need to use some key principles in physics. Let's break it down:

(a) The work done by the rope's force:
The work done by a force can be calculated using the formula:
Work = Force * Distance * cos(theta)

In this case, the force on the block from the rope is given as 5.87 N and directed 29.8° above the horizontal. The distance the block is pulled is given as 4.48 m.

Using the formula, we can calculate the work done as follows:
Work = 5.87 N * 4.48 m * cos(29.8°)

(b) The increase in thermal energy of the block-floor system:
Since the block is being pulled at a constant speed, the net work done on it is zero. Therefore, the work done by the rope's force must be equal to the increase in thermal energy of the block-floor system.

(c) The coefficient of kinetic friction between the block and floor:
To find the coefficient of kinetic friction, we need to determine the normal force acting on the block. The normal force is the force perpendicular to the surface and counterbalances the weight of the block.

The weight of the block can be calculated using the formula:
Weight = mass * acceleration due to gravity

In this case, the mass of the block is given as 2.54 kg and the acceleration due to gravity is approximately 9.8 m/s^2. So, the weight of the block is:
Weight = 2.54 kg * 9.8 m/s^2

The normal force is equal to the weight of the block if the block is on a horizontal surface. Then, the force of friction can be calculated as:
Force of friction = coefficient of kinetic friction * normal force

Since the block is moving at a constant speed, the force of friction is equal in magnitude and opposite in direction to the force applied by the rope.

Using these principles and calculations, we can find the answers to the given questions.