Problem 3- Blocks A, B, and C are connected by ropes and placed as in the figure. Both A and B weigh 22.6 N each, and the coefficient of kinetic friction between each block and the surface is 0.40. Block C descends with constant velocity.

a) Draw free-body diagram of objects A, B, and C.
b) Find the tension in the rope connecting blocks A and B.
c) What is the weight of block C?
d) If the rope connecting A and B were cut, what would be the acceleration of C?

a) To draw the free-body diagrams, we need to identify the forces acting on each block.

For Block A:
- Weight (22.6 N) acting downward.
- Tension force (T) in the rope connecting A and B, acting to the right.
- Friction force (Ff) opposing the motion, acting to the left.

For Block B:
- Weight (22.6 N) acting downward.
- Tension force (T) in the rope connecting A and B, acting to the left.
- Friction force (Ff) opposing the motion, acting to the right.

For Block C:
- Weight (WC) acting downward.

b) To find the tension in the rope connecting blocks A and B, we need to consider the equilibrium condition. Since Block C is descending with constant velocity, the net force on Block C must be zero.

The tension force (T) in the rope connecting A and B is the same for both blocks. Thus, we can write the equation for the vertical forces acting on Block C:

WC = 2 × T

c) To find the weight of Block C (WC), we know that both Block A and Block B weigh 22.6 N each. Since Block C is descending with constant velocity, the net force on Block C must be zero.

Therefore, the weight of Block C (WC) is also 22.6 N.

d) If the rope connecting A and B were cut, Block C would experience a net force equal to the difference between the weights of Block C and the combined weights of Blocks A and B. This net force would cause Block C to accelerate.

To find the acceleration of Block C, we can use Newton's second law:
Net force = mass × acceleration

The net force on Block C, if the rope connecting A and B were cut, is given by:
Net force = WC - (WA + WB)

Since we know the weights of Blocks A, B, and C, we can substitute these values into the equation to find the net force. Once we have the net force, we can divide it by the mass of Block C to find the acceleration.