A box weighing 65.0 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end.

Part a) Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs 24.0 N .

Part b) Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs 43.0 N .

part c)Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs 82.0 N .

To find the force that the table exerts on the box, we need to consider the forces acting on the box.

First, let's define the positive direction as upward. In this case, the weight of the box is acting downward, so it will be negative.

Part a) When the weight hanging on the other side of the pulley weighs 24.0 N:

1. Draw a free-body diagram for the box:
- The weight of the box is acting downward, so it is -65.0 N.
- The force from the table is acting upward, so let's call it T.

______________
|___ T ____|
| ^ |

2. Use Newton's second law (F_net = ma) to find the net force on the box:
Since the box is not accelerating and is in equilibrium, the net force is zero:
0 = T - 65.0 N

3. Solve the equation for T:
T = 65.0 N

Therefore, the force that the table exerts on the box is 65.0 N.

Part b) When the weight hanging on the other side of the pulley weighs 43.0 N:

1. Draw a free-body diagram for the box:
- The weight of the box is acting downward, so it is -65.0 N.
- The force from the table is acting upward, so let's call it T.

______________
|___ T ____|
| ^ |

2. Use Newton's second law (F_net = ma) to find the net force on the box:
Since the box is not accelerating and is in equilibrium, the net force is zero:
0 = T - 65.0 N

3. Solve the equation for T:
T = 65.0 N

Therefore, the force that the table exerts on the box is 65.0 N.

Part c) When the weight hanging on the other side of the pulley weighs 82.0 N:

1. Draw a free-body diagram for the box:
- The weight of the box is acting downward, so it is -65.0 N.
- The force from the table is acting upward, so let's call it T.

______________
|___ T ____|
| ^ |

2. Use Newton's second law (F_net = ma) to find the net force on the box:
Since the box is not accelerating and is in equilibrium, the net force is zero:
0 = T - 65.0 N

3. Solve the equation for T:
T = 65.0 N

Therefore, the force that the table exerts on the box is 65.0 N.