An 80.0 kg box is at rest on a table with a coefficient of static friction of 0.400 and a coefficient of kinetic friction of 0.200. A 20.0 kg mass is connected to the 80.0 kg mass with a rope. The system is released from rest, and the pulley is frictionless and massless.

5. What is the acceleration of the system? If the system does not accelerate, answer zero.
a) 0 m/s$^2$
b) 0.392 m/s$^2$
c) 0.490 m/s$^2$
d) 1.47 m/s$^2$
e) 1.96 m/s$^2$
f) 1.18 m/s$^2$
g) 5.88 m/s$^2$
h) 9.80 m/s$^2$

6. What is the tension in the rope?
a) 0 N
b) 196 N
c) 157 N
d) 313.6 N
e) 235 N
f) 588 N
g) 794 N
h) 980 N

7. What is the frictional force between the 80.0 kg box and the top of the table?
a) 0 N
b) 196 N
c) 157 N
d) 313.6 N
e) 235 N
f) 588 N
g) 794 N
h) 980 N

8. What is the maximum mass that can be hung over the edge of the table if the system is to remain at rest?
a) 4.00 kg
b) 8.00 kg
c) 12.0 kg
d) 16.0 kg
e) 20.0 kg
f) 24.0 kg
g) 28.0 kg
h) 32.0 kg

the net force can be obtained by subtracting the force of kinetic friction from the tension in the rope. Given the masses and the coefficients of friction, the acceleration is found to be 1.18 m/s² (option f).

5. The acceleration of the system can be determined by analyzing the forces acting on the masses. The tension in the rope exerts a force on both masses.

The frictional force between the 80.0 kg box and the table opposes the motion.

As the system is released from rest, the static friction force needs to be overcome before the box starts moving.

The force of static friction is given by the product of the coefficient of static friction and the normal force, which is the weight of the box.

Once the box starts moving, the force of kinetic friction comes into play. It is given by the product of the coefficient of kinetic friction and the normal force.

To calculate the acceleration, we use Newton's second law:

acceleration equals the net force divided by the total mass of the system. As the masses are connected by a rope, they have the same acceleration.

Therefore, the net force can be obtained by subtracting the force of kinetic friction from the tension in the rope.

Given the masses and the coefficients of friction, the acceleration is found to be 1.18 m/s² (option f).

6. The tension in the rope can be determined by analyzing the forces acting on the 20.0 kg mass. The tension is the force transmitted through the rope from the 80.0 kg mass to the 20.0 kg mass.

This force is equal in magnitude but opposite in direction to the force exerted by the 20.0 kg mass on the rope.

Since the masses are connected and have the same acceleration, the tension can be calculated using Newton's second law for the 20.0 kg mass.

The net force acting on it is the tension minus the force of kinetic friction. By substituting the values given in the question, we find that the tension in the rope is 196 N (option b).

7. The frictional force between the 80.0 kg box and the top of the table can be determined using the coefficient of static friction and the normal force.

The normal force is equal to the weight of the box.

The force of static friction opposes the motion and needs to be overcome for the box to start moving.

Once the box is in motion, the force of kinetic friction comes into play. It is given by the product of the coefficient of kinetic friction and the normal force.

In this case, since the box is not accelerating, the frictional force is equal in magnitude to the force of static friction.

Substituting the values given in the question, we find that the frictional force is 313.6 N (option d).

8. The maximum mass that can be hung over the edge of the table without causing the system to accelerate can be determined by analyzing the forces acting on the system.

The system will remain at rest if the tension in the rope is equal to the force of static friction.

We can calculate the maximum tension using the given coefficient of static friction and the weight of the 80.0 kg box.

Once we have the maximum tension, we can determine the maximum mass that can be hung by dividing the tension by the acceleration due to gravity. Substituting the values, we find that the maximum mass is 16.0 kg (option d).

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