AP Physics 1 Exam Question

A 10 kg box is resting on a horizontal surface. The coefficient of static friction between the box and the surface is 0.6. A force of 50 N is applied horizontally to the box, causing it to accelerate.

a) Calculate the tension in the cable attached to the box. b) Determine the normal force acting on the box.

Answer

a) To calculate the tension in the cable attached to the box, we first need to determine the net force acting on the box.

The net force can be calculated using Newton's second law:

Net force = mass × acceleration

Given: Mass of the box (m) = 10 kg Force applied to the box (F) = 50 N

Since the box is accelerating, the net force is not equal to the applied force but includes the frictional force too.

Net force = Force applied - Frictional force

We can calculate the frictional force using the formula:

Frictional force = coefficient of static friction × normal force

Given: Coefficient of static friction (μ) = 0.6

Since the box is resting on a horizontal surface, the normal force is equal to the weight of the box, which can be calculated using:

Weight = mass × acceleration due to gravity

Acceleration due to gravity (g) = 9.8 m/s^2

Weight = 10 kg × 9.8 m/s^2

Now, we can calculate the frictional force:

Frictional force = 0.6 × (10 kg × 9.8 m/s^2)

Finally, we can calculate the net force:

Net force = 50 N - Frictional force

Now, we can use Newton's second law to find the tension in the cable:

Net force = mass × acceleration

Solving for acceleration:

acceleration = Net force / mass

Tension = mass × acceleration = 10 kg × (Net force / mass)

Therefore, the tension in the cable attached to the box is equal to the net force acting on it.

b) The normal force acting on the box is the force exerted by the surface to support the weight of the box.

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

Normal force = weight = 10 kg × 9.8 m/s^2

Explanation

In part (a), we first calculate the frictional force acting on the box using the given coefficient of static friction and the weight of the box. Then, we subtract the frictional force from the applied force to find the net force acting on the box. Finally, using Newton's second law, we find the tension in the cable by dividing the net force by the mass of the box.

In part (b), we determine the normal force acting on the box by using the weight of the box (equal to its mass multiplied by acceleration due to gravity), as the normal force is the force exerted by the surface to support the weight of the box.