AP Physics 1 Exam Question on Tension and Normal Forces

Question: A block of mass 5 kg is attached to a string that passes over a pulley, as shown in the figure below. The block is initially at rest. Find the tension in the string and the normal force exerted on the block by the surface.

Given data:

• Mass of the block, m = 5 kg
• Acceleration due to gravity, g = 9.8 m/s^2
• The angle between the string and the horizontal, θ = 30 degrees

Assume there is no friction between the block and the surface.

Answer: To find the tension in the string and the normal force exerted by the surface, we need to analyze the forces acting on the block.

Step 1: Draw a free-body diagram of the block. We'll consider the forces acting on the block:

• Tension in the string, T (upwards)
• Weight of the block, mg (downwards)
• Normal force, N (perpendicular to the surface)

Step 2: Break down the weight of the block into its components. The weight can be separated into two components:

• mg * sin(θ) = m * g * sin(θ) component acting parallel to the surface
• mg * cos(θ) = m * g * cos(θ) component acting perpendicular to the surface

Step 3: Apply Newton's second law of motion in the vertical direction (parallel to the surface): ΣFy = may

In this case, since the block is at rest, the acceleration in the vertical direction is zero, so ΣFy = 0. By using trigonometric identities: N - m * g * cos(θ) = 0

Solving for N: N = m * g * cos(θ)

Step 4: Apply Newton's second law of motion in the horizontal direction: ΣFx = max

In this case, the acceleration of the block will be caused by the tension in the string T towards the right side. Therefore: T - m * g * sin(θ) = m * a

Since the block is initially at rest, a = 0. Solving for T: T = m * g * sin(θ)

Step 5: Substitute the given values into the equations to calculate the tension in the string and the normal force: N = (5 kg) * (9.8 m/s^2) * cos(30°) N = 42.45 N

T = (5 kg) * (9.8 m/s^2) * sin(30°) T = 24.5 N

Therefore, the tension in the string is 24.5 N, and the normal force exerted by the surface is 42.45 N.

Note: Remember to consider the direction of forces in terms of positive and negative. In this case, the upward direction is considered positive, and the downward direction is considered negative.