AP Physics 1 Exam Question:
A block of mass 2 kg is placed on a smooth inclined plane with an angle of inclination of 30 degrees. The block is initially at rest. After 2 seconds, it reaches a speed of 5 m/s. Assume there is no friction between the block and the inclined plane.
a) Calculate the net force acting on the block.
b) Determine the coefficient of kinetic friction between the block and the inclined plane.
a) To calculate the net force acting on the block, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
Given: Mass of the block, m = 2 kg Initial velocity, u = 0 m/s Final velocity, v = 5 m/s Time, t = 2 seconds
Using the kinematic equation: v = u + at
We can rearrange it to solve for acceleration (a): a = (v - u) / t
Substituting the given values: a = (5 m/s - 0 m/s) / 2 s = 5 m/s / 2 s = 2.5 m/s²
Net force can be calculated using Newton's second law: F_net = m * a
Substituting the known values: F_net = 2 kg * 2.5 m/s² = 5 N
Therefore, the net force acting on the block is 5 Newtons.
b) Since there is no friction between the block and the inclined plane, the net force is due to the gravitational force acting on the block. We can determine the coefficient of kinetic friction (µ) between the block and the inclined plane using the formula:
F_friction = µ * normal force
Since there is no vertical motion, the normal force (N) is equal to the weight of the block.
Weight (W) = mass * acceleration due to gravity (g) = m * g = 2 kg * 9.8 m/s² = 19.6 N
Substituting the known values of normal force and net force: F_friction = µ * 19.6 N 5 N = µ * 19.6 N
Solving for µ: µ = 5 N / 19.6 N = 0.255
Therefore, the coefficient of kinetic friction between the block and the inclined plane is approximately 0.255.