A 31 kg box slides down a 33.0� ramp with an acceleration of 1.30 m/s2.
The acceleration of gravity is 9.81 m/s2 .
Find the coefficient of kinetic friction between the box and the ramp.
To find the coefficient of kinetic friction between the box and the ramp, we can follow these steps:
Step 1: Calculate the net force acting on the box.
The net force can be calculated using Newton's second law, which states that the net force (F_net) is equal to the mass of the object (m) multiplied by the acceleration (a).
F_net = m * a
Given:
Mass of the box (m) = 31 kg
Acceleration (a) = 1.30 m/s^2
Substituting the given values:
F_net = 31 kg * 1.30 m/s^2
F_net = 40.30 N
Step 2: Calculate the gravitational force acting on the box.
The gravitational force (F_gravity) can be calculated using the formula:
F_gravity = m * g
where g is the acceleration due to gravity.
Given:
Acceleration due to gravity (g) = 9.81 m/s^2
Substituting the given values:
F_gravity = 31 kg * 9.81 m/s^2
F_gravity = 303.11 N
Step 3: Calculate the frictional force acting on the box.
The frictional force (F_friction) can be calculated using the formula:
F_friction = μ * F_normal
where μ is the coefficient of kinetic friction, and F_normal is the normal force.
Since the box is on a ramp, the normal force is given by:
F_normal = m * g * cosθ
where θ is the angle of the ramp.
Given:
θ = 33.0 degrees
Substituting the given values:
F_normal = 31 kg * 9.81 m/s^2 * cos(33.0 degrees)
F_normal = 243.73 N
Step 4: Substitute the values into the frictional force equation and solve for μ.
F_friction = μ * F_normal
Substituting the known values:
40.30 N = μ * 243.73 N
Solving for μ:
μ = 40.30 N / 243.73 N
μ = 0.1657
Therefore, the coefficient of kinetic friction between the box and the ramp is approximately 0.1657.