A 13.0 kg box is released on a 33 degree incline and accelerates down the incline at o.20 m/s^2.
A. Find the friction force impeding it's motion
B. What is the coefficient of kinetic friction
F(fr) = μ •N= μ•m• g• cos α
PE = W(fr) +KE,
m•g•h= μ•m• g• s cos α• +m•v²/2,
g•h= μ•g•s•cos α• + v²/2.
You need “h”
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To find the answers to these questions, we need to use Newton's second law of motion and some trigonometry.
A. To find the friction force impeding the box's motion, we can start by calculating the force due to gravity acting on the box. The force due to gravity can be found using the formula:
F_gravity = m * g,
where m is the mass of the box (13.0 kg) and g is the acceleration due to gravity (usually taken as 9.8 m/s^2).
F_gravity = 13.0 kg * 9.8 m/s^2 = 127.4 N.
Next, we need to find the component of the gravitational force that acts parallel to the incline. This can be done using trigonometry. Since the angle of the incline is given as 33 degrees, the component of the gravitational force acting down the incline will be:
F_parallel = F_gravity * sin(33°).
F_parallel = 127.4 N * sin(33°) = 67.2 N.
Finally, since the box is accelerating down the incline, the net force acting on it can be calculated using Newton's second law:
Net force = m * a.
The net force is equal to the force due to gravity acting down the incline (F_parallel) minus the friction force (F_friction):
Net force = F_parallel - F_friction.
Given that the acceleration of the box is 0.20 m/s^2, we can rearrange the equation to solve for F_friction:
F_friction = F_parallel - (m * a).
F_friction = 67.2 N - (13.0 kg * 0.20 m/s^2).
F_friction = 67.2 N - 2.6 N.
F_friction = 64.6 N.
Therefore, the friction force impeding the box's motion is 64.6 N.
B. To find the coefficient of kinetic friction, we can use the equation:
F_friction = u * N,
where F_friction is the friction force (64.6 N), u is the coefficient of kinetic friction, and N is the perpendicular force acting on the box due to the incline.
The perpendicular force, N, can be found using trigonometry:
N = F_gravity * cos(33°).
N = 127.4 N * cos(33°) = 106.0 N.
Now we can calculate the coefficient of kinetic friction:
u = F_friction / N.
u = 64.6 N / 106.0 N.
u ≈ 0.610.
Therefore, the coefficient of kinetic friction is approximately 0.610.