An 17.2 kg box is released on a 35.7° incline and accelerates down the incline at 0.274 m/s2. Find the friction force impeding its motion.
(in N)
How large is the coefficient of friction?
To find the friction force impeding the motion of the box, we need to break down the forces acting on it.
First, we identify the gravitational force acting on the box, which can be calculated using the formula:
Force_gravity = mass * acceleration_due_to_gravity
where the mass is given as 17.2 kg and the acceleration due to gravity is approximately 9.8 m/s^2.
So, Force_gravity = 17.2 kg * 9.8 m/s^2 = 168.56 N.
Next, we need to calculate the component of the gravitational force acting down the incline, which can be found using the formula:
Force_parallel = Force_gravity * sin(angle_of_incline)
where the angle of incline is given as 35.7°.
So, Force_parallel = 168.56 N * sin(35.7°) = 96.07 N.
Now, we can calculate the friction force impeding the motion of the box. The friction force is equal in magnitude but opposite in direction to the force that tends to slide the box down the incline. So, the friction force can be calculated using the formula:
Friction_force = mass * acceleration_along_incline
where the mass is given as 17.2 kg and the acceleration along the incline is given as 0.274 m/s^2.
So, Friction_force = 17.2 kg * 0.274 m/s^2 = 4.71 N.
To find the coefficient of friction, we can use the formula:
Coefficient_of_friction = Friction_force / Force_normal
where the force normal (perpendicular to the incline) can be found using the formula:
Force_normal = Force_gravity * cos(angle_of_incline)
So, Force_normal = 168.56 N * cos(35.7°) = 137.72 N.
Now, we can substitute the values into the formula for the coefficient of friction:
Coefficient_of_friction = 4.71 N / 137.72 N = 0.034.
Therefore, the coefficient of friction is approximately 0.034.