A crate of potatoes of mass 23.0 kg is on a ramp with angle of incline 30° to the horizontal. The coefficients of friction are μs = 0.65 and μk = 0.44. Find the frictional force (magnitude and direction) on the crate if the crate is at rest.
To find the frictional force on the crate when it is at rest, we need to calculate the maximum static friction force.
The formula for the maximum static friction force is given by:
fs = μs * N
Where:
fs is the static friction force
μs is the coefficient of static friction
N is the normal force
To calculate the normal force, we need to resolve the weight of the crate into its components parallel and perpendicular to the incline. The component of weight perpendicular to the incline provides the normal force.
The formula for the normal force is given by:
N = mg * cosθ
Where:
m is the mass of the crate (23.0 kg)
g is the acceleration due to gravity (9.8 m/s²)
θ is the angle of incline (30°)
N = (23.0 kg) * (9.8 m/s²) * cos(30°)
N = 225.12 N
Now, we can calculate the maximum static frictional force:
fs = (0.65) * (225.12 N)
fs = 146.33 N
Therefore, the magnitude of the frictional force on the crate when it is at rest is 146.33 N.
The direction of the frictional force is opposite to the direction in which the crate would slide if it were not at rest, i.e., downhill along the incline.
http://www.jiskha.com/display.cgi?id=1316980083
mu is a way of typing the Greek letter "mu", the coefficent of static friction here.