A skier stands on a 5 degree slope . if the coefficient of static friction is 0.1, does the skier start to slide?
is forcegravity down the slope > friction force?
forcegravity=mgSinTheta
forcefriction=mu*mg*cosTheta
I don't have mass though so what am I supposed to do now?
To determine whether the skier starts to slide, we need to compare the force of gravity pulling the skier down the slope to the maximum force of static friction between the skier's skis and the slope.
The force of gravity acting on the skier can be calculated by multiplying the skier's mass (m) by the acceleration due to gravity (g), which is approximately 9.8 meters per second squared (m/s^2).
The force of gravity (Fg) = m * g
Next, we need to calculate the maximum force of static friction (Fs) using the coefficient of static friction (μs) and the perpendicular force (Fn) acting on the skier. The perpendicular force is the component of the force of gravity that is parallel to the slope.
Fn = m * g * cos(θ)
where θ is the angle of the slope, which is 5 degrees in this case.
The maximum force of static friction (Fs) = μs * Fn
If the force of gravity (Fg) is greater than the maximum force of static friction (Fs), then the skier will start to slide.
Now, let's calculate it step by step:
1. Calculate the perpendicular force (Fn):
Fn = m * g * cos(θ)
= m * 9.8 * cos(5°)
2. Calculate the maximum force of static friction (Fs):
Fs = μs * Fn
= 0.1 * (m * 9.8 * cos(5°))
3. Compare the force of gravity (Fg) and the maximum force of static friction (Fs):
If Fg > Fs, the skier starts to slide. Otherwise, the skier remains stationary.
Remember, the mass of the skier (m) is required to make the calculations.