Answer:
μ = .4842
Explanation:
Assuming constant acceleration and the object is sliding on a level surface:
Let's start off by finding the acceleration of the object.
- v₀ = 19 m/s
- v = 0 m/s
- Δx = 38 m
- a = ?
v² = v₀² + 2aΔx
- 0² = 19² + 2a(38)
- 0 = 361 + 76a
- -361 = 76a
- a = -4.75 m/s²
Now, we can make a free-body diagram and see that the only force opposing the object's motion is the friction force -- this is the only force in the x-direction.
We can use Newton's 2nd Law: F = ma to solve for the coefficient of friction.
F = ma
- F = friction force = μ * N = μ * mg
Now, we have:
The mass cancels out and solving for the coefficient of friction gives us:
We know the acceleration is -4.75 m/s² and g = -9.81 m/s²:
- μ = -4.75/-9.81
- μ = .4842
The coefficient of kinetic friction between the surfaces, assuming constant acceleration and a flat surface, is 0.4842.
