To measure the static friction coefficient between a 1.9 kg block and a vertical wall. A spring (spring constant = 458 N/m) is attached to the block. Someone pushes on the end of the spring in a direction perpendicular to the wall until the block does not slip downward. If the spring in such a setup is compressed by 0.054 m, what is the coefficient of static friction?
mu*forcenormal=mg
mu*kx=mg
solve for mu.
86.9
To solve for the coefficient of static friction (μ), we can use the equation μ * force_normal = mg, where force_normal is the normal force exerted by the wall on the block and mg is the weight of the block.
First, let's find the force_normal:
force_normal = weight of the block
force_normal = 1.9 kg * 9.8 m/s^2 (acceleration due to gravity)
force_normal = 18.62 N
The force exerted by the compressed spring is given by Hooke's Law:
force_spring = k * x
where k is the spring constant (458 N/m) and x is the displacement of the spring (0.054 m).
Substituting the values:
force_spring = 458 N/m * 0.054 m
force_spring = 24.732 N
Since the block is not slipping, the force_spring must equal the force of static friction.
force_spring = force_friction
24.732 N = μ * force_normal
μ = 24.732 N / 18.62 N
μ ≈ 1.327
Therefore, the coefficient of static friction between the block and the wall is approximately 1.327.