Final answer:
The coefficient of friction that will prevent a 33.0 kg mass attached to a compressed spring from moving is approximately 0.099. The force exerted by the spring is calculated using Hooke's law and compared to the force of friction determined by the product of the coefficient of static friction and the normal force.
Step-by-step explanation:
The question asks for the coefficient of friction that will prevent a mass attached to a compressed spring from moving. First, we need to determine the force exerted by the spring when it is compressed.
This force is given by Hooke's law, which states F = k * x, where F is the force, k is the spring constant, and x is the compression distance. In our case, k = 10.0 N/m and x = 3.20 m, so the force exerted by the spring is F = 10.0 N/m * 3.20 m = 32.0 N.
The force of friction f, which equals the maximum force before the mass moves, is given by f = μ * N, where μ is the coefficient of static friction and N is the normal force. On a horizontal surface, the normal force is the weight of the object, N = m * g, where m is the mass and g is the acceleration due to gravity.
For a mass of 33.0 kg, and using g = 9.8 m/s², we get N = 33.0 kg * 9.8 m/s²
= 323.4 N.
To prevent the mass from moving, the force of friction must be at least equal to the force exerted by the spring, so we have f = F.
Therefore, μ * N = F, and solving for μ gives us μ = F / N
= 32.0 N / 323.4 N
≈ 0.099.