To measure the static friction coefficient between a 1.7-kg block and a vertical wall, the setup shown in the drawing is used. A spring (spring constant = 416 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. The spring in such a setup is compressed by 0.054 m. What is the coefficient of static friction?
normal force on wall = k x
= 416 * .054 = 22.5 N
max friction force then is
22.5 mu up
gravity force down = m g = 1.7 (9.81)
= 16.7 N
so
22.5 mu = 16.7
mu = .74
To find the coefficient of static friction between the block and the vertical wall, we can use the concept of equilibrium. When the block does not slip downward, the vertical forces acting on the block must be balanced. The downward force is the weight of the block, given by the mass (m) multiplied by the acceleration due to gravity (g).
First, let's find the weight of the block:
Weight = m * g
Given that the mass of the block is 1.7 kg, and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight:
Weight = 1.7 kg * 9.8 m/s² = 16.66 N (approximately)
Next, let's analyze the forces acting on the block in the horizontal direction. The force due to the spring (Fs) is proportional to the amount the spring is compressed (Δx). The spring force can be calculated using Hooke's Law:
Fs = k * Δx
Where k is the spring constant and Δx is the displacement of the spring. In this case, the spring constant is given as 416 N/m, and the displacement of the spring is 0.054 m:
Fs = 416 N/m * 0.054 m = 22.464 N
The force of static friction (Fs_max) acting on the block is equal and opposite to the force applied by the spring (Fs), to maintain equilibrium. Therefore, Fs_max = Fs = 22.464 N.
Finally, the maximum force of static friction (Fs_max) is equal to the coefficient of static friction (μs) multiplied by the normal force (Fn). In this case, the normal force is equal to the weight (Fn = Weight):
Fs_max = μs * Fn
Plugging in the values, we have:
22.464 N = μs * 16.66 N
Solving for μs:
μs = 22.464 N / 16.66 N ≈ 1.35
Therefore, the coefficient of static friction between the block and the vertical wall is approximately 1.35.