A block begins to slide down a ramp after being elevated to an angle of 55 degrees. What is the coefficient of static friction?

Down the plane forces:

weight: mgSinTheta
Friction up the plane:
mu*mg*CosTheta

set them equal, solve for mu.

To determine the coefficient of static friction, we need to gather more information. Specifically, we need to know if there is any displacement of the block before it starts sliding down the ramp.

The coefficient of static friction (μs) represents the maximum amount of friction force that needs to be overcome to initiate sliding. It depends on the types of surfaces in contact. Given that the block starts sliding down the ramp, we can conclude that the static friction has been overcome.

To determine the coefficient of static friction, we need to use the angle at which the block starts sliding, which is 55 degrees. We can relate this angle to the coefficient of static friction using trigonometry.

Let's assume that the block is on a frictionless ramp with an angle of 55 degrees, and the mass of the block is m. The force due to gravity acting on the block can be split into two components:

1. The component parallel to the ramp's surface (mg sin θ).
2. The component perpendicular to the ramp's surface (mg cos θ).

The maximum static friction force (fs) can be found by multiplying the perpendicular component of the weight by the coefficient of static friction:

fs = μs * (mg cos θ)

Since the block starts sliding, we know that the static friction force has reached its maximum value, fs. Therefore, we can equate fs to the parallel component of the weight:

fs = mg sin θ

Now, we can solve the equation for the coefficient of static friction (μs):

μs * (mg cos θ) = mg sin θ

μs = (mg sin θ) / (mg cos θ)

Simplifying the equation further, we can cancel out the mass (m) and get:

μs = tan θ

In this case, θ is 55 degrees. Therefore, the coefficient of static friction (μs) is the tangent of 55 degrees.

μs = tan 55°

Using a calculator, the value of tan 55° is approximately 1.428.

Thus, the coefficient of static friction (μs) is approximately 1.428.