To determine the coefficient of friction in this scenario, we can analyze the forces acting on the body as it slides down the inclined plane.
Let's assume that the body is on a rough surface, and there are two forces acting on it: the gravitational force (mg) pulling it downwards and the force of friction (f_friction) opposing the motion.
The gravitational force can be broken down into two components: one parallel to the inclined plane (mg sin θ) and the other perpendicular to the inclined plane (mg cos θ), where θ is the angle of the incline (45° in this case).
The force of friction opposes the motion and acts parallel to the inclined plane. It can be calculated using the equation:
f_friction = μ_s * N,
where μ_s is the coefficient of static friction and N is the normal force exerted by the plane on the body.
Since the body is on the verge of sliding, the force of friction is at its maximum value, which is equal to the product of the coefficient of static friction and the normal force.
The normal force (N) can be calculated as the component of the gravitational force perpendicular to the inclined plane, which is:
N = mg cos θ.
Substituting this value into the equation for the force of friction, we get:
f_friction = μ_s * mg cos θ.
Since the body is about to slide down the plane, the force of friction is equal to the component of the gravitational force parallel to the inclined plane. Therefore, we have:
f_friction = mg sin θ.
Setting these two equations equal to each other, we can solve for the coefficient of static friction (μ_s):
μ_s * mg cos θ = mg sin θ.
Canceling out the common factor of mg, we obtain:
μ_s cos θ = sin θ.
Finally, dividing both sides by cos θ, we find:
μ_s = tan θ.
Since the angle of the incline is given as 45°, we have:
μ_s = tan 45° = 1.
Therefore, the coefficient of friction (μ_s) in this scenario is 1.