An 100kg box is placed on the ramp. As one end on the ramp is raised the box begin to move down ward just as the angle of inclination reaches 15 degree . What the coeffenict of static friction between box and ramp .. ?

Question

An 100kg box is placed on the ramp. As one end on the ramp is raised the box begin to move down ward just as the angle of inclination reaches 15 degree . What the coeffenict of static friction between box and ramp .. ?

Answer 1

ma=mgsinα-F(fr)=mgsinα-μN=

=mgsinα-μmgcosα

μ(stat.fr) => a=0

0= mgsinα-μmgcosα
μ=tanα

Answer 2

To determine the coefficient of static friction between the box and the ramp, we need to analyze the forces acting on the box.

When the box is at the point of just beginning to move (the point of impending motion), the force of static friction between the box and the ramp must be equal to the force component acting downwards along the ramp. This force component can be calculated using trigonometry.

First, we need to determine the angle of inclination in radians.

Angle of inclination (θ) = 15 degrees * (π/180) ≈ 0.2618 radians

Next, we need to calculate the force component acting downwards along the ramp, considering the weight of the box.

Force component along the ramp (F) = mass (m) * gravitational acceleration (g) * sin(θ)

Here, the mass of the box (m) is given as 100 kg, and the gravitational acceleration (g) is approximately 9.8 m/s².

F = 100 kg * 9.8 m/s² * sin(0.2618) ≈ 41.41 N

Now that we know the force component along the ramp, we can determine the force of static friction (F_friction).

F_friction = F

Since the box is at the point of just beginning to move, the force of static friction is at its maximum value. The maximum force of static friction (F_friction_max) can be calculated using the equation:

F_friction_max = coefficient of static friction (μ_static) * normal force (F_normal)

The normal force (F_normal) is equal to the weight of the box, which is given by:

F_normal = mass (m) * gravitational acceleration (g)

F_normal = 100 kg * 9.8 m/s² = 980 N

Thus,

F_friction_max = μ_static * 980 N

Since the box is at the point of just beginning to move, the force of static friction is maximum, which equals the force component along the ramp (F).

F_friction_max = F

Therefore, we can equate the maximum force of static friction and the force component along the ramp:

μ_static * 980 N = 41.41 N

Solving for the coefficient of static friction (μ_static):

μ_static = 41.41 N / 980 N ≈ 0.0422

Therefore, the coefficient of static friction between the box and the ramp is approximately 0.0422.