A body of weight 500N is liying on a rough plane inclined at angle 25 with the horizontal, it ir supported.by an effort P, parallel to the plane.determine the minimum and maximum value of P, for the equilibriun can exist if the angle of friction is 20
24
Find full solutions
Dimpol Barua
Answe
To determine the minimum and maximum value of effort P for equilibrium, we need to consider two cases: the body on the verge of sliding up the plane and the body on the verge of sliding down the plane. Let's start with the first case.
1. Body on the verge of sliding up the plane:
Here, the resistive force acting against the motion is the force due to friction. The maximum frictional force can be calculated using the formula: F_friction = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force acting on the body.
Given that the angle of friction is 20 degrees, we can determine μ_s using the formula: μ_s = tan(θ), where θ is the angle of friction. Therefore, μ_s = tan(20) ≈ 0.364.
The normal force N is the component of the weight acting perpendicular to the plane, which can be calculated as: N = mg * cos(θ), where m is the mass of the body and g is the acceleration due to gravity.
Since weight W = mg, and W = 500 N, we can find m = W/g = 500 N/9.8 m/s^2 ≈ 51.02 kg.
Therefore, N = 51.02 kg * 9.8 m/s^2 * cos(25) ≈ 459.82 N.
Now, we can calculate the maximum frictional force (F_friction) as: F_friction = μ_s * N = 0.364 * 459.82 N ≈ 167.32 N.
For equilibrium, the effort P must be equal to or greater than the maximum frictional force: P ≥ 167.32 N.
2. Body on the verge of sliding down the plane:
In this case, the resistive force acting against the motion is the component of weight acting parallel to the plane, which can be calculated as: F_parallel = mg * sin(θ).
Using the given values, F_parallel = 51.02 kg * 9.8 m/s^2 * sin(25) ≈ 213.62 N.
For equilibrium, the effort P must be equal to or less than the component of weight: P ≤ 213.62 N.
Therefore, the minimum value of P is 0 N, and the maximum value of P is 213.62 N in order for equilibrium to exist.