A body of mass 20kg is placed on an inclined plane rising 1 in 100.lf ...
Motion of a Body on an Inclined Plane
Given information:
- Mass of the body, m = 20 kg
- Inclined plane rises 1 in 100 (which means the angle of inclination, θ, is given by tan θ = 1/100)
- Coefficient of friction, μ = 0.25
Force Required to Set the Body in Motion:
To calculate the force required to set the body in motion up the inclined plane, we need to consider the forces acting on the body. These include:
1. Weight of the body (mg): The weight of the body acts vertically downward and can be calculated by multiplying the mass of the body (m) by the acceleration due to gravity (g = 9.8 m/s^2).
2. Normal force (N): The normal force acts perpendicular to the inclined plane and balances the weight of the body. It can be calculated as N = mgcosθ.
3. Force of friction (f): The force of friction opposes the motion of the body and acts parallel to the inclined plane. It can be calculated as f = μN, where μ is the coefficient of friction.
4. Force applied (F): This is the force required to set the body in motion up the inclined plane.
Calculating the Normal Force:
The normal force acts perpendicular to the inclined plane and balances the weight of the body. It can be calculated as N = mgcosθ.
Given that θ = tan^(-1)(1/100), we can find cosθ.
cosθ = 1/√(1 + tan^2θ) = 1/√(1 + (1/100)^2) = 1/√(1 + 1/10000) = 1/√(10001/10000) = 1/√10001 ≈ 0.009999
Therefore, N = mgcosθ = (20 kg)(9.8 m/s^2)(0.009999) ≈ 1.95982 N
Calculating the Force of Friction:
The force of friction opposes the motion of the body and acts parallel to the inclined plane. It can be calculated as f = μN, where μ is the coefficient of friction and N is the normal force.
f = (0.25)(1.95982 N) ≈ 0.489955 N
Calculating the Force Required to Set the Body in Motion:
To set the body in motion up the inclined plane, the applied force (F) must be greater than the force of friction (f). Therefore,
F > f
F > 0.489955 N
The minimum force required to just set the body in motion up the plane is slightly greater than the force of friction, which is approximately 0.489955 N.
A body of mass 20kg is placed on an inclined plane rising 1 in 100.lf ...
Static frictional
force
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