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A body of mass 20kg is placed on an inclined plane rising 1 in 100.lf the coefficient of friction is 0.25 what force applied to just set the body in motion up the plane?
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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.
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.
Community Answer
A body of mass 20kg is placed on an inclined plane rising 1 in 100.lf ...
Static frictional
force
force
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A body of mass 20kg is placed on an inclined plane rising 1 in 100.lf the coefficient of friction is 0.25 what force applied to just set the body in motion up the plane?
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A body of mass 20kg is placed on an inclined plane rising 1 in 100.lf the coefficient of friction is 0.25 what force applied to just set the body in motion up the plane? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A body of mass 20kg is placed on an inclined plane rising 1 in 100.lf the coefficient of friction is 0.25 what force applied to just set the body in motion up the plane? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 20kg is placed on an inclined plane rising 1 in 100.lf the coefficient of friction is 0.25 what force applied to just set the body in motion up the plane?.
A body of mass 20kg is placed on an inclined plane rising 1 in 100.lf the coefficient of friction is 0.25 what force applied to just set the body in motion up the plane? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A body of mass 20kg is placed on an inclined plane rising 1 in 100.lf the coefficient of friction is 0.25 what force applied to just set the body in motion up the plane? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 20kg is placed on an inclined plane rising 1 in 100.lf the coefficient of friction is 0.25 what force applied to just set the body in motion up the plane?.
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