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The force required to move the body up the plane will be minimum if it makes an angle with the inclined plane __________ the angle of friction.
- a)equal to
- b)less than
- c)greater than
Correct answer is option 'A'. Can you explain this answer?
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The force required to move the body up the plane will be minimum if it...
Angle of Minimum Force Required to Move a Body Up an Inclined Plane
When a body is placed on an inclined plane, it tends to slide down due to the gravitational force acting on it. To prevent this, an external force needs to be applied to move the body up the plane. The force required to move the body up the plane is minimum at a particular angle with the inclined plane. Let's discuss this in detail.
Friction
Friction is the force that opposes motion between two surfaces in contact. The frictional force depends on the nature of the surfaces in contact and the force pressing them together. The maximum value of the frictional force is given by:
F_max = μN
where F_max is the maximum frictional force, μ is the coefficient of friction, and N is the normal force.
Angle of Friction
The angle of friction, θ, is defined as the angle between the normal reaction force and the resultant force of the weight and the maximum frictional force. It is given by:
tanθ = μ
Minimum Force Required
To move a body up an inclined plane, the force applied needs to be greater than the gravitational force acting on the body. The minimum force required to move the body up the plane is given by:
F = mgsinα + μmgcosα
where F is the force required, m is the mass of the body, g is the acceleration due to gravity, α is the angle of the inclined plane, μ is the coefficient of friction, and mgcosα is the normal force.
Angle of Minimum Force
The force required to move the body up the plane is minimum when the angle of the inclined plane is equal to the angle of friction. This is because at this angle, the normal force is minimum and the frictional force is maximum, which reduces the force required to move the body up the plane.
Conclusion
The force required to move a body up an inclined plane is minimum when the angle of the inclined plane is equal to the angle of friction. This is because at this angle, the normal force is minimum and the frictional force is maximum, which reduces the force required to move the body up the plane.
When a body is placed on an inclined plane, it tends to slide down due to the gravitational force acting on it. To prevent this, an external force needs to be applied to move the body up the plane. The force required to move the body up the plane is minimum at a particular angle with the inclined plane. Let's discuss this in detail.
Friction
Friction is the force that opposes motion between two surfaces in contact. The frictional force depends on the nature of the surfaces in contact and the force pressing them together. The maximum value of the frictional force is given by:
F_max = μN
where F_max is the maximum frictional force, μ is the coefficient of friction, and N is the normal force.
Angle of Friction
The angle of friction, θ, is defined as the angle between the normal reaction force and the resultant force of the weight and the maximum frictional force. It is given by:
tanθ = μ
Minimum Force Required
To move a body up an inclined plane, the force applied needs to be greater than the gravitational force acting on the body. The minimum force required to move the body up the plane is given by:
F = mgsinα + μmgcosα
where F is the force required, m is the mass of the body, g is the acceleration due to gravity, α is the angle of the inclined plane, μ is the coefficient of friction, and mgcosα is the normal force.
Angle of Minimum Force
The force required to move the body up the plane is minimum when the angle of the inclined plane is equal to the angle of friction. This is because at this angle, the normal force is minimum and the frictional force is maximum, which reduces the force required to move the body up the plane.
Conclusion
The force required to move a body up an inclined plane is minimum when the angle of the inclined plane is equal to the angle of friction. This is because at this angle, the normal force is minimum and the frictional force is maximum, which reduces the force required to move the body up the plane.
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