If a block of mass m is slipping on an incline flat frictionless surface as shown below, then what is the minimum weight needed to pull this 10 kg block up?

If a block of mass m is slipping on an incline flat frictionless surface as shown below, then what is the minimum weight needed to pull this 10 kg block up? Correct Answer F ≥ mg cosθ

CONCEPT:

Friction Force: It is a kind of resisting force that acts between two contact bodies to avoid relative motion between them.

• It is formed due to the close interaction of charged particles at the surface of the bodies due to electromagnetic forces.
• Mathematically it is represented as Friction force = μ N.
• Where N = normal force = m × g
• Normal force: It is a force that is exerted by the surface perpendicular to the body. It is a component of the contact force.

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Explanation:

• From the given condition if a block is placed on an inclined frictionless plane, its Freebody diagram can be represented as given below

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• In this, we can see that normal force is perpendicular to the inclined surface and the rate of acceleration of block will be g cosθ
  i.e., a = g cosθ and N = g sinθ
• This acceleration will cause the block to slip because of frictionless surface and to stop the block from slipping we must apply a force equal or greater than mg cosθ
  F = mg cosθ

Hence the minimum force required to stop the block from slipping is mg cosθ