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Block and pulley

 

This is an A level problem

Students often find questions involving pulleys problematic. The problem seems to be that when a question involves a pulley the forces can be transformed to act in different directions. While we can have a force applies to a rope on one end of a pulley creating one set of vectors because that is transferred through tension in the pulley to another location and can be rotated.

This question is based on a discussion with a student who was confused about a problem in both pulleys and contact forces.

A block with mass = 10kg rests upon a surface with a frictional coefficient (µ) of 0.3.
The block is pulled by an inextensible rope that is looped over a frictionless pulley and to which is attached a mass M. The rope is at an angle of 25° to the horizontal.

 

        

You may assume g = 10 N kg^-1.

What mass is needed to move mass m₁?

 

Hints:
First consider why the terms in the question are so specific.

    Why must it be an inextensible rope? What would happen if the rope could stretch?
    Why must the pulley be frictionless? Does this simplify the question?

As the pulley is frictionless we can ignore it and redraw the question as;
 

 

 

             

What tension is needed in the rope to move mass m₁?

Because the pulley is frictionless this will be the same as the tension support mass m₂. That will give us the weight and thus the mass.

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