VDU_Physics_1_007  
 

 

Solved University-Physics Problems

Physics 1.-  Mechanics: Statics, Equilibrium, Friction 

Javier Montenegro Joo

jmj@VirtualDynamics.Org

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  Statics and Equilibrium.-  
     
  (1) In the fig. the rectangular block of mass m is kept on the ramp (elevation angle A) with the help of the force F along the horizontal rope fixed to the wall and attached to the block. (a) Determine the force F.  (b)  Determine the force F if the rope were parallel to the incline and upwards.

Solution.-

Since vectors can be displaced without rotation vector F may be displaced to the center of mass of the block where the reaction force of the surface, this is the Normal force, is decomposed as Nx and Ny, as it is shown in the sketch:

 
  [01234]

 

 
  Friction Forces.-  
     
  (1) In the fig. blocks m1 and m2 are attached each one to an extreme of a rope passing over a pulley fixed at the edge of a table.  Block m1 undergoes a friction fo on the surface of the table and, both blocks move as indicated. There is no friction between the rope and the pulley. Determine: (a) The coefficient of kinetic friction between m1 and the table (b) The acceleration of the system (c) The tension in the rope.

Solution.-

The acceleration of both blocks as well as the tension in the rope is the same for both blocks.

 
  [56789]

 

 
  (2) In the fig. two blocks m1 and m2 are connected by a rope and both are on an inclined plane which elevates an angle O from the horizontal. Both blocks slide downwards and the coefficients of friction between the plane and the blocks are respectively, U1 and U2,  where U2 > U1. Determine the tension in the rope connecting both blocks and their acceleration.

Solution.-

The acceleration of both blocks as well as the tension in the rope is the same for both blocks.

 
     
 

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