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Solved University-Physics Problems

Physics 1.-  Mechanics:    Static Equilibrium 

Javier Montenegro Joo

jmj@VirtualDynamics.Org

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[1]  In the sketch, the rectangular block of mass m is kept static 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 ramp 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:

 
     
 

[2] The sketch depicts a system of ropes fixed to the walls that has been assembled to hang a 100 kg steel ball. Bearing in mind that the system is in equilibrium, determine the tension in each rope.

Solution.-

As it will be verified after solving the problem:   T1 = mg   and   T2 = T4

 
 

 

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[3] This problem must be solved by applying Lamy’s theorem. In the sketch, a system of ropes fixed to the walls has been assembled to hang a 100 kg steel ball. Determine the tension in each rope, bearing in mind that the system remains static.

Solution.-

Lamy’s Theorem, applies to three coplanar, concurrent and non-aligned forces in equilibrium. 

 
     
 

[4] The sketch depicts a rope passing by the extreme of a tilted pole and holding a 100-kg block at its extreme. The other extreme of the rope is fixed to ground.  Determine the tension in the rope as well as the reaction force at the extreme of the tilted pole. The system is in equilibrium.

Solution.-

(a) In the sketch below, the force F counteracts the effects of the tension and the weight.  Since the three forces, rope tension, reaction of the bar and weight of the block are all acting on the extreme of the bar, this point will be placed at the origin of coordinates of a force diagram.  In part (b) the problem is solved by means of the Lamy’s theorem and, obviously the results are the same.

 
     
 

[5] The sketch depicts a rope passing by the extreme of a tilted bar and holding a 100-kg block at its extreme. The other extreme of the rope is fixed to wall.  Determine the tension in the rope as well as the reaction force at the extreme of the tilted bar, knowing that the system is in equilibrium

Solution.-

The three forces in equilibrium (the rope tension, the reaction on the extreme of the rod and the weight) are acting on the tip of the inclined rod. This problem will be solved by means of Lamy’s theorem.  The only difficulty is identifying the angles opposing the forces.

 
     
 

[6]  In the sketch, a rod is placed against the wall and making an angle of 60with it. A rope tied at 45o   to the wall passes by the extreme of the rod and holds a 150 kg block.  Knowing that the system remains static, determine the tension in the rope and the reaction force the rod applies at the point of contact with the rope.

Solution.-

In the sketch below, F is the reaction force at the tip of the rod; this force equilibrates the tension in the rope and the weight of the block.

 
     
     
     
     
     
     
     
     
 

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