 Worksheet Torque: Rotational Equilibrium Problems
To simplify calculations, you may use g = 10 m/sec2.

Refer to the following information for the next five questions.

Two ropes, having tensions T2 and T3, support a uniform 100-N beam and two weights. If the right weight has a mass of 25 kg and T2 has a tension of 500 N, calculate the tension in T3 as well as the mass of the unknown weight. What equation places the system in vertical equilibrium?

 What equation places the system in horizontal equilibrium?

 What equation places the system in rotational equilibrium?

 What is the value of T3?

 What is the mass of the suspended block?

Refer to the following information for the next six questions.

A 75-kg block is suspended from the end of a uniform 100-N beam. If θ = 30º, what are the values of T2 as well as the horizontal and vertical forces on the hinge? What equation places the system in vertical equilibrium?

 What equation places the system in horizontal equilibrium?

 What equation places the system in rotational equilibrium?

 What is the value of T2?

 What is the magnitude of the vertical force on the hinge?

 What is the magnitude of the horizontal force on the hinge?

Refer to the following information for the next six questions.

A 25-kg bag is suspended from the end of a uniform 100-N beam. If θ = 30º, what are the values of T2 as well as the horizontal and vertical forces on the hinge? What equation places the system in vertical equilibrium?

 What equation places the system in horizontal equilibrium?

 What equation places the system in rotational equilibrium?

 What is the value of T2?

 What is the magnitude of the vertical force on the hinge?

 What is the magnitude of the horizontal force on the hinge?

Refer to the following information for the next six questions.

A 25-kg box is suspended 2/3rd of the way up a uniform 100-N beam. If θ = 37º, what are the values of T1 as well as the horizontal and vertical forces on the hinge? What equation places the system in vertical equilibrium?

 What equation places the system in horizontal equilibrium?

 What equation places the system in rotational equilibrium?

 What is the value of T1?

 What is the magnitude of the vertical force on the hinge?

 What is the magnitude of the horizontal force on the hinge?

Refer to the following information for the next six questions.

A 2-meter, 3-kg ladder rests at an angle of θ = 37º on a rough floor and leans against a rough wall. If the coefficient of friction is µ = 0.4 on both surfaces, how far up the ladder can the 40-kg girl travel before it starts to slip? Write an expression for the friction between the feet of the ladder and the floor.

 Write an expression for the friction between the top of the ladder and the wall.

 What equation places the system in vertical equilibrium?

 What equation places the system in horizontal equilibrium?

 What equation places the system in rotational equilibrium?

 How far up along the ladder can she climb before the ladder starts to slip?

Refer to the following information for the next two questions.

The block is twice as high as it is wide. It is kept in place by a small wedge placed at its lower corner. True or False. As the board is raised, and the block just starts to tip, the block's weight vector will pass through the wedge.
 At what value of θ will the block tip and begin to fall over the wedge?

Refer to the following information for the next two questions.

If the bowling ball weighs 24 N, what is the value of the normal exerted on each point of tangency? Each surface is frictionless. On the left, 50º incline?

 On the right, 40º incline?