Self-Test: Equilibrium Test #1
Suggested Time: 65 minutes

1. A 110 kg object is supported by two ropes attached to the ceiling. What is the tension T in the right-hand rope?

 A. 460 N B. 540 N C. 930 N D. 1300 N

2. A 35 kg uniform plank is balanced at one end by a 55 kg student as shown.

What is the overall length of this plank?

 A. 2.6 m B. 3.3 m C. 5.4 m D. 6.7 m

3. A uniform 1.60 m board rests on two bricks as shown below. The left brick exerts an upward force of 12 N on the board.

What upward force does the right brick exert?

 A. 36 N B. 24N B. 12 N C. 3.0 N

4. What are the units of torque?
 A. N × m B. N/m C. N × s D. N/s

5. In which direction should a force act at point P to hold the boom in equilibrium so that the force will be a minimum?

 A. 1 B. 2 C. 3 D. 4

6. A uniform 16.0 kg boom of length 4.0 m is supported by a rope as shown.

Find the tension in the rope.

 A. 1.0 × 102 N B. 1.2 × 102 N C. 2.0 × 102 N D. 3.0 × 102 N

7. An 85.0 kg mountaineer remains in equilibrium while climbing a vertical cliff. The tension force in the supporting rope is 745 N.

Find the magnitude of the reaction force, F, which the cliff exerts on the mountaineer's feet.

 A. 88.0 N B. 373 N. C. 479 N D.546 N

8. Two forces act on an object as shown. Find the magnitude of the third force required to achieve translational equilibrium.

 A. 15 N B. 33 N C. 47 N D. 65 N

9. A 25 kg block is pulled by a horizontal force. The supporting rope can withstand a maximum tension force of 620 N.

To what maximum angle (theta) can the block be pulled without the rope breaking?

 A. 22° B. 23° C. 67° D. 88°

10. A uniform ladder leans against a frictionless wall as shown.

Which of the following diagrams best shows the forces acting on the ladder?

11. A mass suspended by a string is held 24° from vertical by a force of 13.8 N as shown. Find the mass.

 A. 0.57 kg B. 1.5 kg C. 3.2 kg D. 3.5 kg

12. Two forces, 12 N west and 5.0 N north, act on an object. What is the direction of a third force that would produce static equilibrium?
 A. 23° south of east B. 23° north of west C. 67° south of east D. 67° north of west

13. A trailer carrying a boat is supported by a scale which initially reads 48 kg. The boat (and therefore its centre of gravity) is moved 0.15 m further back on the trailer. The scale now reads 37 kg. Find the mass of the boat.

 A. 3400 kg B. 1700 kg C. 1600 kg D. 440 kg

14. A 0.75 kg board of length 2.60 m initially rests on two supports as shown.

a) What maximum distance, x, from the right-hand support can a 1.20 kg bird walk before the board begins to leave the left-hand support? (5 marks)

b) What force does the right-hand support exert on the board at that instant? (2 marks)

15. A uniform 4.8 m long ladder of mass 16 kg leans against a frictionless vertical wall as shown in the diagram below.

What minimum coefficient of friction would be needed at the base of the ladder to keep it from sliding? (7 marks)

16. A 3.8 m uniform beam is attached to the ceiling with a hinge at A and a cord with a tension of 300 N at B.

Determine the mass of the beam. (7 marks)

17. A floodlight is suspended from two cables as shown below. The tension in the right cable is 140 N.

a) What is the tension in the left cable? (3 marks)

b) What is the mass of the floodlight? (4 marks)

18. A 25 kg droid rests on a 5.0 m long shelf supported by two cables as shown. The mass of the shelf is 12 kg.

Find the tension in each cable. (7 marks)

19. Peter exerts a horizontal force F on a 12 kg bucket of concrete so that the supporting rope makes an angle of 20° with the vertical.

a) Find the tension force in the supporting rope. (5 marks)

b) Peter now exerts a new force which causes the rope to make a greater angle with the vertical. How will the tension force in the supporting rope change? (circle one) (1 mark)

i) The tension force will increase.

ii) The tension force will decrease.

iii) The tension force will remain the same.

20. A 6.0 m uniform beam of mass 25 kg is suspended by a cable as shown. An 85 kg object hangs from one end.

What is the tension in the cable? (7 marks)