Chapter 8 Review

1. How is torque calculated?

T = F x l

2. What are the two requirements for equilibrium?

The net force must be zero, and the net torque must be zero. All the forces must add up to zero and the clockwise torques must be equal to the counterclockwise torques.

3. If you push the knob of a heavy door with a force of 230 N, and the knob is 0.82 meters from the hinge, what is the torque applied?

T = F x l T = 230 x 0.82 T = Nm

4. What force is needed to provide the same torque on the door in problem three if you apply this force halfway between the knob and the hinge?

T = F x l = F x 0.41 F = 460 N

5. A 50 kg child sits 3 meters from the fulcrum of a seesaw. Where must the fat physics teacher (150 kg) sit to balance the seesaw?

50 x g x 3 = 150 x g x l 150 = 150 x l l = 1 m

6. Two workers lift a heavy beam (800 N, 4 meters long) by the ends. The beam is not uniform; the center of gravity is 1.5 meters from the heavy end. What force must each worker apply to lift the beam?

Pick the heavy end as the pivot point. CWCCW 800 x 1.5 = F L x 4 F L = 300 N F H + F L = 800 F H = 800 F H = 500 N

7. A gymnast (mass of 45 kg) is on the balance beam (5 meters, 30 kg). The beam is held by two support bars, attached 1 meter from each end. If the gymnast is standing 2 meters from the left end, what is the upward force supplied by each support?

Pick the left end as the pivot point. CW CCW 30g x g x 1 = F R x 3 F R = 300 N F L + F R = 750 F L = 750 F L = 450 N

8. A uniform horizontal beam with a length of 6 meters and a weight of 120 N is attached at one end to a wall by a pin so the beam can rotate. The opposite end of the beam is supported by a cable attached to the wall above the pin. The cable makes an angel of 60º with the beam. A) What torque is produced by the weight of the beam?

a. T = F x l T = 120 x 3 T = 360 Nm

B) What torque is produced by the tension in the cable? 360 Nm, torque must be balanced, bar is not changing its rotation.

C) What is the vertical component of the tension in the cable that produces equilibrium?

c. T = F x l 360 Nm = F x 6 F = 60 N

D) What is the tension in the cable needed to keep the beam in equilibrium?

Sin 60º = opp/hyp Sin 60º = 60 N / T T = 60 / Sin 60º T = 69 N

9. What are the six simple machines? What are the two basic types?

Lever, wheel and axle, pulley, inclined plane, wedge, screw lever type and inclined plane type machines

10. How do most simple machines multiply force?

By making you apply your force over a longer distance to produce a larger force over a smaller distance.

11. What is the law of machines?

Work output cannot exceed work input. W.O. < W.I.

12. An inclined plane is 6 meters long and is used to raise a box 2 meters above the ground. What is the ideal mechanical advantage of the inclined plane?

IMA = d I / d O IMA = 6m / 2m IMA = 3

13. If the box lifted in problem 12 has a weight of 1200 N, what is the work output?

W.O. = F O x d O W.O. = 1200 x 2 W.O. = 2400 J

14. If there is no friction on the inclined plane described above, what force must be applied to the box to push it up the plane? What is the work input in this case?

2400 = F I x 6 F I = 400 N 2400 J No friction, no energy lost to heat.

15. Due to friction, the actual force applied to the box described above to push it up the plane is 600 N. What is the actual mechanical advantage of the inclined plane? What is the work input in this case?

AMA = F O / F I AMA = 1200 / 600 AMA = 2 W.I. = F I x d I W.I. = 600 x 6 W.I. = 3600 J

16. Including friction, what is the efficiency of the inclined plane described in problems 12 through 15?

e = W.O. / W. I. e = F O x d O / F I x d I e = 1200 x 2 / 600 x 6 e = 2400 J / 3600 J e = %

17. A fellow student tells you he has a machine that will produce 1000 N of force over a distance of 3 meters if you apply a force of 500 N over 4 meters. Is this possible? What law does this situation violate?

e = W.O. / W. I. e = F O x d O / F I x d I e = 1000 x 3 / 500 x 4 e = 3000 J / 2000 J e = 1.5 or 150 % This is not possible as a machine cannot produce more work than is put in. This violates the law of machines.