Week 9 - Modesto Junior College

1 Week 9 3. When you turn while running, you must lean in the direction of a turn or risk falling over. If you lean left as you turn left, why don t you fall over to the left? The leftward frictional force on your feet keeps you balanced. 4. If a motorcycle accelerates too rapidly, its front wheel will rise up off the pavement. During this stunt the pavement is exerting a forward frictional force on the rear wheel. How does that frictional force cause the front wheel to rise? The huge forward force on the bottom of the rear wheel produces a torque on the motorcycle and rider about their combined center of mass. If this torque is large enough, it overcomes the motorcycle's natural forward-back stability and the motorcycle rotates so that its front wheel leaves the pavement.

2 5. As a skateboard rider performs stunts on the inside of a U-shaped surface, he often leans inward toward the middle of the U. Why does leaning keep him from falling over? As long as the inward force from the U-shaped surface points toward the skaterboard s center of mass, the skaterboard doesn t begin rotating. 6. Most racing cars are built very low to the ground. While this design reduces air resistance, it also gives the cars better dynamic stability on turns. Why are these low cars more stable than taller cars with similar wheel spacings? The torques that friction exerts on a car when it pushes on the car's wheels can cause the car to tip over. But if the car's center of mass is very low, the lever arm of the frictional forces is small and the torques that friction produces about the car's center of mass are small.

3 With only small torques acting on it, the car stays upright because of its natural static stability. 7. The crank of a hand-operated kitchen mixer connects to a large gear. This gear meshes with smaller gears attached to the mixing blades. Since each turn of the crank makes the blades spin several times, how is the force you exert on the crank handle related to the forces the mixing blades exert on the batter around them? The torque you exert on the crank is much larger than the torque the blades exert on the batter. 8. The starter motor in your car is attached to a small gear. This gear meshes with a large gear that s attached to the engine s crankshaft. The starter motor must turn many times to make the crankshaft turn just once.

4 How does this gearing allow modest forces inside the starter motor to turn the entire crankshaft? Since the starter motor must turn many times in order for the crankshaft to turn just once, the starter motor can use small forces exerted over long distances to produce large forces on the engine exerted over short distances. 9. A bread-making machine uses gears to reduce the rotational speed of its mixing blade. While its motor spins about 50 times each second, the blade spins only once each second. The motor provides a certain amount of work each second, so why does this arrangement of gears allow the machine to exert enormous forces on the bread dough? Each second, the blade pushes the dough a short distance. To do significant work, the force it exerts on the dough must be large.

5 10. The chain of a motorcycle must be quite strong. Since the motorcycle has only one sprocket on its rear wheel, the top of the chain must pull forward hard to keep the rear wheel turning as the motorcycle climbs a hill. Why would replacing the motorcycle s rear sprocket for one with more teeth make it easier for the chain to keep the rear wheel turning? The more teeth there are on the rear sprocket, the farther the chain must travel before the rear wheel turns once. The chain still does the same amount of work in turning the rear wheel once, but it can now do it while pushing the rear sprocket a longer distance, so the force it exerts on the sprocket must be smaller. 11. As you clear the sidewalk with a leaf blower, the blower pushes you away from the leaves.

6 What is pushing on the blower so that it can push on you? As the blower pushes air toward the leaves, that air pushes the blower away from the leaves. 12. When a sharpshooter fires a pistol at a target, the gun recoils backward very suddenly, leaping away from the target. Explain this recoil effect in terms of the transfer of momentum. The gun transfers forward momentum to the bullet, so the bullet must transfer an equal but oppositely directed amount of momentum to the gun. 13. Which action will give you more momentum toward the north: throwing one shoe southward at 10 m/s or two shoes southward at 5 m/s? They are equivalent. 14. Do both of the actions in Exercise 13 take the same amount of energy?

7 If not, which one requires more energy? Throwing one shoe at 10 m/s takes more energy than throwing two shoes at 5 m/s, even though the momentum transfer is the same in both cases. 15. You are propelling yourself across the surface of a frozen lake by hitting tennis balls toward the southern shore. From your perspective, each ball you hit heads southward at 160 km/h. You have a huge bag of balls with you and are already approaching the northern shore at a speed of 160 km/h (100 mph). When you hit the next ball southward, will you still accelerate northward? Yes. 16. Can you use the tennis ball scheme of Exercise 15 to propel yourself to any speed, or are you limited to the speed at which you can hit the tennis balls?

8 You can reach any speed you like, so long as you start with enough of your total mass in the form of tennis balls. 17. You and a friend are each wearing roller skates. You stand facing each other on a smooth, level surface and begin tossing a heavy ball back and forth. Why do you drift apart? The ball transfers momentum between you so that you acquire momentum in the opposite direction from your friend. 18. The time it takes a relatively small object to orbit a much larger object doesn t depend on the mass of the small object. Use an astronaut who is walking in space near the space shuttle to illustrate that point. The astronaut and the space shuttle both fall toward the ground at the same rate and their paths around the earth are essentially identical.

9 That's why the astronaut and shuttle hover next to one another, despite the absence of any forces between them. 19. As the moon orbits the earth, which way is the moon accelerating? Directly toward the earth. Additional Questions: 1. Explain static stability (hint: the answer is NOT an object s stability at rest. ) a. An object s tendency to return to stable equilibrium after being slightly disturbed. 2. As a tricycle is tipped over more and more, at what point does it no longer become statically stable? a. Once the CG is no longer positioned over the base of support. 3. Why don t tricycles have good dynamic stability? a. During turns, they have the tendency to roll over. 4. Why are bicycles dynamically stable? a. Because they tend to steer automatically in whatever direction they lean.

10 5. A properly designed bicycle must have its front wheel touching the ground behind the steering axis (see Fig. ). What is the problem if the front wheel touches the ground in front of the steering axis? a. The steering wheel will turn in the opposite direction of the lean. 6. Explain how leaning while turning on a bicycle help keeps the rider from tipping over. a. When leaning, the resultant of the frictional and support forces on the tires will pass through the CG of the rider and bicycle, therefore creating zero torque. 7. Explain how a rocket engine propels itself. a. Chemical energy is converted to kinetic energy in the form of rapidly moving particles. The particles move backwards while the rocket moves forward in order to conserve momentum.