Homework 4 Questions

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?

A sprocket with more teeth would be larger and so would require less torque (force) to produce the same rotation.

As a comet approaches the sun, it arcs around the sun more rapidly. Explain.

An orbiting object sweeps out equal areas in equal times. Closer to sun requires faster speed.

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?

Both will give the same momentum.

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?

Each time the ball is thrown or caught, its momentum is transferred to the skater involved

Spacecraft in low earth orbit take about 90 minutes to circle the earth. Why can't they be made to orbit the earth in half that amount of time?

Halving the time would require an orbit traveling inside the earth.

Mars has a larger orbital radius than the earth. Compare the solar years on those two planets

Mars' orbital year is longer than the earth's.

Consider two actions: throwing one shoe southward at 10 m/s or two shoes southward at 5 m/s? Do both of these actions take the same amount of energy? If not, which one requires more energy?

One shoe at 10 m/s takes more energy.

As you clear the sidewalk with a leaf blower, the blower pushes you away from the leaves. What is pushing on the blower so that it can push on you?

The air coming out of the blower.

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 shuttle have vastly different masses, but both orbit the much-larger earth at the same rate.

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 car's low center of mass means a smaller lever arm for the frictional force with the ground.

If the bottom of your bicycle's front wheel becomes caught in a storm drain, your bicycle may flip over so that you travel forward over the front wheel. Explain this effect in terms of rotation, torque, and center of mass.

The force of the drain on the front wheel is very large and the direction of the force passes beneath the center of mass, so it produces an enormous torque rotating the bicycle forward.

Which object is exerting the stronger gravitational force on the other, the earth or the moon, or are the forces equal in magnitude?

The force of the earth on the moon is equal to the force of the moon on the earth.

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 force you exert on the crank is greater than the force on the batter.

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 transfers equal (backward) momentum to the gun.

To free an Apollo spacecraft from the earth's gravity took the efforts of a gigantic Saturn V rocket. Freeing a lunar module from the moon's gravity took only a small rocket in the lunar module's base. Why was it so much easier to escape from the moon's gravity than from the earth's?

The less-massive moon has a much smaller escape velocity than the earth.

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 line of the frictional force passes beneath the center of mass, and so produces a backward torque.

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?

The support force from the surface of the U is at an angle, and leaning keeps his center of mass in line with the support force.

When you turn while riding a bike, 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 torque produced by leaning left counterbalances the torque produced by the ground on the tires, so there is no net torque about the center of mass.

As the moon orbits the earth, which way is the moon accelerating?

Toward the earth.

Sprinters start their races from a crouched position with their bodies well forward of their feet. This position allows them to accelerate quickly without tipping over backward. Explain this effect in terms of torque and center of mass.

When the runner takes off there will be a large frictional force of the ground against their feet, which will produce a large torque rotating them backward. The fact that their center of mass is well forward of their feet means that there will be a counterbalancing torque rotating them forward, which will keep them from toppling.

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.

You are propelling yourself northward 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 (100 mph). You have a huge bag of balls with you. Can you use this scheme to propel yourself to any speed, or are you limited to the speed at which you can hit the tennis balls?

You could potentially reach any speed, except for factors like air resistance and friction with the ice.