Chapter 9/10

When no air resistance acts on a fast-moving baseball, its acceleration is

downward, g

When an elevator accelerates upward, your weight reading on a scale is

greater The support force pressing on you is greater, so you weigh more.

What would happen to the Earth if the Sun became a black hole?

Letting the equation for gravity guide our thinking, we see that no mass changes, no distance from center-to-center changes, so there would be NO change in force between the shrunken Sun and Earth.

An automobile speedometer is configured to read speed proportional to the rotational speed of its wheels. If larger wheels, such as those of snow tires, are used, will the speedometer reading be high or low - or no different?

The speedometer will read too low.

When an elevator cable breaks, the elevator falls freely, so your weight reading on a scale is

zero There is still a downward gravitational force acting on you, but gravity is not felt as weight because there is no support force, so your weight is zero.

If the polar ice caps of the Earth were to melt, the oceans would be deeper by about 30 m. What effect would this have on the Earth's rotation?

Earth day's would become longer due to the decrease in rotational speed. When the icecaps melt, they would be spread around the globe more evenly and move farther away from the axis of rotation.

Why must you bend forward when carrying a heavy load on your back?

You bend forward in order to shift your center of gravity over your feet so you don't fall backwards. In order for an object to be stable, a vertical line drawn from the center of gravity must fall within the base of the object.

If you weigh yourself in an elevator, you will weigh more when the elevator

accelerates upward The support provided by the floor of an elevator is the same whether the elevator is at rest of moving at a constant velocity. Only accelerated motion affects weight.

To tighten a bolt, you push with a force of 100 N at the end of a wrench handle that is 0.35 m from the axis of the bolt. (a) What torque are you exerting? (b) If you move your hand inward to be only 0.10 m from the bolt, what force do you have to exert to achieve the same torque? (c) Do your answers depend on the direction of your push relative to the direction of the wrench handle? (Why or why not?)

35 350 Yes, because in order to achieve the maximum torque the force must be perpendicular to the handle of the wrench.

If a trapeze artist rotates once each second while sailing through the air, and contracts to reduce her rotational inertia to one fourth of what it was, how many rotations per second will result?

4

Neglecting air drag, a ball tossed at an angle of 30° with the horizontal will go as far downrange as one that is tossed at the same speed at an angle of

60° Same initial-speed projectiles have the same range when their launch angles add up to 90°. Why this is true involves a bit of trigonometry - which, in the interest of time, we will not pursue here.

The occupant inside a future rotating space habitat feels that she is being pulled by artificial gravity against the outer wall of the habitat (which becomes the "floor"). Explain what is going on in terms of Newton's laws and centripetal force.

According to Newton's first law of motion, objects will travel at a constant velocity in a straight line until acted on by an outside force. The occupant is pushed against the wall by centrifugal force, and at every moment her tendency is to move in a straight line path, but the floor intercepts her path by pressing against her feet.

Why is it easier to carry the same amount of water in two buckets, one in each hand, than in a single bucket?

One bucket creates toque that you have to learn against, while with two buckets the new torque is zero.

Which will have the greater acceleration rolling down an incline - a bowling ball or a volleyball?

The bowling ball wins The bowling ball will win because it has the least amount of rotational inertia and the bulk of its mass is closer to the rotational axis.

Strictly speaking, as more and more skyscrapers are built on the surface of the Earth, does the day tend to become longer or shorter?And strictly speaking, does the falling of autumn leaves tend to lengthen or shorten the 24-hour day? What physical principle supports your answers?

The day tends to become longer. Falling leaves shorten the 24-hour day. The conservation of angular momentum states that the angular speed decreases as the radial distance of mass increases. Skyscrapers increase the radial distance from the Earth's spin axis which makes the Earth rotate slower and the days are a bit longer. Falling leaves decrease the radial distance from the Earth's spin axis which makes the Earth rotate faster and the days a bit shorter.

You sit at the middle of a large turntable at an amusement park as it is set spinning and then allowed to spin freely. When you crawl toward the edge of the turntable, does the rate of the rotation increase, decrease, or remain unchanged? What physics principle supports your answer?

The rate of roration decreases. The rate of rotation decreases as you crawl out to the rim while rotational inertia increases is accordance with the conservation of angular momentum.

A long track balanced like a seesaw supports a golf ball and a more massive billiard ball with a compressed spring between the two. When the spring is released, the balls move away from each other. What principles do you use for your explanation?

The track will remain in equilibrium. It will remain in equilibrium because the torques are equal. The golf ball will have a small force but a large lever arm while the billiard ball has a large force but a small lever arm.

When an elevator accelerates downward, your weight reading on a scale is

less The support force pressing on you is less, so you weigh less. Would you weigh less in an elevator that moves downward at constant velocity?

The force of gravity between two planets depends on their

masses and distance apart The equation for gravitational force cites only the masses and distances as variables. Rotation and atmospheres are irrelevant.

When you toss a projectile sideways, it curves as it falls. It will be an Earth satellite if the curve it makes

matches the curved surface of the Earth For an 8-km tangent, the Earth curves downward 5 m. Therefore, a projectile traveling horizontally at 8 km/s will fall 5 m in that time and follow the curve of the Earth.

If the masses of two planets are each somehow doubled, the force of gravity between them

quadruples Note that both masses double. Then double x double = quadruple

The velocity of a typical projectile can be represented by horizontal and vertical components. Assuming negligible air resistance, the horizontal component of the velocity along the path of the projectile

remains the same Since there is no force horizontally, no horizontal acceleration occurs.