Chapter 8 Physics HW 3

A projectile falls beneath the straight-line path it would follow if there were no gravity. How many meters does it fall below this line if it has been traveling for 1 s? For 2 s?

5 m, 20 m

If you throw a stone horizontally from the top of a cliff, one second after leaving your hand its vertical distance below the top of the cliff is

5m

If you're on a Ferris wheel at a carnival, seated 10 m from the Ferris wheel's axis that makes a complete rotation each minute, your linear speed is

62.8 m/min.

An astronaut in the International Space Station cannot stand on a weighing scale. But an astronaut inside a rotating space station (not yet built) can stand on a weighing scale. Explain.

An astronaut inside a rotating space station would be pressed against a supporting floor by centrifugal force due to spinning. The "down" direction to the astronaut would be away from the axis of rotation.

Consider three axes of rotation for a pencil: along the lead, at right angles to the lead at the middle, and at right angles to the lead at one end. Rate the rotational inertias about each axis from smallest to largest.

Axis along the lead, through the center, through one end

A ball is thrown upward at velocities and angles shown. From greatest to least, rank them by their vertical components of velocity.

B C A D

From greatest to least, rank them by their horizontal components of velocity. A ball is thrown upward at velocities and angles shown.

B D A C

The experimenter from the video rotates on his stool, this time holding his empty hands in his lap. You stand on a desk above him and drop a long, heavy bean bag straight down so that it lands across his lap, in his hands. What happens?

He spins slower.

How is a flywheel constructed to maximize its rotational inertia?

Most of the mass is concentrated far from the axis.

A stone is thrown upward at an angle. What happens to the horizontal component of its velocity as it rises? As it falls?

Rising or falling, it does not change.

Why does the gravity in the Space Shuttle compare with the gravity on Earth the way it does?

The Space Shuttle and the surface of the Earth are about the same distance from the center of the Earth.

Why do the astronauts in the Space Shuttle float around?

The Space Shuttle is in free fall, so the shuttle and the astronauts inside it are continuously falling toward the Earth. They thus experience apparent weightlessness.

How does the force of gravity between two bodies change when the distance between them is doubled?

The force decreases to ¼ of its initial value.

How does the rotational inertia of the rod with the mass toward the bottom compare with the rotational inertia of the mass toward the top?

The rotational inertia of the rod with the mass closer to the top is greater than the rotational inertia of the rod with the mass closer to the bottom.

When Dr. Hewitt cuts the broom right through the center of gravity, how do the weights of the two sides of the broom compare?

The shorter side, where the bristles of the broom are, has a greater weight than the handle.

How does the torque due to the weight of one side of the broom exerted around the balance point compare with the torque exerted by the weight of the other side of the broom around the balance point?

The torque due to the weight of the shorter side (the bristles of the broom) is equal in magnitude to the torque due to the weight of the longer side, and opposite in direction.

If you are not wearing a seat belt in a car that rounds a curve, and you slide across your seat and slam against a car door, what kind of force is responsible for your slide: centripetal, centrifugal, or no force?

There is no force as viewed by someone outside the car. To them you move in a straight line.

Why are occupants of the International Space Station weightless?

They are in free fall.

When you whirl a can at the end of a string in a circular path, what is the direction of the force you exert on the can?

Toward the center of the circle

A bullet fired horizontally from a rifle begins to fall

as soon as it leaves the barrel.

Where is the center of gravity of the broom that Dr. Hewitt holds up?

at the balance point

When you do somersaults, you'll more easily rotate when your body is

curled into a ball shape.

If a turntable's rotational speed is doubled, then the linear speed of a pet hamster sitting on the edge of the record will

double.

The force of Earth's gravity on a capsule in space increases as it comes closer. When the capsule moves to half its distance, the force toward Earth is then

four times greater.

A ball is tossed upward. Neglecting air drag, the acceleration along its path is

g downward.

For orbits of greater altitude, is the period longer or shorter? Is the speed faster or slower?

The period is longer and the speed is slower.

If Earth's mass decreased to one-half its original mass with no change in radius, then your weight would

decrease to half.

If Earth's radius somehow increased with no change in mass, your weight would

decrease.

While a rock thrown upward at 50 degrees to the horizontal rises, neglecting air drag, its vertical component of velocity

decreases

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

ω =3 rotations per second

A bullet fired horizontally over level ground hits the ground in 0.5 second. If it had been fired with twice the speed it would have hit the ground in

0.5s

A gun with a muzzle velocity of 100 m/s is fired horizontally from a tower. Neglecting air resistance, how far downrange will the bullet be 1 second later?

100m

A projectile is launched upward at an angle of 70° from the horizontal and strikes the ground a certain distance downrange. For what other angle of launch at the same speed would this projectile land just as far away?

20°

When air resistance is neglected, why does the vertical component of velocity for a projectile change with time, whereas the horizontal component of velocity doesn't change?

Gravity is a purely vertical force.

A stone is thrown upward at an angle. What happens to the magnitude of the vertical component of its velocity as it rises? As it falls?

It decreases while rising, but it increases while falling.

Predict how the vertical component of the velocity will change with time after the projectile is fired.

It first decreases to zero and then increases in the opposite direction.

Is it easier for a circus performer to balance a long rod held vertically with people hanging off the other end, or the same long rod without the people at the other end, and why?

It is easier for the performer to balance a long rod held vertically with people at the other end because the rotational inertia is greater.

Is it easier to balance a long rod with a mass attached to it when the mass is closer to your hand or when the mass is farther away?

It is easier when the mass is farther from your hand.

To tighten a bolt, you push with a force of 76 NN at the end of a wrench handle that is 0.27 mm from the axis of the bolt. If you move your hand inward to be only 0.10 mm from the bolt, find the force that you should exert to achieve the same torque. Do your answers depend on the direction of your push relative to the direction of the wrench handle?

Part A T=(76)(0.27) T=21 N*m Part B T= F' (m) 21 N*m= F(.10m) F= 210N Part C Yes

Why does the rotational inertia of the rod with the attached mass closer to your hand compare the way it does with the rotational inertial of the rod with the attached mass farther away?

Rotational inertia depends on whether the mass is farther or closer to the point of rotation. The farther the mass is, the higher the rotational inertia.

Part B Part complete The following diagrams are the same as those from Part A. Again considering only the two objects shown in each pair, this time rank the strength, from strongest to weakest, of the gravitational force acting on the object on the right.

Strong Sun earth moon asteroid hydrogen atom- weak

On a rotating turntable, how do tangential speed and rotational speed vary with distance from the center?

Tangential speed increases with distance. Rotational speed is constant.

How does the gravity in the Space Shuttle compare with the gravity on Earth's surface?

The gravity in the Space Shuttle is approximately equal to the gravity on the surface of the Earth.

Predict how the horizontal component of the velocity will change with time after the projectile is fired.

it stays constant

The following diagrams are the same as those from Part A. This time, rank the pairs from left to right based on the size of the acceleration the asteroid on the left would have due to the gravitational force exerted on it by the object on the right, from largest to smallest.

largest acceleration Sun Earth Moon Asteroid Hydrogen Atom smallest acceleration

The Moon does not crash into Earth because

moon has a sufficient tangential speed

While a rock thrown upward at 50 degrees to the horizontal rises, neglecting air drag, its horizontal component of velocity

remains unchanged.

The following five diagrams show pairs of astronomical objects that are all separated by the same distance ddd. Assume the asteroids are all identical and relatively small, just a few kilometers across. Considering only the two objects shown in each pair, rank the strength, from strongest to weakest, of the gravitational force acting on the asteroid on the left.

strongest Sun Earth Moon Asteroid hydrogen atom- weakest more mass more gravity?

The hang time of a basketball player who jumps a vertical distance of 2 feet (0.6 mm) is about 2/3 second. What will be the hang time if the player reaches the same height while jumping 4 feet (1.2 mm) horizontally?

t=2/3s

Consider Earth and the Moon. As you should now realize, the gravitational force that Earth exerts on the Moon is equal and opposite to that which the Moon exerts on Earth. Therefore, according to Newton's second law of motion __________.

the Moon has a larger acceleration than Earth, because it has a smaller mass

A boy plays solitary seesaw by placing the seesaw's fulcrum one-eighth the distance from where he sits at one end. Which weighs more?

the boy

If you place a pipe over the end of a wrench when trying to rotate a stubborn bolt, effectively making the wrench handle twice as long, you'll multiply the torque by

two