Physics Concepts - Chapters 7-9

A child is practicing for a BMX race. His speed remains constant as he goes counterclockwise around a level track with two nearly straight sections and two nearly semicircular sections, as shown in the aerial view of the figure. (a) What are the directions of his velocity at points A, B, and C? For each point, choose one: north, south, east, west, or nonexistent. (b) What are the directions of his acceleration at points A, B, and C?

(a) A-north B-west C- south (b) A-west B- nonexistent C- east Explanation: A < C= D >B = E Points B and E show zero acceleration bc speed is constant Points C and D have equal acceleration

(a) Give an example in which the net force acting on an object is zero, yet the net torque is nonzero. (b) Give an example in which the net torque is zero, yet the net force is nonzero.

(a) Consider two people pushing with equal magnitude forces in opposite directions and at opposite ends of a table. The net force will be zero, yet the net torque is not zero. (b)Consider a falling body. The net force acting on it is its weight, yet the net torque about the center of gravity is zero.

Describe the path of a moving object in the event that the object's acceleration is constant in magnitude at all times and (a) perpendicular to its velocity; (b) parallel to its velocity.

(a) If the acceleration is constant in magnitude and perpendicular to the velocity, the object is moving in a circular path at constant speed. (b) If the acceleration is parallel to the velocity, the object moves in a straight line, and is either speeding up (v and a in same direction) or slowing down (v and a in opposite direction)

A pendulum consists of a small object called a bob hanging from a light cord of fixed length, with the top end of the cord fixed, as represented. The bob moves without friction, swinging equally high on both sides. It moves from its turning point A through point B and reaches its maximum speed at point C. (a) At what point does the bob have non-zero radial acceleration and zero tangential acceleration? What is the direction of its total acceleration at this point? (b) At what point does the bob have nonzero tangential acceleration and zero radial (centripetal) acceleration? What is the direction of its total acceleration at this point? (c) At what point does the bob have both nonzero tangential and radial acceleration? What is the direction of its total acceleration at this point?

(a) Point C. The total acceleration here is centripetal acceleration, straight up. (this is pointing to the center of the circular motion) tangential acceleration at this point is zero because the the tension and mg are equal to eachother. nothing in the x direction that causes tangential acceleration. (b) Point A. The speed at A is zero where the bob is reversing direction. The total acceleration here is tangential acceleration, to the right and downward perpendicular to the cord. we are unbalanced in the x direction, therefore there is tangential acceleration in the x direction Because there is no velocity at the change in direction there is also no acceleration. (c) Point B. The total acceleration here is to the right and pointing in a direction somewhere in between the tangential and radial directions, depending on their relative magnitudes

Objects moving along a circular path have a centripetal acceleration provided by a net force directed towards the center. Identify the force(s) providing the centripetal acceleration in each of these cases: (a) a planet in circular orbit around its sun; (b) a car going around an unbanked, circular turn; (c) a rock tied to a string and swung in a vertical circle, as it passes through its highest point; and (d) a dry sock in a clothes dryer as it spins in a horizontal circle.

**the acceleration that causes angular motion** a) The suns gravity is pulling on the earth to keep it from going in a straight line. b) The frictional force exerted from the ground is pulling the car towards the center allowing it to have centripetal acceleration c) at the highest point, the only force acting on it is gravity which is providing a centripetal acceleration on the rock. d) the normal force from the walls of the dryer is what is keeping the sock moving which is causing a centripetal acceleration. The sock on the wall is exerting a force. the force is always pointed towards the center of the circular motion.

Is it possible for a car to move in a circular path in such a way that it has a tangential acceleration but no centripetal acceleration?

Any object that moves such that the direction of its velocity changes had an acceleration. A car moving in a circular path will always have a centripetal acceleration.

A cat usually lands on its feet regardless of the position from which it is dropped. A slow-motion film of a cat falling shows that the upper half of its body twists in one direction while the lower half twists in the opposite direction. Why does this type of rotation occur?

As the cat falls, angular momentum must be conserved. Thus, if the upper half of the body twists in one direction, something must get an equal angular momentum in the opposite direction. Rotating the lower half of the body in the opposite direction satisfies the law of conservation of angular momentum

The water supply for a city is often provided from reservoirs built on high ground. Water flows from the reservoir, through pipes, and into your home when you turn the tap on your faucet. Why is the water flow more rapid out of a faucet on the first floor of a building than in an apartment on a higher floor?

At lower elevation, the water pressure is greater because pressure increases with increasing depth below the water surface in the reservoir (or water tower). The penthouse apartment is not so far below the water's surface. The pressure behind a closed faucet is weaker there and the flow weaker from an open faucet. Your fire department likely has a record of the precise elevation of every fire hydrant.

It has been suggested that rotating cylinders about 10 miles long and 5 miles in diameter be placed in space for colonies. The purpose of their rotation is to simulate gravity for the inhabitants. Explain the concept behind this proposal.

Consider an individual standing against the inside wall of the cylinder with her head pointed toward the axis of the cylinder. As the cylinder rotates, the person tends to move in a straight-line path tangent to the circular path followed by the cylinder wall. As a result, the person presses against the wall, and the normal force exerted on her provides the radial force required to keep her moving in a circular path. If the rotational speed is adjusted such that this normal force is equal in magnitude to her weight on Earth, she will not be able to distinguish between the artificial gravity of the colony and ordinary gravity.

Because of Earth's rotation about its axis, you weigh slightly less at the equator than at the poles. Why?

Consider one end of a string connected to a spring scale and the other end connected to an object, of true weight w. The tension T in the string will be measured by the scale and construed as the apparent weight. We have w-T=ma. This gives T=w-ma. Thus, the apparent weight is less than the actual weight by the term ma. At the poles the centripetal acceleration is non-zero, and the apparent weight is less than the true weight. you are closer to the sun if at the equators than if at the poles. the r gets lightly smaller. thus the force from the sun pulling on you is greater. this is how it relates to the tension pulling on the block. you have a greater force pulling up on you so your normal force against the earth is lighter.

Four solid, uniform objects are placed in a container of water. Rank their densities from highest to lowest.

D, A, C, B

Suppose an alien civilization has a space station in circular orbit around its home planets. The station's orbital radius is twice the planet's radius. (a) If an alien astronaut has weight w just before launch from the surface, will she be weightless when she reaches the station and floats inside of it? (b) If not, what will be the ratio of her weight in orbit to her weight on the planet's surface?

F = G(M1m2) / r^2 a) No, she will not be weightless. There is still a little bit of gravity acting on her from the planet b) Her weight in orbit will be one fourth less than her weight on the planet's surface. This is because the radius is twice as big and as you double the radius, since it is squared, it will quadruple. And when radius increases, force (being indirectly proportionate) will decrease by a factor of four.

Will an ice cube float higher in water or in an alcoholic beverage?

Ice cubes will float lower in a mixed drink because the mixture of alcohol and water is less dense than water. In a less dense liquid a greater volume of liquid must be displaced to equal the weight of the floating ice. Density of water is approx 1g/ml Density of Ice is approx 0.93g/ml Denisty of 100% pure ethanol is 0.79g/ml Thus Ice would not float at all in 100% pure ethanol.

Why can't you put your heels firmly against a wall and then bend over without falling?

In order for you to remain in equilibrium, your center of gravity must always be over your point of support, *the feet*. If your heels are against the wall, your center of gravity cannot remain above your feet when you bend forward, so you lose your balance. center of mass cannot change if you are against a wall.

(a) Is it possible to calculate the torque acting on a rigid object without specifying an origin? (b) Is the torque independent of the location of the origin?

NO! It is easy to state "find the torque caused by these forces". But that is a meaningless statement. What is always required -- or meant or implied -- is "find the torque with respect to such-and-such center of rotation that is caused by these forces". Sometimes -- because of a drawing or some limitation such as the hinges on a door -- we may not specifically state that "with respect to such-and-such center of rotation" but that information is required before the statement has any meaning! if you think about it a torque vector is oriented in the 3D-Euclidian space. the point of orientation is relative to some orgin in a chosen coordinate system. Now if you take the coordinate system away then you just have the vector part of the torque. this would imply that the direction and magnitude of the torque would be assumed and not computed, because the torque equation doesn't allow it to calculated without the origin specified(i.e. transformations from manifold-to-maniflold can occur). therefore, the torque cannot be computed without an origin, because it would cease to exist as a torque vector.this might not seem so obvious, but try the following problem and take away the origin from your coordinate system and try the same problem with the origin in the coordinate system(hint: use spherical coordinates). think about the torgue developed by the rotation of the Earth go through the calculation. keeping what I previously said in mind one should realize the validity of this rationalization No, the axis must be specified: torque = (distance from the axis) X (force). (X is the vector cross-product in this case - meaning the angle also matters.)

If you see an object rotating, is there necessarily a net torque acting on it?

No. An object in motion will remain in motion until an applied force changes it. A net torque is not required to keep the object rotating if it is already rotating.

Tornadoes and hurricanes often lift the roofs of houses. Use the Bernoulli effect to explain why. Why should you keep your windows open under these conditions?

Opening the windows results in a smaller pressure difference between the exterior and interior of the house and, therefore, less tendency for severe damage to the structure due to the Bernoulli effect. What is the Bernoulli effect?

One of the predicted problems due to global warming is that ice in the polar ice caps will melt and raise sea levels everywhere in the world. is that more of a worry for ice (a) at the North Pole, where most of the ice floats on water; (b) at the South Pole, where most of the ice sits on land; (c) both at the North and South Poles equally; or (d) at neither pole?

Rise in water level depends on the amount of water displaced by ice and when it has melted. When it is ice the volume displaced = volume immersed but it s equal to the volume of equal weight of water which always remains same whether it is ice or water. When it is ice it has more volume but that extra volume remains out of water.

A person stands a distance R from a door's hinges and pushes with a force F directed perpendicular to its surface. By what factor does the applied torque change if the person's position and force change to (a) 2R and 2F (b) 2R and F, (c) R and F/2, (d) R/2 and F/2

T = R x F a. 4RF b. 2RF c. RF/2 d. RF/4

Stars originate as large bodies of slowly rotating gas. Because of gravity, these clumps of gas slowly decrease in size. What happens to the angular speed of a star as it shrinks? Explain.

The angular momentum of the gas cloud is conserved. Thus the product Iω remains constant. Hence, as the cloud shrinks in size, its moment of inertia decreases, so its angular speed ω must increase L (angular momentum) = Iω

The cars in a soapbox derby have no engines; they simply coast downhill. Which of the following design criteria is best from a competitive point of view? The car's wheels should (a) have large moments of inertia (b)be massive (c) be hoop-like wheels rather than solid disks (d) be large wheels rather than small wheels (e) have small moments of inertia

The car's wheels should have small moments of inertia Explanation: Moment of Inertia is the force needed to get things moving, so a smaller MoI would get the derby cart going faster.

Why does a long pole help a tightrope walker stay balanced?

The long pole had a large moment of inertia about an axis along the rope. An unbalanced torque will then produce only a small angular acceleration of the performer-pole system, to extend the time available to regain balance The pole helps to stabilize their center of mass. If the person begins to lean to the left, the right side of the pole can be tilted downward to correct the shift of weight and will become stable again. A long pole increases the moment of inertia of the tightrope walker(recall moment of inertia varies as mr2; hence long poleequals larger r). We know that angular momentum is L = Iω. If the tightrope walker starts losing his balance on the rope, he will rotate around the rope a lot more slowly with a large moment of inertia than if he had a small moment of inertia. This buys him time, so to speak, to adjust the pole and re-balance himself.

An object executes circular motion with constant speed whenever a net force of constant magnitude acts perpendicular to the velocity. What happens to the speed if the force is not perpendicular to the velocity?

The speed changes. Explanation: The tangential force component causes tangential acceleration. The component of force tangential to the path causes a tangential acceleration.

If a car's wheels are replaced with wheels of greater diameter, will the reading of the speedometer change? Explain:

The speedometer will be inaccurate. The speedometer measures the number of tire revolutions per second, so its reading will be too low. It will be lower because if the radius goes up, the angular velocity will increase since they are indirectly proportionate.

A pail of water can be whirled in a vertical circular path such that no water is spilled. Why does the water remain in the pail, even when the pail is upside down above your head?

The tendency of the water is to move in a straight-line path tangent to the circular path followed by the container. As a result, at the top of the circular path, the water presses against the bottom of the pail, and the normal force exerted by the pail on the water provides the radial force required to keep the water moving in its circular path. centripetal acceleration downward due to gravity. This means that the bucket is pushing down on the water and so the water is pushing against the pail the centripetal acceleration of the water is greater than the acceleration of the gravity meaning it will push against the bucket and not fall out.

An ice cube is placed in a glass of water. What happens to the level of the water as the ice melts?

The water level remains the same when the ice cube melts. A floating object displaces an amount of water equal to its own weight. Since water expands when it freezes, one ounce of frozen water has a larger volume than one ounce of liquid water

The density of air is 1.3 kg/m^3 at sea level. From your knowledge of air pressure at ground level, estimate the height of the atmosphere. As a simplifying assumption, take the atmosphere to be of uniform density up to some height, after which the density rapidly falls to zero. (In reality, the density of the atmosphere decreases as we go up.)

Well, you need to give us a second measurement at some altitude for us to deduce what the density ratio is. Space officially begins at 100km, or 62.2 miles; but there's still some trace atmosphere that a satellite would need to contend with. To answer the question as it was intended (not as nature "really works"), use the fact that air pressure at ground level is 101.3 kPa. The question then is, since pressure = rho g h, plug in rho and g and find h. 101,300 Pa = (1.3 kg/m^3) (9.8 m/s^2) h Noting that 1 Pa = 1 N/m^2 = 1 kg/(m s^2), we will get h in meters, it's 7951 meters = about 8 km. This is sometimes called the "equivalent height" of the atmosphere, meaning exactly that it's the height the atmosphere would have if you could somehow force all of it to have the same density it has at the bottom.

Many people believe that a vacuum created inside a vacuum cleaner causes particles of dirt to be drawn in. Actually, the dirt is pushed in. Explain.

Your moving air in a vacuum cleaner, there is no central "vaccum". a series of fans move air, the moving air pushes the dirt until it is caught by a filter medium which the air is small enough to get through but the dirt is not. The air is then expelled from the device. I guess you could use pistons to move the air as well, but either way your compressing air not pulling air away.

Water flows along a streamline down a river of constant width. over a short distance the water slows from speed v to v/3. Which of the following can you correctly conclude about the river's depth? a) It became deeper by a factor of 3 b) It became shallower by a factor of 3 c) It became deeper by a factor of 3^2 d) It became shallower by a factor of 3^2

a ??

A disc rotates about an axis through its center. Point A is located on its rim and point B is located exactly halfway between the center and the rim. What is the ratio of (a) the angular velocity wa to that of wb and (b) the tangential velocity va to that of vb?

a) 1.00 Both of them are moving with an equal angle although they are a different distance from the center. Because of this, there is a ratio of 1. b) 2.00 The tangential speed is the linear speed it would be going if it didn't have centripetal acceleration. A is moving more distance over the same amount of time as B. It is moving double the distance since the radius of B is half of the radius of A. V = rw A = 2w B = 1w

Two point masses are the same distance R from an axis of rotation and have moments of inertia Ia and Ib. (a) If Ib = 4Ia, what is the ratio mb/ma of the two masses? (b) At what distance from the axis of rotation should mass A be placed so that Ib = Ia?

a) Ib/Ia = 4 so mb/ma =4 b) 2R x^2 = mbR^2/ma = x = square root of mbR/ma = 2R

Orbiting spacecraft contain internal gyroscopes that are used to control their orientation. (a) Apply the principle of conservation of angular momentum to determine the direction a spacecraft will rotate if an internal gyroscope begins to rotate in the counterclockwise direction. (b) How many mutually perpendicular gyroscopes with fixed axes of rotation are required to have full control over the spacecraft's orientation?

a) clockwise - to cancel it out. angular momentum has to be conserved. b) 3 because there are 3 dimensions. x, y, and z

Equal volumes of two fluids are added to the U-shaped pipe as shown in Figure. The pipe is open at both ends and the fluids come to equilibrium without mixing. (a) Which fluid has the higher density, fluid A or fluid B? (b) What is the ratio Pb/Pa of the fluid densities?

a) fluid B b) 4

A car of mass m follows a truck of mass 2m around a circular turn. Both vehicles moved at speed v. (a) What is the ratio of the truck's net centripetal force to the car's net centripetal force? (b) At what new speed vtruck will the net centripetal force acting on the truck equal the net centripetal force acting on the car still moving at the original speed v?

a) mv^2/r everything is the same except for the masses, so 2:1 ratio b) the square root of v/2

An object is acted on by a single nonzero force of magnitude F. (a) Is it possible for the object to have zero acceleration a? (b) Is it possible for the object to have zero angular acceleration a? (c) Is it possible for the object to be in mechanical equilibrium?

a) no, not possible b) yes. You need a torque, force and radius must be perpendicular. So because there is only a singular force, there is not another perpendicular force or torque acting on it, therefore it doesn't have angular acceleration. c) NO. it is not possible for the object to be in mechanical equilibrium since there is a single force acting on it. If there was no force, no acceleration and no angular acceleration than it would be possible.

Water flows along a streamline through the pipe shown in figure. Point A is higher than points B and C, and the pipe has a constant radius until it expands between B and C. From highest to lowest, (a) rank the flow speeds at points A, B, and C and (b) rank the pressures at points A, B, and C.

a) va=vb>vc b) Pc>Pb>Pa

Gravity is an example of a central force that acts along the line connecting two spherical masses. As a planet orbits its sun, (a) how much torque does the sun's gravitational force exert on the planet? (b) What is the change in the planet's orbital angular momentum?

a) zero b) zero

A person in a boat floating in a small pond throws an anchor overboard. What happens to the level of the pond? a) It rises b) It falls c) It remains the same

b why?

A solid disk and a hoop are simultaneously released from rest at the top of an incline and roll down without slipping. Which object reaches the bottom first? a) the one that has the largest mass arrives first. b) the one that has the largest radius arrives first c) the hoop arrives first d) the disk arrives first e) the hoop and the disk arrive at the same time

d Explanation: The disk gets there first because it has the smaller moment of inertia, so less of the energy finishes up as rotational energy, instead becoming transnational energy and getting the disc moving faster.

The three containers are filled with water to the same level. Rank the pressures at the bottom of the containers a) Pa>Pb>Pc b) Pa>Pb=Pc c) Pa=Pb>Pc d) Pa<Pb<Pc e) Pa=Pb=Pc

e ???

A mouse is initially at rest on a horizontal turntable mounted on a frictionless, vertical axle. As the mouse begins to walk clockwise around the perimeter, which of the following statements must be true of the turntable? a) It also turns clockwise b) It turns counterclockwise with the same angular velocity as the mouse c) it remains stationary d) It turns counterclockwise because angular momentum is conserved e) It turns clockwise because mechanical energy is conserved

e) It turns counterclockwise because angular momentum is conserved

In a tape recorder, the tape is pulled past the read-write heads at a constant speed by the drive mechanism. Consider the reel from which the tape is pulled: As the tape is pulled off, the radius of the roll of remaining tape decreases. (a) How does the torque on the reel change with time? (b) If the tape mechanism is suddenly turned on so that the tape is quickly pulled with a large force, is the tape more likely to break when pulled from a nearly full reel or from a nearly empty reel?

nearly full Explanation: We can assume fairly accurate that the driving motor will run at a constant angular speed and at a constant torque. (a) As the radius of the take-up reel increases, the tension in the tape will decrease, in accordance with the equation: T = T constant/ R take up As the radius of the source reel decreases, given a decreasing tension, the torque in the source reel will decrease even faster, as the following equation shows: T source = TR source = T constant R source / R take up (b) In the case of a sudden jerk on the tape, the changing angular speed of the source reel becomes important. If the source reel is full, then the moment of inertia will be large and the tension in the tape will be large. If the source reel is nearly empty, then the angular acceleration will be large instead. Thus, the tape will be more likely to break when the source reel is nearly full. One sees the same effect in the case of paper towels: It is easier to snap a towel free when the roll is new than when it is nearly empty.

During inhalation, the pressure in the lungs is slightly less than external pressure and the muscles controlling exhalation are relaxed. Under water, the body equalizes internal and external pressures. Discuss the condition of the muscles if a person under water is breathing through a snorkel. Would a snorkel work in deep water?

no The external pressure exerted on the chest by the water makes it difficult to expand the chest cavity and take a breath while under water so it would not be possible to use a snorkel in deep water. No. To be able to breathe in deep water you would need to exert pressure to on the water to be able to expand your lungs to suck in air. Without the high pressure air that would help to balance the water pressure, it would be difficult to expand your lungs.

If you toss a textbook into the air, rotating it each time about one of the three axes perpendicular to it, you will find that it will not rotate about one of those axes. (Try placing a strong rubber band around the book before the toss so that it will stay closed.) The book's rotation is stable about those axes having the largest and smallest moments of inertia, but unstable about the axis of intermediate moment. Try this on your own to find the axis that has this intermediate moment of inertia.

the axis passing through the center of the textbook and perpendicular to its spine Explanation: The principle axis that runs along the shortest, intermediate, and longest edges each go through the books center of mass, and those axes have the highest, intermediate, and lowest moment of inertia respectively, so the intermediate moment of inertia would be the middle of the spine. the one axis where the length and width are constantly switching it will not rotate.

Once ski jumpers are airborne, why do they bend their bodies forward and keep their hands at their sides?

they try to reduce air friction and form an airfoil to produce lift They are trying their best at being an airplane wing so they can get the greatest distance.

Figure shows aerial views from directly above two dams. Both dams are equally long (the vertical dimension in the diagram) and equally deep (into the page in the diagram). The dam on the left holds back a very large lake, while the dam on the right holds back a very narrow river. Which dam has to be built more strongly?

they would be the same, regardless of how much water is behind the dam.