Physics 221 Exam 2

Three identical wheels are all spinning with the same angular velocity ω. The total angular momentum of the 3-wheel system has magnitude L. One of the three wheels is flipped upside-down, while the magnitude of its angular velocity remains constant. What is the magnitude of the new angular momentum of the 3-wheel system ?

(1/3) L

A block slides on a track from A to B to C to D. The section from A to B to C is frictionless, but for the section from C to D the coefficient of friction is not zero.Is the block's mechanical (ordered) energy increasing, decreasing, or constant in (a) region AB, (b) region BC, and (c) region CD?

(a) constant (b) constant (c) decreasing

Two identical carts labeled A and B are initially resting on an air track. The coordinate system for describing the system is shown. The cart on the right, cart B is given a push to the left and is released. The clock is then started. At t = 0, cart B moves in the direction shown with a speed v0. They hit and stick to each other. The graphs below describe some of the variables associated with the motion as a function of time. For the experiment described and for each item in the list below, identify which graph is a possible display of that variable as a function of time assuming a proper scale. "The system" refers to carts A and B together. (i) the momentum of cart A (ii) the momentum of cart B (iii) the total momentum of the system (iv) the total kinetic energy of the system

(i) #1, (ii) #3, (iii) #6, (iv) #2

The radius of the aorta is ~ 10 mm = 10-2 m and the blood flowing through it has a speed ~ 300 mm/s = 0.3 m/s. A capillary has a radius ~ 4×10-3 mm = 4×10-6 m, but there are literally billions of them. The average speed of blood through the capillaries is ~ 5×10-4 m/s. (i) Calculate the effective cross sectional area of the capillaries and (ii) the approximate number of capillaries.

(i) 0.188 m2, (ii) 3.75*109

Two carts on an air track are pushed towards each other. Initially, cart 1 moves in the positive x direction and cart 2 moves in the negative x direction. They bounce off each other elastically. The graphs at the right describe some of the variables associated with the motion as a function of time. For the experiment described and for each item in the list below, identify which graph is a possible display of that variable as a function of time. If none apply, choose N (for none). (i) the momentum of cart 1 (ii) the position of cart 1. (iii) the position of cart 2.

(i) D, (ii) B, (iii) N

A centrifuge in a medical laboratory rotates at an angular speed of 3600 rev/min. When switched off, it rotates 50 times before coming to rest. What is the constant angular acceleration of the centrifuge?

-226.2/s2

A boy holds a 40 N weight at arm's length for 10 s. His arm is 1.5 m above the ground. The work done by the force of the boy on the weight while he is holding it is

0

Blood and water have the same contact angle with glass. The density of blood is 5% higher than that of water. (ρblood= 1.05 ρwater) While you make your capillary action measurements you find that water rises in the same tube a factor 1.69higher than a blood sample. The surface tension of water at the same temperature is 0.073 N/m. What is the surface tension of the blood sample?

0.045 N/m

A piece of clay with mass m = 0.01 kg collides with the floor at speed of 8 m/s and sticks. The collision takes 0.02 s. The magnitude of the impulse the piece of clay receives in this collision is

0.08 kgm/s2

A 65 kg physics student is at rest on a 5 kg sled that also holds a chunk of ice with a mass of 2 kg. The student throws the ice horizontally with a speed of 10 m/s relative to the ground. If the sled slides over a frozen pond without friction, how fast (in m/s) are the sled and student traveling with respect to the ground after throwing the chunk of ice?

0.286 m/s

Suppose the flow rate of blood in a coronary artery has been reduced to 0.846 times its normal value by plaque deposits, and that the pressure difference across the artery has not changes. By what factor has the radius of the artery been reduced, assuming no turbulence occurs?

0.959

Angular speed is measured in units of s-1, which is rad/s. How many degrees correspond to 1 radian?

1 rad = 57.3 degrees

A car engine delivers 2.2 * 104 W to its wheels when moving at a constant speed of 17.1 m/s. What is the magnitude of the resistive force (in N) acting on the automobile at that speed?

1,287

Two particles of masses 2 g and 8 g are separated by a distance of 6 cm. The distance of their center of mass from the heavier particle is

1.2 cm

How much negative pressure, with respect to atmospheric pressure, do your lungs have to produce, so you can you suck water through a straw to a height of 15 cm?

1.5 kPa

A gardener is watering her garden from a hose. With the water pressure full blast holding the hose horizontally she can just reach a distance of 12 m, but needs to water an area up to 16 m away. By what fraction must she reduce the cross-sectional area of the hose, still keeping the hose horizontal, to be able to water this area?

1/4

As a bacterium swims through water it propels itself with its flagella so as to overcome the frictional drag forces and move at, more or less, constant velocity of 100 micrometer/s for periods of time. If the frictional drag force on a bacterium is 0.1 N, how much work does the bacterium do in 1 s?

10 microJoule

An intravenous (IV) system is supplying saline solution to a patient at the rate of 0.09 cm3/s through a needle of radius 0.2 mm and length 6.36 cm. What gauge pressure (in Pa) is needed at the entrance of the needle to cause this flow? Assume that the viscosity of the saline solution to be the same as that of water, η = 1.0*10-3 Pa-s, and that the gauge pressure of the blood in the vein is 1500 Pa. Enter an integer.

10,610

A centrifuge starts from rest. Its angular acceleration α is constant for 17 s. Its final angular speed is ω = 282 revolutions per second. What is its angular acceleration α in units of s-2?

104.2

An 4.5 kg object gains height 7.6 while being accelerated from rest to a final speed of 7.2 m/s by an external force. What was the net work (in J) done on the object? Let g = 9.8 m/s2.

117

Two blocks of mass M and 3 M are placed on a horizontal frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them. A cord holding them together is burned, after which the block of mass 3 M moves to the right with a speed of 5 m/s. What is the speed of the block of mass M?

15 m/s to the left

A 4.6 kg object has kinetic energy 2,520 J. What is the magnitude of its momentum (in kg m/s)?

152

In SI units, what is the change in the magnitude of the momentum of a 1,399 kg car that accelerates uniformly along a straight line from a speed of 5 m/s to a speed of 17 m/s in 6 s?

16,788

A 2 kg block of wood is floating in water. What is the magnitude of the buoyant force acting on the block?

19.6 N

A bicycle's wheels have a radius of 33 cm. The bicycle is traveling at a speed of 6.5 m/s. What is the angular speed of the front tire?

19.7 rad/s

A 1 kg rock is suspended by a massless string from one end of a meter stick at the 0 cm mark. What is the mass m suspended from the meter stick at the 75 cm mark if the system is balanced?

2 kg

In SI units, what is the magnitude the net force acting on a 1,186 kg car that accelerates uniformly along a straight line from a speed of 3 m/s to a speed of 18 m/s in 6 s?

2,965

A 1.5 kg toy car moving in the positive x direction with speed 3.1 m/s hits a toy car of equal mass moving in the positive y-direction with speed of 4 m/s. If the collision is perfectly inelastic, calculate the speed of the cars (in m/s) right after the collision.

2.5

A certain pump can exert a negative gauge pressure of 23.6 kPa. It is used to suck a liquid out of a bucket up a thin pipe. A 10.6 m column of the liquid exerts a pressure of 100 kPa. To what maximum height ( in m) can the liquid be sucked up the pipe by this pump? Enter a number with two digits behind the decimal point.

2.5

A wheel with moment of inertia 0.05 kgm2 rotates about a fixed axis. Its kinetic energy is 1,503 J. What is ts angular speed ω in s-1?

245

A Venturi tube may be used as a fluid flow meter. If the fluid flow rate in m3/s is 2.4 * 10-3 and the radius R1 = 2 *10-2 m of the inlet tube is 2 times the radius R2 of the outlet tube, and the fluid is water (ρ = 1000 kg/m3), find the pressure difference P1 - P2 in units of kPa.

27.4

Substance A has a density of 2.0 g/cm3 and substance B has a density of 3.0 g/cm3. In order to obtain equal masses of these two substances, the ratio VA/VB of the volume of A to the volume of B has to be equal to

3 : 2

An 4.6 kg object gains height 5.4 m while being accelerated from rest to a final speed of 7.7 m/s by an external force. What was the work (in J) done on the object by this force? Let g = 9.8 m/s2.

380

A piece of clay with mass m = 0.01 kg collides with the floor at speed of 8 m/s and sticks. The collision takes 0.02 s. The magnitude of the average force the piece of clay experiences during the collision is

4 N

Open the simulation Under Pressure (Links to an external site.). You used this simulation in studio session 8. Show the ruler and grid. On Mars, what is the pressure in kPa 1.5 m below the surface of a basin filled with water?

43.9

Mercury has an unusually large surface tension γ = 0.465 N/m. Calculate the excess pressure inside a drop of mercury 4 mm in diameter.

465 Pa

A block of wood of uniform density floats so that exactly half of its volume is underwater. What is the density of the block?

500 kg/m3

A beaker containing 5.0 kg of water is on a weighing scale. A 0.8 kg block of metal that has density 8*103 kg/m3 that is attached to a string is lowered completely into water without touching the bottom. Assume that the beaker is massless, and water has density 103 kg/m3, and g = 10 m/s2.What is the reading on the scale?

51 N

A 50 g meter stick lies on the x-axis with its left edge (the 0 cm mark) at the origin. A 62 g mass is attached to the stick at x = 80 cm and a 20 g mass is attached at x = 10 cm. Find the x-coordinate of the center of mass of the system in cm.

58

A 2 kg mass is at x = 0 m, y = 2 m, and a 3 kg mass is at x = 2 m, y = 0 m. The x- and y-coordinates, respectively, of the center of mass of this system are

6/5 m, 4/5 m

A wheel starts from rest with constant angular acceleration α. It requires 2.7 s to make 40 revolutions. What is its angular acceleration α in s-2?

69

A nozzle with a radius of 0.18 cm is attached to a garden hose with a radius of 1.33 cm. If the speed of the water in the hose is 1.46 m/s, what is the speed of the water in the nozzle in m/s?

79.71

A ball (mass 0.10 kg) is initially moving to the left at 40 m/s. After hitting the wall, the ball is moving to the right at 40 m/s. What is the impulse of the ball receives during its collision with the wall?

8 kg m/s to the right

The brake system in most cars makes use of a hydraulic system. This system consists of a fluid filled tube connected at each end to a piston. Assume that the piston attached to the brake pedal has a cross sectional area of one half a square inch and the piston attached to the brake pad has a cross section area of two square inches. When you apply a force of 20 pounds to the piston attached to the brake pedal, the force at the brake pad will be

80 pounds

A soap bubble with radius of 3.0 cm is floating in air. What is the pressure difference across the two surfaces of the bubble? The surface tension of soapy water is γ = 69 * 10-3 N/m

9.2 N/m2

Three forces labeled A, B, C are applied to a rod which pivots on an axis through its center. Which force produces the torque with the largest magnitude about this axis?

A

Fluid is flowing from left to right through the pipe. Points A and B are at the same height, but the cross-sectional areas of the pipe differ. Points B and C are at different heights, but the cross-sectional areas are the same. Rank the pressures at the three points, from highest to lowest.

A, B, C

Consider three drinking glasses. All three have the same area base, and all three are filled to the same depth with water. Glass A is wider at the top than at the bottom, glass B is cylindrical and so holds less water than A. Glass C is narrower at the top than at the bottom, and so holds less water than B. Which glass has the greatest liquid pressure at the bottom?

All three have equal pressure at the bottom

The picture below shows 5 blocks. The blocks have equal volumes but different masses. The blocks are placed in an aquarium tank filled with water and blocks 2 and 5 come to rest as shown in the figure. Which answer is correct?

Block 3 will come to rest in the same position as block 5

Two objects, A and B, have the same volume and are completely submerged in a liquid, although A is deeper than B. Which object, if either, experiences the greater buoyant force?

Both objects experience the same buoyant force

You have heard the tried and true phrase "it is like running in to a brick wall". Now it is time to dig a little deeper and modify the phrase. Assume you are in a car driving and come in contact with this proverbial brick wall. Your car can do three things after the strike: it can go through, come to stop or bounce back. Select the option which will be the most dangerous to you assuming similar collision times.

Bouncing back

A disk is spinning with angular velocity ω as shown. It begins to speed up. While it is speeding up, what are the (i) directions of its angular velocity ω (ii) and its angular acceleration α?

C, C

An object moves with constant speed in the clockwise direction along the circular path shown below. At the point indicated by the black dot, in which direction is the angular velocity vector ω pointing?

D

Modeling a meter stick as a forearm, compare the force FB that the biceps has to exert to keep the forearm horizontal to the weight of the forearm FW = mg. Let d = 10 cm and the distance from where the biceps muscle attached to the center of mass be d' = 40 cm.

FB = 5 mg

In soap box car races, the cars are boxes with wheels. They begin at rest at the top of a hill, and at the start of the race they all begin rolling down the hill. The soap box car that reaches the bottom of the hill first is the winner. You have entered a soap box car race where the rule is that all the wheels and cars must have equal mass. Since you have taken Physics, you know that it is worse to have wheels with spokes (where the mass is mostly on the rim) rather than solid wheels because

Given the same torque, the wheels with spokes have a higher rotational mass or moment of inertia and therefore will have a smaller angular acceleration.

Suppose you are riding on a merry - go - round and you move out to the edge. What happens to the rotational rate of the system?

It decreases because angular momentum is conserved and the moment of inertia increases.

Consider the earth spinning from west to east on its axis. It is slowing down in its rotation due to friction with the air. Using the right hand rule, in what direction is the frictional torque?

N pole to S pole

Two objects with masses m1 and m2, respectively, are initially at rest, and then are acted on by the same net force F for the same amount of time ∆t. If m2 = 4m1, which object will have the largest kinetic energy?

Object 1 with mass m1

Two moving objects have masses m1 and m2, respectively. If m2 = 4m1, and both have the same kinetic energy, which has more momentum?

Object 2 with mass m2

Which of the following statements is false?

Plaque deposit on an artery or arteriole wall causes an increase in local blood pressure and can lead to bursting of that vessel

A DVD is rotating with an ever increasing speed. How do the angular velocity, angular acceleration, tangential velocity, and tangential acceleration compare at points P and Q?

Points P and Q have the same angular velocity and the same angular acceleration

Which one of the following is Bernoulli's equation not involved in explaining?

The buoyant force on a floating iceberg

Assume a disk and a ring with the same radius roll down an incline of height h and angle theta. If they both start from rest at t = 0, which one will reach the bottom first?

The disk

A sphere, a hoop, and a cylinder, all with the same mass M and the same radius R, are rolling along, all with the same speed v. Which has the most total kinetic energy?

The hoop

Blood flows through a section of a horizontal artery that is partially blocked by a deposit along the artery wall. A hemoglobin molecule moves from the wider region into the narrower region. What happens to the pressure acting on the molecule as it moves from the wider into the narrower region?

The pressure decreases

Suppose that there is a partial blockage of the aorta, which normally pumps about 5 L of blood per minute. If the diameter of the aorta were reduced by 30%, what increase in blood pressure gradient would be needed to obtain the normal flow rate? (Assume that Poiseuille's law applies.)

The pressure gradient would have to increase by a factor of 4.2

Blood flows through a section of a horizontal artery that is partially blocked by a deposit along the artery wall. A hemoglobin molecule moves from the narrow region into the wider region. What happens to the pressure acting on the molecule as it moves from the narrow to the wider region?

The pressure increases

Both the disk and the ring have the same mass, and the same radius. Which has the larger moment of inertia I about the center?

The ring

Two bubbles are connected by a hollow tube plus a valve. What will happen once the valve between the two is opened?

The small bubble will drain into the big bubble

In your dorm room you watch the Vols play in an out-of-town game. It is a cliff hangers and the winner will be determined in the last few seconds of play. Everybody is taking their bathroom break right after the game ends. As the toilets flush and hands are washed, the faucet pressure is noticeably reduced, even though the supply pipe to the rooms can carry all the water needed. Why?

The water has to speed up in the supply pipe and therefore the pressure drops in the pipe

Which of the following assumptions is not made in the derivation of Bernoulli's equation?

There is negligible gravity

A pocket watch and Big Ben are both keeping perfect time. Which minute hand has the larger angular speed ω?

They both have the same ω

Why do elastic balls bounce so well?

They store energy through compression, like a spring.

Two carts collide on a nearly frictionless track. (See lab 6, experiment 3.)Cart 1 has mass m1 = 2 kg and cart 2 has mass m2 = 1 kg. For the velocities of the carts before and after the collision we obtain the following data. v1i = 10 cm/s and v2i = 1 cm/s. v1f = 7 cm/s and v2f = 7 cm/s. To within 1% uncertainty, which of the statements below are true?

This is a perfectly inelastic collision The total momentum of the two carts is conserved

Suppose you are on a cart, initially at rest on a frictionless, horizontal track. You throw a series of identical balls against a wall that is rigidly mounted to the cart. If the balls are thrown at a steady rate and bounce straight back, is the cart put into motion?

Yes, it starts to move to the left and keeps on gaining speed

Suppose you work in the E.R. and a choking patient comes in with their trachea half obstructed. (The diameter is half of what it was before the obstruction.) You manage to correct the problem and send them on their way safely, explaining that such obstructions are particularly dangerous because

a half -blocked airway passes only 1/16 the regular amount of air

In an experiment water rose by capillary attraction through two columns of soils, one with coarse grains (column 1) and the other with fine gains (column 2). In which column did the water rise to greater height?

column 2

A drum major is given two batons, one gold and one plastic. He is told that both batons have the same mass. He tries spinning each one and finds that the plastic one is much easier to start and stop spinning. He correctly concludes that the plastic baton, in comparison to the gold baton

has more of its mass distributed towards the center

A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms

his angular momentum remains the same

Consider a block of wood floating on water. If you push down on the top of the block until it is completely submerged, the buoyant force on it

increases

When the kinetic energy of a moving object increases by a factor of 16, the magnitude of its momentum

increases by a factor of 4

The SI units for viscosity are

kg/(m-s)

Water pours gently from an open hose because it

lost energy throughout its trip to the hose end

The density of freshwater is 1 g/cm3and the density of seawater is 1.03 g/cm3. A ship will float

lower in freshwater than in seawater

A radioactive nucleus of mass M moving along the positive x-direction with speed v emits an α-particle of mass m. If the α-particle proceeds along the negative x-direction, the centre of mass of the system (made of the daughter nucleus and the α-particle) will

move along the positive x-direction with speed equal to v

Rockets receive their forward propulsion through

pushing against the exhaust

Dimples on a golf ball hit without spin

reduce drag

Some children are riding on the outside edge of a merry-go-round. Ignore friction in the rotation of the merry-go-round. Consider the "system" of the children plus the merry-go-round. At the same time, the children all move towards the center of the merry-go-round. When they do this

the angular momentum of the system stays constant

After clearing the bar on a high jump, you land softly on a giant mattress. Landing on a mattress is more comfortable than landing on a sand heap of equal size because

the force the mattress exerts on you to stop your descend is much less than the force the sand heap would exert on you

A baseball bat with uniform density is cut at the location of its center of mass as shown in the figure. The piece with the smaller mass after the cut is

the piece on the left

A beaker is filled with water to the rim. Gently you place a toy duck in the beaker and some of the water spills out. The duck floats. The weight of the beaker with the duck floating in it is

the same as its weight before adding the duck

Two objects with different masses collide and stick to each other. Compared to before the collision, the system of two objects after the collision has

the same total momentum but less total kinetic energy

When blood flows into an aneurysm

the speed decreases and the pressure increases.

The four things that affect the amount of water flowing through a hose are

water viscosity, hose length, inlet and outlet pressure difference, and hose diameter

Two carts A and B are moving towards each other as shown in the diagram. They collide and come to rest at the point of impact. From this observation we can conclude that the carts

were moving with momenta equal in magnitude and opposite in direction.

A man jumps off of a bridge towards a river below. As he falls, he feels himself spinning forward (clockwise in diagram). To keep from hitting the water head-first, the man should

windmill his arms clockwise to keep upright

The graph shows the acceleration of a cart with mass m = 0.555 kg, moving initially with constant speed, as a function of time, as a force F = ma stops the cart. Estimate the initial momentum of the cart in units of kgm/s.

~0.6

A mass m is lowered gently onto a vertical spring of length L with spring constant k until it just touches the spring. Let y be the distance the spring is compressed and v be the velocity of the mass. The mass is released from rest. Which of the following is the equation for conservation of energy?

½mv2 + ½ky2 + mg(L - y) = mgL

A student sees the following question on an exam: A flywheel with mass 120 kg and radius 0.6 m, starting at rest, has an angular acceleration of 0.1 rad/s2. How many revolutions has the wheel undergone after 10 s? Which single formula might the student use to answer the question?

θf = θi+ ωi(tf-ti)+ ½ α(tf-ti)2

A small wheel and a large wheel are connected by a belt. The small wheel is turned at a constant angular speed ωs. How does the angular speed of the large wheel ωL compare to that of the small wheel?

ωs > ωL