Physics 221 Final

The mechanical energy of a mass-spring system is 0.142 J. If the force constant of the spring of 285 N/m and the mass is 0.71 kg, what is the amplitude of the oscillatory motion in cm?

3.16

In any process, the maximum amount of heat that can be converted into mechanical energy

depends on the intake and exhaust temperatures.

In the figure below, two point sources S1 and S2, which are in phase, emit identical sound waves of wavelength 2.0 m. If L1 = 39 m and L2 = 36 m, what type of interference occurs at point P?

destructive interference

In the figure, student a has a mass of 95 kg and student b has a mass of 77 kg. They sit in identical office chairs facing each other. Student a places his bare feet on the knees of student b, as shown. Student a then suddenly pushes outward with his feet, causing both chairs to move. During the push, and while the students are still touching one another

each student exerts the same amount of force on the other.

An object with mass m moves through free space with constant velocity. The magnitude of the force required to maintain this motion is equal to

zero

How many nodes and antinodes are shown in the standing wave below?

three nodes and two antinodes

If you double the radiating surface area of a star while keeping its temperature constant, its power output increases by a factor of

2

A string is clamped at both ends and plucked so it vibrates in a standing wave between two extreme positions as shown by the dashed lines below. If the string has length L and the frequency of oscillation of this mode is f, the speed of the waves on that string is

(2/3) f L

A container with a piston-lid contains an ideal gas at temperature Ti = 27 oC (300 K) and a volume V0. The temperature is increased to Tf = 127 oC while the pressure is kept constant. What is the new volume?

(4/3) V0

(A) Can two force vectors of unequal magnitude sum to zero net force? (B) Can three force vectors of equal magnitude sum to zero net force?

(A) no, (B) yes

The intensity of sound wave A is 100 times that of sound wave B. Relative to wave B the sound level of wave A is

+20 dB

A traveling wave is described by the equation y(x,t) =( 0.07 m) cos(40.6 x + 245 t ), where x is measured in meter and t in seconds. What is the velocity of this wave in units of m/s?

-6

A point source of sound waves emits a disturbance with a power of 50 W = 50 J/s into a surrounding homogeneous medium. What is the intensity of the sound at a distance of 10 m from the source?

0.04 W/m²

The specific heat of aluminum is 0.215 kcal/(kgoC). A 3 kg block of aluminum is heated from 10oC to 150oC. What is the change in the internal energy (in units of kcal) of the block?

0.215 * 3* (150-10) = 90.3 kcal

A 0.5 kg mass oscillates about the equilibrium position on a vertical spring with spring constant 10 N/m. Where is its equilibrium position measured from the unstretched spring position (without the hanging mass)?

0.49 m

What is the period (in s) of a simple pendulum of length 0.61 m and mass 0.19 kg near the surface of a planet where the gravitational acceleration is 13.7 m/s2?

1.33

A vibrating source generates a harmonic wave on a string under constant tension. If the power delivered to the string is doubled, by what factor does the amplitude change?

1.41

A ball is thrown directly downward with an initial speed of 8 m/s from a height of 30 m. After what time interval does the ball strike the ground?

1.78 s

The temperature in a furnace used to melt Aluminum is 660 oC. What is the average kinetic energy of the air molecules in the furnace?

1.93*10-20 J

Find the natural frequency of vibration of the salt molecule NaCl given its effective mass of 13.9 atomic mass units and a spring constant of 100 N/m.

10¹³ Hz

A copper pipe is 17 m long at 0 oC. If the temperature is increased to 41 oC, by how much (in mm) does its length change? Linear expansion coefficients α for copper: 17*10-6/oC

11.85

The temperature in oF is -248. What is the temperature in K?

118

What is the maximum coefficient of performance of a heat pump that takes heat from outdoors at a temperature of 0.9 oC and delivers it indoors at a temperatute of 23.9 oC.

12.9

A 0.3 kg block of aluminum is heated at atmospheric pressure such that its temperature increases from 13 oC to 61 oC. What is the change in the internal energy (in J) of the block of aluminum? The specific heat of aluminum is 9*102 J/(kg K).

12960

What is vrms (root mean square speed) of a He atom in m/s at 284 K temperature?

1330

A refrigerator has a coefficient of performance equal to 7.1. If the refrigerator absorbs 101.4 J of thermal energy from a cold reservoir in each cycle, find the work done on the system each cycle (in J).

14.3

Gas in a container is at a pressure of 1.7 atm and a volume of 5.2 m3. What is the work (In kJ) done by the gas if it expands at constant pressure to a volume 13.9 m3? Use 1 atm = 101 kPa.

1494

A 1 kg block of aluminum is heated at atmospheric pressure such that its temperature increases from 22 oC to 40 oC. What is the change in the internal energy (in J) of the block of aluminum? The specific heat of aluminum is 9*102 J/(kg K). Enter an integer.

16200

A tank having a volume of 0.15 m3 contains helium gas at 150 atm. How many balloons can the tank blow up, if each filled balloon is a sphere of radius 0.14 m at an absolute pressure of 1.2 atm?

1631

A thermodynamic system undergoes a process in which its internal energy decreases by 1326 J. If at the same time 569 J of thermal energy is transferred to it, how much work (in J) is done by the system?

1895

How much thermal energy (in kcal) is required to change a 38 g ice cube from a solid at - 16.2 oC to steam at 12.8 oC above boiling?

27.9

Heat is added at a rate of 10.0 kJ/min to a 0.5 kg solid sample starting at t = 0 min. What is the melting temperature of the sample?

283 K

A standing wave is established on a 1.2 m long string fixed at both ends. The string vibrates in four segments when driven at 120 Hz. What is the fundamental frequency?

30 Hz

The temperature on a nice summer day is 84 oF. What is the temperature on the absolute (Kelvin) temperature scale?

302 K

Data: cice = 0.50 cal/(g oC) , cwater = 1.00 cal/(g oC), csteam = 0.48 cal/(g oC), L(ice-water) = 80 cal/g , L(water-steam) = 540 cal/g How much heat is given off if 0.5 kg of steam at 373 K is converted into ice at 273 K?

360 kcal

An ideal reversible engine takes in 5 kJ of energy via heat transferred in from a 500 K burner and exhausts heat at 300 K during each closed cycle in the PV plane. The amount of heat exhausted at 300 K each cycle is

3kJ

A stationary source S generates circular outgoing waves on a lake. The wave speed is 5.0 m/s and the crest-to-crest distance is 2.0 m. A person in a motorboat heads directly toward S at 3.0 m/s. To this person, the frequency of these waves is:

4 Hz

In the cyclic process on an ideal gas shown in the adjoining PV diagram, what is the net work done by the gas during the cycle?

4 PV

A piano tuner detects 3 beats per second when she is tuning a string to a tuning fork of frequency 440 Hz. When she tightens the string, which increases the frequency of the string, the frequency of the beats initially goes down, and as she keeps increasing the frequency of the string, the frequency of the beats starts to increase. What was the original frequency of the string?

437 Hz

A box with a total surface area of 1.2 m2 and a wall thickness of 4 cm is made of an insulating material. A 10 W electric heater inside the box maintains the inside temperature at 15 oC above the outside temperature. What is the thermal conductivity of the insulating material in units of kcal/(s oC m)?

5.3 10-6

A mass-spring system oscillates with an amplitude of 4.8 cm. If the force constant of the spring of 296 N/m and the mass is 0.28 kg, what is the magnitude of the maximum acceleration of the mass in m/s2?

50.7

Calculate the magnitude of rate of heat flow (in kJ/s = kiloWatts) by conduction through 1.9 cm thick Aluminum plate with an area of 4.0 m2, if the temperature difference between the two sides is 12.4 oC. Thermal conductivity of Al: 4.9*10-2 (kcal/sec)/(oC m) 1 kcal = 4186 J

535

At which temperature do the molecules of an ideal gas have 3 times the kinetic energy they have at 32oF?

546

Beats are produced when two tuning forks, one of frequency 240 Hz and another of frequency 246 Hz are sounded together. The frequency of the beats is

6 Hz

By how much does the entropy of 100 g of water at 100 oC change if the water is very slowly converted into steam at 100 oC? The latent heat of vaporization of water is 540 kcal/kg = 2260 kJ/kg.

606 J/K

A rope has a mass of 2.5 kg and a length of 9.1 m. It is fixed at both ends. If the frequency of the first harmonic on this rope is 0.85 Hz, what is the tension of this rope in N? Enter a number with one digit behind the decimal point.

65.7

A 2.3 kg block of copper is heated at atmospheric pressure such that its temperature increases from 6 oC to 90 oC. How much heat (in J) is absorbed by the block of copper? The specific heat of copper is 0.092 (kcal/(kgoC)) 1 kcal = 4186 J

74404

Ethyl alcohol boils at 172 oF. What is Celsius equivalent of this temperature?

78 °C

An alarm clock makes a sound that has intensity 60 dB at a distance of 1 m. What is the sound intensity of 100 such clocks which are all 1 m away?

80 dB

A microwave oven is rated at 1000 W. At sea level, how long will it take to bring a cup of water (250 ml) to boil from room temperature (20 °C)? Assume the specific heat capacity of the cup itself is negligible. (for water: cw = 4190 J/(kg K), 1 ml = 1 cm3 = 1 g)

84 s

A 0.500 kg mass is attached to a spring of constant 150 N/m. A driving force F(t) = (12.0 N)cos(ωt) is applied to the mass, and the damping coefficient b is 6.00 Ns/m. What is the amplitude of the steady-state motion if ω is equal to half of the natural frequency ω0 of the system?

9.7 cm

A gas is in a container with a piston lid and is taken from thermodynamic state, 1, to a new thermo-dynamic state, 2, by several different paths, A, B, and C, in the P-V plane. The internal energy of the gas increases during the process. The work done by the gas is largest for path

A

We observe the harmonic motion of an object. Its position as a function of time shown in the graph below is given by x = 1* cos(π t), where x is measured in meter and t is measured in seconds. What are the amplitude (A), the period (T), and frequency (f) of the motion?

A: 1 m, T: 2 s, f: 0.5 Hz

When I bake a sweet potato in the oven, I always put it on a thin sheet of aluminum foil. This is because sometimes the potato exudes a sugary juice that burns and makes a hard-to-clean-up mess if it drips on the bottom of the oven. When I'm ready to take the potato out of the hot (400o F) oven after an hour of cooking, I find I can pick up the aluminum foil with my bare hands without getting burned. Why?

Because the aluminum foil has a low specific heat and not much mass, so even at a high temperature it doesn't have a lot of thermal energy in it to burn me.

A grandfather clock is running slow. The period of its pendulum is too long. To shorten the period and make the clock run faster, you should.

decrease the length of the pendulum.

The total entropy of the universe is always increasing. So, when water freezes, the entropy of the water is increasing.

False

Pressure vs. volume graphs for a certain gas undergoing five different cyclic processes are shown to the right. During which cycle does the gas do the greatest positive work?

IV

In the figures (a), (b), (c), (d) and (e) below, S is a source of sound of real frequency f and L is a listener. The speeds of the source and the listener are equal (v) in all cases except in (e) where the source is at rest and the listener is moving with speed v (as in the other cases). There is no wind. From the statements below, pick out the wrong statement.

In the case shown in fig (d) the apparent frequency as heard by the listener is less than the real frequency of the source

A car's speed changes from 20 mph to 60 mph. By what factor does its kinetic energy change?

It will increase by a factor of 9.

An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude A of oscillation is doubled, how does this affect the oscillation period T and the object's maximum speed vmax?

T remains the same and vmax doubles.

A rock is thrown straight up from the surface of the Earth. Which one of the following statements describes the energy transformation of the rock as it rises? Neglect air resistance.

The KE decreases and the PE increases.

On a humid summer day, perspiration does not cool you off much. Why?

The air is almost saturated with water vapor and there is almost no net evaporation.

A bullet is fired horizontally from a rifle on the Moon (no air, g = 1.6 m/s2) with initial speed v0. Assuming a level and endless ground, which statement is false?

The flight time increases as v0 increases.

A gas is in a container with a piston lid and is taken from thermodynamic state, 1, to a new thermo-dynamic state, 2, by several different paths, A, B, and C, in the P-V plane. The internal energy of the gas increases during the process. The internal energy change is largest for path

The internal energy change is the same for the three paths.

You fill two identical mugs with coffee, but the coffee in one mug is at a higher temperature than that in the other mug. You place the two mugs simultaneously in a microwave oven and turn it on briefly. As a result, you add 1 Joule of thermal energy to each mug. Which mug experiences the larger increase in entropy (if any)?

The mug containing the colder coffee experiences the larger increase in entropy.

Which of the statements below is wrong?

The net force acting on the pendulum bob is F = -mgsinθ. The period increases with amplitude because this force increases faster than harmonic restoring force F= -mgθ.

Water is flowing smoothly through the pipe shown in the diagram. (A middle, B small, C large)

The pressure is lowest in section B.

A 200 Hz sound wave has a measured wavelength of 1.675 m. Which of the following statements are true? You can choose more than one statement.

The wavelength of the 400 Hz wave is ~ 80 - 85 cm. The speed of the 200 Hz wave is ~335 m/s.

Suppose you are spending your weekend on roller skates trying to get momentum from somewhere. Which of the following will give you momentum in the north direction?

Throwing your keys southward.

Data: cice = 0.50 cal/(g oC) , cwater = 1.00 cal/(g oC), csteam = 0.48 cal/(g oC), L(ice-water) = 80 cal/g , L(water-steam) = 540 cal/g Which requires the most energy?

Vaporize 0.5 gram of water at T = 100°C

Can an object's velocity change direction when its acceleration is constant?

Yes, this is possible, and a rock thrown straight up is an example.

At a given temperature

all the molecules in a gas have the same average kinetic energy.

The Doppler effect is characteristic of

all traveling waves

A star with a surface temperature of 6000 K appears yellow in color. A star with a surface temperature of 4000 K will

appear reddish in color

Sound waves

are longitudinal waves

The P-V diagram below shows six curved paths (connected by vertical paths) that can be followed by a gas. Which two of them should be part of a closed cycle if the net work done by the gas is to be at its maximum positive value?

c and e

Living cells constitute a low entropy state of matter. Living cells

can exist because they help increase the entropy of the rest of the universe.

A car travels over a dirt road that contains a series of equally spaced bumps (a so-called "washboard" road). While traveling at a given speed the driver experiences a very jarring ride. When the driver drives at a higher speed, however, the ride gets smoother. That is because

going faster in the car forces the suspension to oscillate at a frequency higher than its natural frequency.

A heat engine extracts usable work by permitting

heat to flow from a hotter object to a colder object.

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

In a mixture of hydrogen, oxygen, and nitrogen gases at a given temperature, the molecules having the greatest average speed are those of

hydrogen

In any process, the maximum amount of mechanical energy that can be converted into thermal energy

is 100%

You have an empty 20 oz. soda bottle and you blow air over the opening to excite a fundamental standing wave. Now, you slice off the bottom of the bottle (it's plastic) without changing its length very much. You blow over the opening and excite a fundamental standing wave in the bottle with its bottom end open. The frequency of the standing wave in the second case

is higher than that in the first case.

A string is clamped at both ends and then plucked so that it vibrates in a standing mode between two extreme positions a and c. Let upward motion correspond to positive velocities. When the string is in position b, the instantaneous velocity of points along the string

is zero, positive, or negative, depending on the position along the string.

A hand moves to produce a periodic wave. You are making a movie. You freeze the movie and get this snapshot. If you advance the movie one frame, the knot at point A would be

lower

The volume of a gaseous sample is increased from V1 to V2 in three different ways. A-->B: isobaric process A-->C: isothermal process A-->D: adiabatic process Then the work done by the gas is

maximum in the isobaric process.

Two thermometers, one calibrated in oF and one in oC, are used to measure the same temperature. The numerical reading on the Fahrenheit thermometer

may be equal, higher or lower than that on the Celsius thermometer, depending on the temperature.

A hypothetical engine operates in a cycle taking in 10,000 J from a hot reservoir and 5000 J from a cold reservoir. In the cycle it performs 15,000 J of work. Such an engine

obeys the first law but violates the second law of thermodynamics.

Assume we can change the equilibrium state of a system via two different processes. Assume that the initial and the final state are the same. Which of the quantities ΔU, ΔQ, ΔW, and ΔT must be the same for the two processes?

only ΔU and ΔT

The longer the wavelength of a sound wave

the lower is its pitch

In simple harmonic motion

the magnitude of the acceleration is greatest at the maximum displacement.

The maintenance of the life cycle depends on

the presence of a source and a sink of energy.

Suppose you have an aquarium. You have a solid plastic decoration and a rock of about the same volume but the rock has twice the mass. Both are totally submerged in the water. The buoyant force on the plastic object is about

the same as that on the rock.

A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest amplitude oscillation, the frequency of the applied force should be

the same as the natural frequency of the oscillator.

You are watching a semi truck bounce up and down on a spring. (Yep it's a toy.) At the topmost point in the truck's path,

the truck's velocity is zero but its acceleration is downward.

The liquid level in a glass thermometer rises as the temperature increases because

the volume expansion coefficient of glass is less than that of the liquid.

A sine wave and a square wave cannot have the same

tone quality

Sound does not pass through

vacuum

While a guitar string is vibrating, you gently touch the midpoint of the string to ensure that the string does not vibrate at that point. The lowest-frequency standing wave that could be present on the string

vibrates at twice the fundamental frequency.

In a popular classroom demonstration, a cotton ball is placed in the bottom of a strong test tube. A plunger fits inside the tube and it makes an air-tight seal. It is then pushed down very rapidly, and the cotton flashes and burns. This happens because

when the air gets compressed its temperature increases.