Deck 7: Conservation of Energy

Question 1

Susana ascends a mountain via a short, steep trail. Sean ascends the same mountain via a long, gentle trail. Which of the following statements is true?

A) Susana gains more gravitational potential energy than Sean.
B) Susana gains less gravitational potential energy than Sean.
C) Susana gains the same gravitational potential energy as Sean.
D) To compare energies, we must know the height of the mountain.
E) To compare energies, we must know the lengths of the two trails.

Answer 1

Susana gains the same gravitational potential energy as Sean.

Question 2

The reference point for gravitational potential energy

A) must be at the initial position of the object.
B) must be at the final position of the object.
C) must be at ground level.
D) must be at the lowest position ever reached by the object.
E) can be chosen arbitrarily.

Answer 2

can be chosen arbitrarily.

Question 3

Which potential energy versus displacement curve best represents that of an extended spring?

A) 1
B) 2
C) 3
D) 4
E) 5

Answer 3

3

Question 4

When the potential energy U(r) is given as in Figure A, then the force is given in Figure B by curve

A) 1
B) 2
C) 3
D) 4
E) 5

Question 5

Calculate the work done by a force, , around a closed path, first going from P₁ (1,1) to P₂ (4,4) along path a and returning along path b.

A) 0 J
B) 3 J
C) 7 J
D) 13 J
E) 17 J

Question 6

A block with a mass M = 4.85 kg is resting on a slide that has a curved surface. There is no friction. The speed of the block after it has slid along the slide sufficiently far for its vertical drop to be 19.6 m is

A) 19.6 m/s
B) 384 m/s
C) 73 m/s
D) 43.2 m/s
E) The problem cannot be solved because the shape of the curved slide is not given.

Question 7

The potential energy function for a conservative force acting in the x direction on a particle is shown below. The number of points where the net force on the particle is equal to zero are

A) B and D.
B) C and E.
C) B, C, D, and E.
D) A and F.
E) any point between C and D.

Question 8

A 5200-kg cable car in Hong Kong is pulled a distance of 360 m up a hill inclined at 12º from the horizontal. The change in the potential energy of the car is

A) 1.8 $\times$ 10⁷ J
B) 1.2 $\times$ 10⁷ J
C) 3.8 $\times$ 10⁶ J
D) 6.0 $\times$ 10⁷ J
E) 1.8 $\times$ 10⁶ J

Question 9

Which of the following statements is true?

A) Friction is a conservative force and does negative work.
B) Potential energy may be defined by the equation U(x) = -dF(x)/dx
C) The work done by a conservative force between two points depends on the path taken between those points.
D) A conservative force cannot change a body's total energy.
E) The work done by a conservative force while a body moves at constant velocity must be zero.

Question 10

A woman runs up a flight of stairs. The gain in her gravitational potential energy is U. If she runs up the same stairs with twice the speed, what is her gain in potential energy?

A) U
B) 2U
C) U
D) 4U
E) U

Question 11

The graph shows a plot of the gravitational potential energy U of a 1-kg body as a function of its height h above the surface of a planet. The acceleration due to gravity at the surface of the planet is

A) 0 m/s²
B) 9.8 m/s²
C) 6.0 m/s²
D) 3.0 m/s²
E) None of these is correct.

Question 12

A block of mass m starts from position 1 and moves up a frictionless inclined plane with an initial speed v. At some later time the block has moved down the plane and at position 2 has a speed u. If a and b are the heights above the bottom of the plane, the magnitude of u can be determined from

A) u² = v² - 2g(a - b)
B) u² = v² + 2g(a + b)
C) u² = v² + 2g(a - b)
D) u² = v² + 2g(b - a)
E) u² = v² + g(a - b)

Question 13

Which of the following statements is NOT correct?

A) The work done by a conservative force on an object is independent on the path taken.
B) The work done by a conservative force on an object along path A $\to$ B is negative that of path B $\to$ A.
C) The force due to gravity is an example of a conservative force.
D) Friction is an example of a conservative force.
E) The work done by friction on an object depends on the path taken.

Question 14

A spring with force constant k = 300 N/m is compressed 9.0 cm. What is the potential energy in the spring?

A) 1.2 $\times$ 10⁴ J
B) 2.4 J
C) 2.7 $\times$ 10⁴ J
D) 27 J
E) 1.2 J

Question 15

The potential energy function for a conservative force acting in the x direction is shown in the figure on the right. Where would the particle experience a force directed to the right?

A) between A & B and E & F
B) between B & C and C & D
C) between B & C and D & E
D) at points B and D
E) at points C and E

Question 16

According to Quantum Chromodynamics, the force that keeps quarks confined within a proton (or neutron) increases as the separation between the individual quarks increases. Which statement below best represents this scenario?

A) The quarks are tied together by nonstretchable strings.
B) The quarks are tied together by elastic strings.
C) The quarks move independently of each other.
D) The force between the quarks has a 1/r² behavior like gravity.
E) The potential energy of a quark decreases with separation.

Question 17

In magazine car tests an important indicator of performance is the zero to 60 mph (0 to 96.6 km/h) acceleration time. A time below 6 s is considered to be extremely quick. If a car with mass 1300 kg were dropped vertically from a great height, how long would it take to go from zero to 60 mph and what would the magnitude of the change in gravitational potential energy be during this time? (neglect air resistance)

A) 2.74 s and 17.4 kJ
B) 2.74 s and 468 kJ
C) 2.74 s and 468 MJ
D) 0.37 s and 468 MJ
E) 2.74 s and 17.4 MJ

Question 18

Calculate the work done by a force, , along the path (0,0) $\to$ P₁ (2,0) $\to$ P₂ (2,2).

A) 2 J
B) 4 J
C) 6 J
D) 8 J
E) 10 J

Question 19

Which of the following statements is true?

A) The kinetic and potential energies of an object must always be positive quantities.
B) The kinetic and potential energies of an object must always be negative quantities.
C) Kinetic energy can be negative but potential energy cannot.
D) Potential energy can be negative but kinetic energy cannot.
E) None of these statements is true.

Question 20

A 75-kg man climbs the stairs to the fifth floor of a building, a total height of 16 m. His potential energy has increased by

A) 1.2 $\times$ 10⁴ J
B) 5.9 $\times$ 10⁴ J
C) 4.7 $\times$ 10⁴ J
D) 3.8 $\times$ 10⁴ J
E) 5.9 $\times$ 10³ J

Question 21

Use the figure to the right for the next problems.
A flexible rope of mass m and length L = L₁ + L₂, hangs over a frictionless peg, as shown in the figure.
What is the speed of the rope when it just slides off the peg?

A)
B)
C)
D)
E)

Question 22

A simple pendulum has a bob of mass M. The bob is on a light string of length . The string is fixed at C. At position A, the string is horizontal and the bob is at rest. The bob is released from A and swings to B, where the string is vertical. The tension in the string when the bob first reaches B is

A)
B) 2Mg
C) Mg
D) Mg
E) None of these is correct.

Question 23

A child is sitting on the seat of a swing with ropes 10 m long. Her father pulls the swing back until the ropes make a 37º angle with the vertical and then releases the swing. If air resistance is neglected, what is the speed of the child at the bottom of the arc of the swing when the ropes are vertical?

A) 11 m/s
B) 8.8 m/s
C) 14 m/s
D) 6.3 m/s
E) 12 m/s

Question 24

A block of mass, m, is pushed up against a spring, compressing it a distance x, and is then released. The spring projects the block along a frictionless horizontal surface, giving the block a speed v. The same spring projects a second block of mass 4m, giving it a speed 3v. What distance was the spring compressed in the second case?

A) x
B) 2x
C) 3x
D) 4x
E) 6x

Question 25

A roller coaster starts from rest at point A. If you ignore friction and take the zero of potential energy to be at C,

A) the kinetic energy of the coaster at D will be equal to its potential energy at A.
B) the kinetic energy of the coaster at E will be equal to its potential energy at C.
C) the kinetic energy of the coaster at C will be equal to its potential energy at B.
D) the kinetic energy of the coaster at B will be equal to its potential energy at C.
E) None of these is correct.

Question 26

A projectile of mass m is propelled from ground level with kinetic energy of 450 J. At the exact top of its trajectory, its kinetic energy is 250 J. To what height above the starting point does the projectile rise?

A) m
B) m
C) m
D) m
E) m

Question 27

Assuming the incline to be frictionless and the zero of gravitational potential energy to be at the elevation of the horizontal line,

A) the kinetic energy of the block just before it collides with the spring will be equal to mgh.
B) the kinetic energy of the block when it has fully compressed the spring will be equal to mgh.
C) the kinetic energy of the block when it has fully compressed the spring will be zero.
D) the kinetic energy of the block just before it collides with the spring will be kx².
E) None of the above statements will be true.

Question 28

The surface shown in the figure is frictionless. If the block is released from rest, it will compress the spring at the foot of the incline

A) 4.00 m
B) 3.24 m
C) 1.57m
D) 0.989 m
E) None of these is correct.

Question 29

A mass, m, slides down a frictionless incline and hits a spring with spring constant k. Find the spring compression when the acceleration of the mass is zero.

A) mg/k
B) mg cos $\theta$ /k
C) mg sin $\theta$ /k
D) mgh sin $\theta$ /(kx)
E) None of the above statements is correct.

Question 30

You ride a roller coaster car of mass 1500 kg down a frictionless track a distance H = 23m above the bottom of a loop as shown. If the loop is 15 m in diameter, the downward force of the rails on your car when it is upside down at the top of the loop is

A) 4.6 $\times$ 10⁴ N
B) 3.1 $\times$ 10⁴ N
C) 1.7 $\times$ 10⁴ N
D) 0.98 kN
E) 1.6 $\times$ 10³ N

Question 31

The block shown in the figure is sliding on a frictionless surface. Its speed when it reaches the level portion of the surface on which it is sliding will be

A) 3.14 m/s
B) 7.67 m/s
C) 9.81 m/s
D) 13.3 m/s
E) None of these is correct.

Question 32

A roller coaster starts from rest at point A. If you ignore friction and take the zero of potential energy to be at C,

A) the kinetic energy of the coaster at D will be equal to its potential energy at A.
B) the kinetic energy of the coaster at E will be equal to its potential energy at C.
C) the kinetic energy of the coaster at C will be equal to its potential energy at A.
D) the kinetic energy of the coaster at B will be equal to its potential energy at C.
E) None of these is correct.

Question 33

Assuming the incline to be frictionless and the zero of gravitational potential energy to be at the elevation of the horizontal line,

A) the kinetic energy of the block just before it collides with the spring will be equal to mgh.
B) the kinetic energy of the block when it has fully compressed the spring will be equal to mgh.
C) the potential energy of the block when it has fully compressed the spring will be zero.
D) the energy stored in the spring plus the gravitational potential energy of the block when it has fully compressed the spring will be equal to mgh.
E) None of the above statements will be true.

Question 34

Two unequal masses hang from either end of a massless cord that passes over a frictionless pulley. Which of the following is true about the gravitational potential energy (U) and the kinetic energy of the system (K) after the masses are released from rest?

A) $\Delta$ U < 0 and $\Delta$ K > 0
B) $\Delta$ U = 0 and $\Delta$ K > 0
C) $\Delta$ U < 0 and $\Delta$ K = 0
D) $\Delta$ U = 0 and $\Delta$ K = 0
E) $\Delta$ U > 0 and $\Delta$ K < 0

Question 35

A body falls through the atmosphere (consider air resistance) gaining 20 J of kinetic energy. How much gravitational potential energy did it lose?

A) 20 J
B) more than 20 J
C) less than 20 J
D) It is impossible to tell without knowing the mass of the body.
E) It is impossible to tell without knowing how far the body falls.

Question 36

A woman on a bicycle traveling at 10 m/s on a horizontal road stops pedaling as she starts up a hill inclined at 3.0º to the horizontal. If friction forces are ignored, how far up the hill does she travel before stopping?

A) 5.1 m
B) 30 m
C) 97 m
D) 10 m
E) The answer depends on the mass of the woman.

Question 37

Release mass m on a string from rest at point A. As it passes the lowest point B, the tension in the string is

A) impossible to determine; the answer depends on the length of the string.
B) mg
C) 2mg
D) 3mg
E) None of these is correct.

Question 38

The total mechanical energy of any system is

A) always the work done by gravity.
B) the difference between the kinetic and potential energy at any point.
C) the sum of the kinetic and potential energy at any point.
D) the sum of the translational and rotational kinetic energies at any point.
E) the potential energy of a spring at any displacement.

Question 39

The block shown in the figure is sliding on a frictionless surface. Its speed when it has traveled 9 m along the horizontal surface will be

A) 3.14 m/s
B) 7.67 m/s
C) 9.81 m/s
D) 13.3 m/s
E) None of these is correct.

Question 40

Use the figure to the right for the next problems.
A flexible rope of mass m and length L = L₁ + L₂, hangs over a frictionless peg, as shown in the figure.
What is the change in potential energy when the end of the rope just slides off the peg?

A) mgL
B) mgL₁
C) mgL₂
D) mgL₁²/(L)
E) mgL₁L₂/(L)

Question 41

Consider a motion in which a particle goes from A $\to$ B along path 1 and from B back to A along path 2, as shown.
W(AB, 1) = work in going from A $\to$ B along path 1.
W(BA, 2) = work in going from B $\to$ A along path 2.
If only conservative forces are acting, then

A) W(AB, 1) > W(BA, 2)
B) W(AB, 1) < W(BA, 2)
C) W(AB, 1) + W(BA, 2) > 0
D) W(AB, 1) + W(BA, 2) < 0
E) W(AB, 1) + W(BA, 2) = 0

Question 42

A mass m is released from a height 60 cm from the right-hand side of the track shown in the diagram at right. There is only friction acting on the mass on the horizontal portion 35 cm either side of the midpoint O, with a kinetic coefficient of friction of $\mu$ _k = 0.5. Determine what is the velocity of the block the first time it passes through the midpoint, and on which side of the midpoint does it stop?

A) 3.4 m/s, R
B) 3.9 m/s, R
C) 3.9 m/s, L
D) 2.9 m/s, L
E) 2.9 m/s, R

Question 43

Use the figure to the right to answer the next problems.
An object of mass m = 100 g slides down without rolling a rough incline from a height H = 60 cm. At
h = 30 cm, the object flies off the incline. The coefficient of kinetic friction is 0.4, and the angle $\theta$ = 30 ^$\circ$ .

-How far from the base of the elevated incline does the object hit the floor?

A) 14.8 cm
B) 17.5 cm
C) 21.9 cm
D) 24.6 cm
E) None of these is correct.

Question 44

Use the figure to the right for the next problem.
An object of mass m = 200 g slides down a frictionless ramp from a height H = 60 cm. Near the bottom of the ramp, the path changes into an arc of a circle with radius r = 20 cm. The arc has coefficient of kinetic friction $\mu$ _k = 0.4. The
angle $\theta$ = 120 ^$\circ$ and points P₁ and P₂ which are the ends of the arc, are at the same height.

-What is the speed of the object at point P₁?

A) 1.1 m/s
B) 2.5 m/s
C) 3.1 m/s
D) 3.4 m/s
E) 4.1 m/s

Question 45

A hanging block A (m_A = 15 kg) is connected by a light cable and a pulley wheel to a second block B (m_B = 10 kg) situated at the bottom of a frictionless inclined plane with angle 30 ^$\circ$ to the horizontal. If the hanging block is released from rest 5 m above the ground, find the maximum distance that block B travels up along the inclined plane.

A) 9.0 m
B) 4.0 m
C) 2.3 m
D) 7.3 m
E) 6.5 m

Question 46

A system comprising two blocks is shown, one of which is on an inclined plane. The pulley is of negligible mass and is frictionless. The system starts from rest at position 1 and accelerates. Measurements taken when the blocks reach position 2 indicate that
(1)the kinetic energy of block A has changed by 330 J;
(2)the potential energy of block A has changed by 588 J;
(3)the kinetic energy of block B has changed by 110 J; and
(4)the potential energy of block B has changed by 98 J.
The amount of mechanical energy that has been converted to heat because of friction is

A) 12 J
B) 50 J
C) 258 J
D) 478 J
E) 710 J

Question 47

Use the figure to the right for the next problem.
An object of mass m = 200 g slides down a frictionless ramp from a height H = 60 cm. Near the bottom of the ramp, the path changes into an arc of a circle with radius r = 20 cm. The arc has coefficient of kinetic friction $\mu$ _k = 0.4. The
angle $\theta$ = 120 ^$\circ$ and points P₁ and P₂ which are the ends of the arc, are at the same height.

-What is the kinetic energy of the object at point P₂?

A) 0.27 J
B) 0.71 J
C) 0.98 J
D) 1.25 J
E) none of the above

Question 48

Use the figure to the right to answer the next problems.
An object of mass m = 100 g slides down without rolling a rough incline from a height H = 60 cm. At
h = 30 cm, the object flies off the incline. The coefficient of kinetic friction is 0.4, and the angle $\theta$ = 30 ^$\circ$ .

-According to the mass-energy relationship, how much energy is released if 1 kg of matter were converted to energy?

A) 1 J
B) 9 J
C) 3 $\times$ 10⁸ J
D) 3 $\times$ 10¹⁶ J
E) 9 $\times$ 10¹⁶ J

Question 49

A 10-kg box is pushed up a plane inclined at 37º with the horizontal. The box starts from rest and is pushed 5 m along the incline with a uniform acceleration of 2 m/s². The coefficient of kinetic friction is 0.20 and the pushing force is parallel to the plane. The increase in the potential energy of the box is

A) 0.10 kJ
B) 0.29 kJ
C) 0.36 kJ
D) 0.46 kJ
E) 0.39 kJ

Question 50

A 10-kg box is at the top of a 5-m plane inclined at 37º with the horizontal. The box starts from rest and slides down the plane. The coefficient of kinetic friction is 0.20. The magnitude of the change in the potential energy of the box is

A) 30 kJ
B) 0.10 kJ
C) 0.29 kJ
D) 0.46 kJ
E) 0.39 kJ

Question 51

A 5-kg blob of putty is dropped from a height of 10.0 m above the ground onto a light vertical spring the top of which is 5 m above the ground. If the spring constant k = 200 N/m and the blob compresses the spring by 1.50 m, then find the amount of energy lost in sound and thermal energy.

A) 20.0 J
B) 169 J
C) 266 J
D) 438 J
E) 94.0 J

Question 52

A 4.0-kg block starts from rest and slides 5.0 m down a plane inclined at 60º to the horizontal. The coefficient of kinetic friction between the surface and the block is 0.20. The work done by friction on the block is

A) 98.0 J
B) 19.6 J
C) 3.92 J
D) 3.40 J
E) 64.0 J

Question 53

A 5-kg mass with initial velocity 20 m/s slides along a frictionless horizontal surface then up a frictionless ramp (2 m long and at an angle 30 degrees to the horizontal) and onto a second horizontal surface. The block slides over a rough surface 15 m in length ( $\mu$ _k = 0.4) before moving again on a frictionless surface and then impacting upon an uncompressed spring. If the block compresses the spring a distance 2 m, what is the spring constant k for the spring?

A) 304 N/m
B) 451 N/m
C) 84.0 N/m
D) 32.8 N/m
E) 353 N/m

Question 54

A mass m is released from a height 75 cm from the right-hand side of the track shown in the diagram at right. There is only friction acting on mass along the horizontal portion 30 cm either side of the midpoint O, with a kinetic coefficient of friction of $\mu$ _k = 0.4. Determine how high it reaches the second time it passes over to the left side, and in which direction is it moving when it stops?

A) 27 cm, R
B) 3.0 cm, R
C) 27 cm, L
D) 3.0 cm, L
E) 51 cm, R

Question 55

A mass m is released from a height 80 cm from the right-hand side of the track shown in the diagram at right. There is only friction acting along the horizontal portion 30 cm either side of the midpoint O with a kinetic coefficient of friction of $\mu$ _k = 0.4. Determine (i) how many times does the mass m pass through the midpoint O, and (ii) how far from the midpoint does it come to rest.

A) 6, .1 m
B) 6, .2 m
C) 3, .2 m
D) 3, .1 m
E) 1, 2 cm

Question 56

A 3-kg block sits on an incline where the top half of the incline has a coefficient of kinetic friction of 0.5 and the bottom half is frictionless. The angle of inclination is 35 degrees. If the block is released and travels 10 m along the rough part of the incline and then 10 m along the smooth part before it makes contact with the spring (k = 200 N/m), calculate the distance the spring is compressed.

A) 1.47 m
B) 1.56 m
C) 2.16 m
D) 2.43 m
E) 1.39 m

Question 57

Use the figure to the right for the next problem.
An object of mass m = 200 g slides down a frictionless ramp from a height H = 60 cm. Near the bottom of the ramp, the path changes into an arc of a circle with radius r = 20 cm. The arc has coefficient of kinetic friction $\mu$ _k = 0.4. The
angle $\theta$ = 120 ^$\circ$ and points P₁ and P₂ which are the ends of the arc, are at the same height.

-A 5-kg box is pushed 5 m up a plane that is inclined at 30º with the horizontal. The coefficient of kinetic friction between the box and the plane is 0.20. The change in potential energy of the box is approximately

A) 12.5 J
B) 34.2 J
C) 123 J
D) 345 J
E) 403 J

Question 58

Use the figure to the right to answer the next problems.
An object of mass m = 100 g slides down without rolling a rough incline from a height H = 60 cm. At
h = 30 cm, the object flies off the incline. The coefficient of kinetic friction is 0.4, and the angle $\theta$ = 30 ^$\circ$ .

-What is the speed of the object just after it leaves the ramp?

A) 2.40 m/s
B) 1.34 m/s
C) 0.77 m/s
D) 0.54 m/s
E) None of these is correct.

Question 59

You drive a golf ball from A and it travels to B. The weight of the ball is w. The decrease in its potential energy is given by

A) (r + t)w
B) (a + s + t)w
C) (a + b)w
D) (a + b + c)w
E) None of these is correct.

Question 60

Use the figure to the right for the next problem.
An object of mass m = 200 g slides down a frictionless ramp from a height H = 60 cm. Near the bottom of the ramp, the path changes into an arc of a circle with radius r = 20 cm. The arc has coefficient of kinetic friction $\mu$ _k = 0.4. The
angle $\theta$ = 120 ^$\circ$ and points P₁ and P₂ which are the ends of the arc, are at the same height.

-The work done by a conservative force between two points is

A) always positive.
B) always dependent upon the time.
C) always independent of the path.
D) zero.
E) never completely recoverable.

Question 61

Newtonian mechanics, compared to Einstein's Special Relativity is valid if

A) an object is traveling at a constant velocity.
B) an object has a very small mass.
C) the kinetic energy of an object is much less than its rest mass.
D) an object is not traveling at the speed of light.
E) the kinetic energy of an object is much greater than its rest mass.

Question 62

When a hydrogen atom absorbs a photon with E = 4.089 $\times$ 10^-19 J, what is the frequency of the photon?

A) 6.17 $\times$ 10¹⁴ Hz
B) 2.45 $\times$ 10¹⁸ Hz
C) 2.55 $\times$ 10⁸ Hz
D) 6.623 $\times$ 10³⁴ Hz
E) None of these is correct.

Question 63

The rest mass of a proton is 1.67 $\times$ 10^-27 kg. From this information one can conclude that the rest energy of a proton is

A) 1.50 $\times$ 10^-10 MeV
B) 3.13 MeV
C) 847 MeV
D) 939 MeV
E) 742 MeV

Question 64

The binding energy of a deuteron is 2.22 MeV. This means that

A) deuterons can be broken up by bombarding them with electromagnetic radiation possessing energy of at least 2.22 MeV.
B) deuterons can be broken up by bombarding them with particles possessing energy of at least 2.22 MeV.
C) if the deuterons are bombarded with particles whose energy exeeds 2.22 MeV, the excess energy appears as kinetic energy of the outgoing particles.
D) if the deuterons are bombarded with particles whose energy is less than 2.22 MeV, they will not be decomposed into their constituent parts.
E) all of these are correct.

Question 65

Which of the following are units of mass?

A) MeV
B) MeV·c²
C) c²/MeV
D) 1/MeV
E) MeV/c²

Question 66

If you drive at the posted speed limit of 70 mph on the interstate, what is the fraction of your speed compared to the speed of light?

A) 6.48 $\times$ 10^-8
B) 1.04 $\times$ 10^-7
C) 2.33 $\times$ 10^-7
D) 3.73 $\times$ 10^-7
E) None of these is correct.

Question 67

Use the figure to the right to answer the next problems.
An object of mass m = 100 g slides down without rolling a rough incline from a height H = 60 cm. At
h = 30 cm, the object flies off the incline. The coefficient of kinetic friction is 0.4, and the angle $\theta$ = 30 ^$\circ$ .

-The minimum amount of energy released in an electron-positron annihilation is

A) 0
B) 0.511 MeV
C) 1.022 MeV
D) 2.044 MeV
E) None of these is correct.

Question 68

When an electron in a hydrogen atom jumps from n = 2 to n = 1, the photon emitted is of frequency f = 4.572 $\times$ 10¹⁴ Hz. What is the energy of the photon?

A) 2.187 $\times$ 10^-15 J
B) 3.029 $\times$ 10^-19 J
C) 3.33 $\times$ 10^-9 J
D) 6.623 $\times$ 10^-34 J
E) None of these is correct.

Question 69

Which of the following are units of energy?

A) MeV
B) MeV·c²
C) c²/MeV
D) 1/MeV
E) MeV/c²

Question 70

A proton has a rest mass of 938 MeV. From this information one can conclude that the rest mass of a proton is

A) 5.00 $\times$ 10^-19 kg
B) 1.50 $\times$ 10^-10 kg
C) 1.67 $\times$ 10^-27 kg
D) 1.04 $\times$ 10^-8 kg
E) 2.34 $\times$ 10^-29 kg

Question 71

An electron has a rest mass of 0.511 MeV. From this information one can conclude that the rest mass of an electron is

A) 9.08 $\times$ 10^-31 kg
B) 8.82 $\times$ 10^-14 kg
C) 2.94 $\times$ 10^-22 kg
D) 5.68 $\times$ 10^-12 kg
E) None of these is correct.

Question 72

By what fraction does your mass increase when you and your car travel down the highway at 70 mph? Assume that the total mass of your car and occupant is 2000 kg.

A) 5.38 $\times$ 10^-15
B) 1.08 $\times$ 10 ^-11
C) 3.23 $\times$ 10^-6
D) 9.68 $\times$ 10⁵
E) None of these is correct.

Question 73

The rest mass of an electron is 9.11 $\times$ 10^-31 kg. From this information one can conclude that the rest energy of an electron is

A) 8.20 $\times$ 10^-14 MeV
B) 0.512 MeV
C) 2.73 $\times$ 10^-22 J
D) 0.00171 MeV
E) 0.171 MeV