Deck 7: Conservation of Energy

Question 1

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

Answer 1

0 J

Question 2

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 2

Susana gains the same gravitational potential energy as Sean.

Question 3

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 3

can be chosen arbitrarily.

Question 4

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 5

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 6

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 7

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 8

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 9

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 10

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

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

Question 11

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 12

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 13

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 14

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 15

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 16

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 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

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 19

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 20

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 21

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 22

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 23

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 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

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 26

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 27

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 28

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 29

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 30

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 31

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 32

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 33

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 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

Use the figure to the right for the next problem. 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 36

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 37

Use the figure to the right for the next problem. 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 38

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 39

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 40

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 41

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 42

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 $\times$ ^-22 kg
D)5.68 $\times$ 10 ^-12 kg
E)None of these is correct.

Question 43

Which of the following are units of mass?

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

Question 44

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 45

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 46

Which of the following are units of energy?

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

Question 47

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 48

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 49

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 50

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 51

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 52

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 53

Use the figure to the right to answer the next problem. 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 = 30
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 54

Use the figure to the right to answer the next problem. 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 = 30
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 55

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

Question 56

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.