Deck 9: Work and Kinetic Energy

Question 1

If the dot product of two nonzero vectors is zero,the vectors must be perpendicular to each other.

Answer 1

True

Question 2

Determine the scalar product of = 6.0 + 4.0 - 2.0 and = 5.0 - 6.0 - 3.0 .

A)30 + 24 + 6
B)30 - 24 + 6
C)12
D)60
E)undefined

Answer 2

12

Question 3

Two men,Joel and Jerry,push against a wall.Jerry stops after 10 min,while Joel is able to push for 5.0 min longer.Compare the work they do.

A)Both men do positive work,but Joel does 75% more work than Jerry.
B)Both men do positive work,but Joel does 50% more work than Jerry.
C)Both men do positive work,but Jerry does 50% more work than Joel.
D)Both men do positive work,but Joel does 25% more work than Jerry.
E)Neither of them does any work.

Answer 3

Neither of them does any work.

Question 4

Determine the angle between the directions of vector = 3.00 + 1.00 and vector = -3.00 + 3.00 .

A)26.6°
B)30.0°
C)88.1°
D)117°
E)45.2°

Question 5

If a force always acts perpendicular to an object's direction of motion,that force cannot change the object's kinetic energy.

Question 6

Two boys searching for buried treasure are standing underneath the same tree.One boy walks east and then north.The other boy walks west and then north.Find the scalar product of their net displacements from the tree.

Question 7

The value of the dot product of two vectors depends on the particular coordinate system being used.

Question 8

What is the angle between the vector = +3 - 2 - 3 and the +y-axis?

A)115°
B)65°
C)25°
D)155°
E)90°

Question 9

Two objects,one of mass m and the other of mass 2m,are dropped from the top of a building.When they hit the ground

A)both of them will have the same kinetic energy.
B)the heavier one will have twice the kinetic energy of the lighter one.
C)the heavier one will have four times the kinetic energy of the lighter one.
D)the heavier one will have times the kinetic energy of the lighter one.

Question 10

Which of the graphs in the figure represents a spring that gets less stiff the more it is stretched?

A)Graph a
B)Graph b
C)Graph c
D)Graph d

Question 11

The angle between vector = 2.00 + 3.00 and vector is The scalar product of vectors and is 3.00.If the x component of vector is positive,what is vector .

A)
B)
C)
D)
E)

Question 12

The scalar product of vector = 3.00 + 2.00 and vector is 10.0.Which of the following vectors could be vector ?

A)2.00 + 4.00
B)4.00 + 6.00
C)5.00 + 4.00
D)12.0
E)2.00 + 2.00

Question 13

If two nonzero vectors point in the same direction,their dot product must be zero.

Question 14

Consider a plot of the displacement (x)as a function of the applied force (F)for an ideal elastic spring.The slope of the curve would be

A)the spring constant.
B)the reciprocal of the spring constant.
C)the acceleration due to gravity.
D)the reciprocal of the acceleration of gravity.
E)the mass of the object attached to the spring.

Question 15

Which of the graphs in the figure illustrates Hooke's Law?

A)Graph a
B)Graph b
C)Graph c
D)graph d

Question 16

A 4.0-kg object is moving with speed 2.0 m/s.A 1.0-kg object is moving with speed 4.0 m/s.Both objects encounter the same constant braking force,and are brought to rest.Which object travels the greater distance before stopping?

A)the 4.0-kg object
B)the 1.0-kg object
C)Both objects travel the same distance.
D)It is impossible to know without knowing how long each force acts.

Question 17

A rectangular box is positioned with its vertices at the following points: A = (0,0,0)C = (2,4,0)E = (0,0,3)G = (2,4,3)
B = (2,0,0)D = (0,4,0)F = (2,0,3)H = (0,4,3)
If the coordinates all have three significant figures,the angle between the line segments AG and AH is closest to:

A)21.8°.
B)22.5°.
C)26.6°.
D)36.9°.
E)45.0°.

Question 18

A 3.00-kg ball swings rapidly in a complete vertical circle of radius 2.00 m by a light string that is fixed at one end.The ball moves so fast that the string is always taut and perpendicular to the velocity of the ball.As the ball swings from its lowest point to its highest point

A)the work done on it by gravity and the work done on it by the tension in the string are both equal to -118 J.
B)the work done on it by gravity is -118 J and the work done on it by the tension in the string is +118 J.
C)the work done on it by gravity is +118 J and the work done on it by the tension in the string is -118 J.
D)the work done on it by gravity is -118 J and the work done on it by the tension in the string is zero.
E)the work done on it by gravity and the work done on it by the tension in the string are both equal to zero.

Question 19

If = 3 - + 4 and = x + - 5 ,find x so will be perpendicular to .

Question 20

A stock person at the local grocery store has a job consisting of the following five segments: (1)picking up boxes of tomatoes from the stockroom floor
(2)accelerating to a comfortable speed
(3)carrying the boxes to the tomato display at constant speed
(4)decelerating to a stop
(5)lowering the boxes slowly to the floor.
During which of the five segments of the job does the stock person do positive work on the boxes?

A)(1)and (5)
B)(1)only
C)(1),(2),(4),and (5)
D)(1)and (2)
E)(2)and (3)

Question 21

You carry a 7.0 kg bag of groceries above the level floor at a constant velocity of 75 cm/s across a room that is room.How much work do you do on the bag in the process?

A)0.0 J
B)82 J
C)158 J
D)134 J

Question 22

An object is acted upon by a force that represented by the force vs.position graph in the figure.What is the work done as the object moves
(a)from 4 m to 6 m?
(b)from 6 m to 12 m?

Question 23

Find the net work done by friction on the body of a snake slithering in a complete circle of radius.The coefficient of friction between the ground and the snake is 0.25,and the snake's weight is

A)-330 J
B)0 J
C)-3300 J
D)-670 J

Question 24

Three forces,F₁ = 20.0 N,F₂ = 40.0 N,and F₃ = 10.0 N act on an object with a mass of 2.00 kg which can move along a frictionless inclined plane as shown in the figure.The questions refer to the instant when the object has moved through a distance of 0.600 m along the surface of the inclined plane in the upward direction.Calculate the amount of work done by
(a)F₁
(b)F₂
(c)F₃.

Question 25

In the figure,two identical ideal massless springs have unstretched lengths of 0.25 m and spring constants of 700 N/m.The springs are attached to a small cube and stretched to a length L of 0.30 m as in Figure A.An external force P pulls the cube a distance D = 0.020 m to the right and holds it there.(See Figure B.)The external force P,that holds the cube in place in Figure B,is closest to

A)28 N.
B)25 N.
C)21 N.
D)18 N.
E)14 N.

Question 26

A spring stretches by when a object is attached.What is the weight of a fish that would stretch the spring by

A)199 N
B)91.0 N
C)145 N
D)279 N

Question 27

Block A (0.40 kg)and block B (0.30 kg)are on a frictionless table (see figure).Spring 1 connects block A to a frictionless peg at 0 and spring 2 connects block A and block B.When the blocks are in uniform circular motion about 0,the springs have lengths of 0.60 m and 0.40 m,as shown.The springs are ideal and massless,and the linear speed of block B is 2.0 m/s.If the spring constant of spring 1 is equal to 30 N/m,the unstretched length of spring 1 is closest to

A)0.51 m.
B)0.52 m.
C)0.53 m.
D)0.54 m.
E)0.55 m.

Question 28

A force = 12 N - 10 N acts on an object.How much work does this force do as the object moves from the origin to the point

A)46 J
B)266 J
C)37 J
D)62 J

Question 29

In the figure,a 700-kg crate is on a rough surface inclined at 30°.A constant external force P = 5600 N is applied horizontally to the crate.As the force pushes the crate a distance of 3.00 m up the incline,the speed changes from 1.40 m/s to 2.50 m/s.How much work does gravity do on the crate during this process?

A)-10,300 J
B)-3400 J
C)+10,300 J
D)+3400 J
E)zero

Question 30

An airplane flies 120 km at a constant altitude in a direction 30.0° north of east.A wind is blowing that results in a net horizontal force on the plane due to the air of 2.40 kN in a direction 10.0° south of west.How much work is done on the plane by the air?

A)-2.71 × 10⁸ J
B)-0.985 × 10⁸ J
C)-221 × 10⁸ J
D)221 × 10⁸ J
E)0.821 × 10⁸ J

Question 31

A traveler pulls on a suitcase strap at an angle 36° above the horizontal.If of work are done by the strap while moving the suitcase a horizontal distance of 15 m,what is the tension in the strap?

A)75 N
B)61 N
C)85 N
D)92 N

Question 32

Block A (0.40 kg)and block B (0.30 kg)are on a frictionless table (see figure).Spring 1 connects block A to a frictionless peg at 0 and spring 2 connects block A and block B.When the blocks are in uniform circular motion about 0,the springs have lengths of 0.60 m and 0.40 m,as shown.The springs are ideal and massless,and the linear speed of block B is 2.0 m/s.If the distance that spring 2 stretches is 0.060 m,the spring constant of spring 2 is closest to

A)18 N/m.
B)20 N/m.
C)22 N/m.
D)24 N/m.
E)26 N/m.

Question 33

A force on a particle depends on position such that F(x)= (3.00 N/ ) + (6.00 N/m)x for a particle constrained to move along the x-axis.What work is done by this force on a particle that moves from x = 0.00 m to x = 2.00 m?

A)10.0 J
B)20.0 J
C)-48.0 J
D)24.0 J
E)48.0 J

Question 34

A student slides her 80.0-kg desk across the level floor of her dormitory room a distance 4.00 m at constant speed.If the coefficient of kinetic friction between the desk and the floor is 0.400,how much work did she do?

A)128 J
B)3.14 kJ
C)26.7 J
D)1.26 kJ
E)24.0 J

Question 35

An object attached to an ideal massless spring is pulled across a frictionless surface.If the spring constant is 45 N/m and the spring is stretched by 0.88 m when the object is accelerating at what is the mass of the object?

A)20 kg
B)17 kg
C)22 kg
D)26 kg

Question 36

In the figure,a constant external force P = 160 N is applied to a 20.0-kg box,which is on a rough horizontal surface.While the force pushes the box a distance of 8.00 m,the speed changes from 0.500 m/s to 2.60 m/s.The work done by friction during this process is closest to

A)-1040 J.
B)+1110 J.
C)+1170 J.
D)+1040 J.
E)-1170 J.

Question 37

A graph of the force on an object as a function of its position is shown in the figure.Determine the amount of work done by this force on the object during a displacement from x = -2.00 m to x = 2.00 m.(Assume an accuracy of 3 significant figures for the numbers
On the graph.)

A)-12.0 J
B)-3.00 J
C)-1.00 J
D)12.0 J
E)3.00 J

Question 38

A graph of the force on an object as a function of its position is shown in the figure.Determine the amount of work done by this force on an object that moves from x = 1.0 m to x = 6.0 m.(Assume an accuracy of 2 significant figures for the numbers on the graph.)

A)26 J
B)29 J
C)22 J
D)35 J
E)27 J

Question 39

For the vectors shown in the figure,assume numbers are accurate to two significant figures.The scalar product × is closest to

A)zero.
B)16.
C)45.
D)-16.
E)-45.

Question 40

A crane lifts a 425 kg steel beam vertically a distance of How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s²? Neglect frictional forces.

A)5.8 × 10⁵ J
B)3.4 × 10⁵ J
C)4.0 × 10⁵ J
D)4.9 × 10^{5 J}

Question 41

A 5.00-kg box slides 4.00 m across the floor before coming to rest.What is the coefficient of kinetic friction between the floor and the box if the box had an initial speed of 3.00 m/s?

A)1.13
B)0.587
C)0.115
D)0.229
E)0.267

Question 42

A person pushes horizontally on a heavy box and slides it across the level floor at constant velocity.The person pushes with a 60.0 N force for the first at which time he begins to tire.The force he exerts then starts to decrease linearly from 60.0 N to 0.00 N across the remaining How much total work did the person do on the box?

A)619 J
B)826 J
C)495 J
D)925 J

Question 43

A 4.00-kg mass is attached to a very light ideal spring hanging vertically and hangs at rest in the equilibrium position.The spring constant of the spring is 1.00 N/cm.The mass is pulled downward 2.00 cm and released.What is the speed of the mass when it is 1.00 cm above the point from which it was released?

A)0.0443 m/s
B)0.0744 m/s
C)0.0201 m/s
D)0.0866 m/s
E)The mass will not reach the height specified.

Question 44

How much energy is needed to change the speed of a 1600 kg sport utility vehicle from 15.0 m/s to 40.0 m/s?

A)1.10 MJ
B)10.0 kJ
C)20.0 kJ
D)40.0 kJ
E)0.960 MJ

Question 45

A worker lifts a 20.0-kg bucket of concrete from the ground up to the top of a 20.0-m tall building.The bucket is initially at rest,but is traveling at 4.0 m/s when it reaches the top of the building.What is the minimum amount of work that the worker did in lifting the bucket?

A)3.92 kJ
B)400 J
C)560 J
D)4.08 kJ
E)160 J

Question 46

A force F = bx³ acts in the x direction,where the value of b is 3.7 N/m³.How much work is done by this force in moving an object from to

A)42 J
B)13 J
C)50 J
D)57 J

Question 47

A ball is thrown upward at an angle with a speed and direction such that it reaches a maximum height of 16.0 m above the point it was released,with no appreciable air resistance.At its maximum height it has a speed of 18.0 m/s.With what speed was the ball released?

A)25.3 m/s
B)22.2 m/s
C)33.0 m/s
D)29.2 m/s
E)36.9 m/s

Question 48

An unusual spring has a restoring force of magnitude F = (2.00 N/m)x + (1.00 N/m²)x²,where x is the stretch of the spring from its equilibrium length.A 3.00-kg object is attached to this spring and released from rest after stretching the spring 1.50 m.If the object slides over a frictionless horizontal surface,how fast is it moving when the spring returns to its equilibrium length?

A)2.06 m/s
B)4.33 m/s
C)3.27 m/s
D)5.48 m/s
E)1.50 m/s

Question 49

The coefficient of the restitution of an object is defined as the ratio of its outgoing to incoming speed when the object collides with a rigid surface.For an object with a coefficient of 0.78,what fraction of the object's kinetic energy is lost during a single collision?

A)39%
B)16%
C)47%
D)61%

Question 50

A 1000.0 kg car is moving at If a truck has 18 times the kinetic energy of the car,how fast is the truck moving?

A)45 km/h
B)63 km/h
C)54 km/h
D)36 km/h

Question 51

In the figure,two boxes,each of mass 24 kg,are at rest and connected as shown.The coefficient of kinetic friction between the inclined surface and the box is 0.31.Find the speed of the boxes just after they have moved 1.6 m.

Question 52

A constant horizontal pull acts on a sled on a horizontal frictionless ice pond.The sled starts from rest.When the pull acts over a distance x,the sled acquires a speed v and a kinetic energy K.If the same pull instead acts over twice this distance:

A)The sled's speed will be 2v and its kinetic energy will be 2K.
B)The sled's speed will be 2v and its kinetic energy will be K .
C)The sled's speed will be v and its kinetic energy will be 2K.
D)The sled's speed will be v and its kinetic energy will be K .
E)The sled's speed will be 4v and its kinetic energy will be 2K.

Question 53

A 1500-kg car accelerates from 0 to 25 m/s in 7.0 s with negligible friction and air resistance.What is the average power delivered by the engine? (1 hp = 746 W)

A)50 hp
B)60 hp
C)70 hp
D)80 hp
E)90 hp

Question 54

A 7.0-kg rock is subject to a variable force given by the equation
F(x)= 6.0 N - (2.0 N/m)x + (6.0 N/m²)x²
If the rock initially is at rest at the origin,find its speed when it has moved 9.0 m.

Question 55

It requires 49 J of work to stretch an ideal very light spring from a length of 1.4 m to a length of 2.9 m.What is the value of the spring constant of this spring?

A)15 N/m
B)44 N/m
C)29 N/m
D)22 N/m

Question 56

In the figure,two identical springs have unstretched lengths of 0.25 m and spring constants of 300 N/m.The springs are attached to a small cube and stretched to a length L of 0.36 m as in Figure A.An external force P pulls the cube a distance D = 0.020 m to the right and holds it there.(See Figure B.)The work done by the external force P in pulling the cube 0.020 m is closest to

A)0.12 J.
B)0.060 J.
C)6.0 J.
D)12 J.
E)0.80 J.

Question 57

A 1000 kg car experiences a net force of 9500 N while decelerating from 30.0 m/s to 23.4 m/s.How far does it travel while slowing down?

A)18.5 m
B)17.4 m
C)20.2 m
D)21.9 m

Question 58

The force on a 3.00-kg object as a function of position is shown in the figure.If an object is moving at 2.50 m/s when it is located at x = 2.00 m,what will its speed be when it reaches x = 8.00 m? (Assume that the numbers on the graph are accurate to 3 significant figures.)

A)3.25 m/s
B)3.70 m/s
C)4.10 m/s
D)2.90 m/s
E)4.50 m/s

Question 59

In the figure,a 900-kg crate is on a rough surface inclined at 30°.A constant external force is applied horizontally to the crate.While this force pushes the crate a distance of 3.0 m up the incline,its velocity changes from 1.2 m/s to 2.3 m/s.How much work does friction do during this process?

A)-3700 J
B)-7200 J
C)+3700 J
D)+7200 J
E)zero

Question 60

You slam on the brakes of your car in a panic,and skid a certain distance on a straight,level road.If you had been traveling twice as fast,what distance would the car have skidded,under identical conditions?

A)It would have skidded 4 times farther.
B)It would have skidded 2 times farther.
C)It would have skidded times farther.
D)It would have skidded 1/ times farther.
E)It would have skidded 1/2 as far.

Question 61

A child pulls on a wagon with a horizontal force of If the wagon moves horizontally a total of in what is the average power generated by the child?

A)18 W
B)22 W
C)24 W
D)27 W

Question 62

Calculate the minimum average power output necessary for a person to run up a 12.0 m long hillside,which is inclined at 25.0° above the horizontal,in 3.00 s.You can neglect the person's kinetic energy.Express your answer in horsepower.(1 hp = 746 W)

A)1.24 hp
B)2.93 hp
C)1.86 hp
D)0.740 hp

Question 63

How long will it take a 7.08 hp motor to lift a 250 kg beam directly upward at constant velocity from the ground to a height of 45.0 m? Assume frictional forces are negligible.(1 hp = 746 W)

A)20.9 s
B)1.56 × 10⁴ s
C)2.18 × 10⁴ s
D)39.7 s

Question 64

The work performed as a function of time for a process is given by where What is the instantaneous power output at

A)99 W
B)69 W
C)139 W
D)208 W

Question 65

A car needs to generate in order to maintain a constant velocity of on a flat road.What is the magnitude of the total resistive force acting on the car (due to friction,air resistance,etc.)? (1 hp = 746 W)

A)2.05 × 10³ N
B)2.75 N
C)1.03 × 10³ N
D)2.87 × 10³ N

Question 66

If electricity costs 6.00¢/kWh (kilowatt-hour),how much would it cost you to run a 120 W stereo system 4.0 hours per day for 4.0 weeks?

A)$0.81
B)$0.12
C)$1.38
D)$2.27