Deck 11: Static Equilibrium

Question 1

The potential energy of an object is given by U(x)= x⁴ - x²,where U is measured in joules and x is measured in meters.At which position is the object in unstable equilibrium?

A)only at 0
B)only at 0.707 m
C)only at -0.707 m
D)at both +0.707 m and -0.707 m
E)There isn't a location where the object is in unstable equilibrium.

Answer 1

only at 0

Question 2

An object is in static equilibrium.It's then moved a short distance to the right and released.If the equilibrium is neutral,then what will happen next?

A)It will continue moving to the right.
B)It will move back to the left.
C)It will remain stationary in the new position.
D)There isn't enough information to determine what will happen next.

Answer 2

It will remain stationary in the new position.

Question 3

A 20-kg child sits on a see saw on the playground,3.0 m from the pivot.A 2^nd child is seated on the other side of the pivot and 2.00 m from the pivot.The mass of the second child needed to lift the first child off the ground is

A)20 kg.
B)30 kg.
C)40 kg.
D)50 kg.

Answer 3

30 kg.

Question 4

A 30-kg uniform ladder 12 m long is leaning against a frictionless wall at an angle of 50 degrees above the horizontal.A 45-kg boy climbs 5.0 m up the ladder.What is the magnitude of the force exerted by the ladder on the wall?

A)200 N
B)110 N
C)280 N
D)140 N
E)550 N

Question 5

A 343-kg solid granite cube with each side 52 cm long rests on a level floor.What is the magnitude of the force that is applied directly upward on one of the vertical sides of the cube to just start lifting the bottom edge on that side off the floor?

A)1240 N
B)1680 N
C)4360 N
D)841 N
E)3360 N

Question 6

The potential energy of an object is given by U(x)= x⁴ - x²,where U is measured in joules and x is measured in meters.At which position is the object in stable equilibrium?

A)only at 0
B)only at 0.707 m
C)only at -0.707 m
D)at both +0.707 m and -0.707 m
E)There isn't a location where the object is in stable equilibrium.

Question 7

A construction supervisor of mass M = 80.0 kg is standing on a board of mass m = 30.0 kg.Two sawhorses at a distance L = 4.00 m apart support the board.If the man stands a distance x₁ = 1.25 m away from sawhorse 1 as shown,what is the force that the board exerts on that sawhorse?

A)785 N
B)396 N
C)687 N
D)392 N
E)294 N

Question 8

A 5.0-m long uniform ladder leans against a smooth wall and its base rests on a rough floor.The ladder has a mass of 18.0 kg and its base is a distance of 2.3 m from the wall.If the ladder is to remain in place,what frictional force must be exerted by the floor on the ladder?

A)45 N
B)68 N
C)73 N
D)94 N

Question 9

A 5.00-m long uniform ladder leans against a smooth wall and its base rests on a rough floor.The ladder has a mass of 18.0 kg and its base is a distance of 2.30 m from the wall.A person of mass 80.0 kg climbs 2.50 m up the ladder.If the ladder is to remain in place,what frictional force must be exerted by the floor on the ladder?

A)100 N
B)150 N
C)205 N
D)249 N
E)300 N

Question 10

A 25-kg uniform ladder 8.0 m long is leaning against a frictionless wall at an angle of 75 degrees above the horizontal.A 40-kg boy climbs 6.0 m up the ladder.What is the magnitude of the frictional force exerted on the ladder by the floor?

A)200 N
B)110 N
C)280 N
D)140 N
E)550 N

Question 11

A 33-kg bowling ball is held up on a frictionless vertical wall by a string.The string goes from the bowling ball to an attachment point on the wall directly above the ball.The string makes an angle of 34 ^$\circ$ with respect to vertical.The horizontal force that the wall exerts on the ball is

A)324 N.
B)480 N.
C)195 N.
D)521 N.
E)218 N.

Question 12

A flat,horizontal uniform plank is supported underneath by a triangular wedge which itself rests on flat,level ground.An object that has the same weight as the plank is placed on the left end of the plank.Where must the wedge be placed under the plank in order for the system to be in equilibrium?

A)1/6 the length of the plank from the left end
B)1/5 the length of the plank from the left end
C)1/4 the length of the plank from the left end
D)1/3 the length of the plank from the left end

Question 13

A basketball is at rest on top of a smooth rounded hill.This is an example of which kind of equilibrium?

A)stable
B)unstable
C)neutral
D)None are correct.

Question 14

A uniform plank of length 5.00 m and weight 225 N rests horizontally on two supports.The left support is directly under the left end of the plank and 1.10 m of the plank extends past the right support.How far can a person who weighs 450 N walk on the plank to the right of the right support before the plank just begins to tip?

A)0.25 m
B)0.50 m
C)0.55 m
D)0.70 m

Question 15

During a picnic,you and two of your friends decided to have a three-way tug of war using three ropes tied in a knot in the middle.All of you pull with forces of the same magnitude,550 N.Alice pulls to the south and Bob pulls 30 ^$\circ$ north of east.What is the angular orientation of your rope so that the knot stays at rest?

A)30 ^$\circ$ north of west
B)to the north
C)30 ^$\circ$ south of east
D)to the west
E)None are correct.

Question 16

A construction supervisor of mass M = 80.0 kg is standing on a board of mass m = 30.0 kg.Two sawhorses at a distance L = 4.00 m apart support the board.If the man stands a distance x₁ = 1.25 m away from sawhorse 1 as shown,what is the force that the board exerts on the other sawhorse?

A)785 N
B)396 N
C)687 N
D)392 N
E)294 N

Question 17

An object is in static equilibrium.It's then moved a short distance to the right and released.If the equilibrium is unstable,then what will happen next?

A)It will continue moving to the right.
B)It will move back to the left.
C)It will remain stationary in the new position.
D)There isn't enough information to determine what will happen next.

Question 18

A 12-kg granite slab that is 2.2 m long is leaning against a frictionless vertical wall,with the base of the slab 55 cm away from the wall.What is the force of friction that the floor must exert on the base of the slab to keep it from moving?

A)153 N towards the wall
B)153 N away from the wall
C)1190 N away from the wall
D)1190 N towards the wall
E)296 N towards the wall

Question 19

An object is in static equilibrium.It's then moved a short distance to the right and released.If the equilibrium is stable,then what will happen next?

A)It will continue moving to the right.
B)It will move back to the left.
C)It will remain stationary in the new position.
D)There isn't enough information to determine what will happen next.

Question 20

A 5.00-m long uniform ladder leans against a smooth wall and its base rests on a rough floor.The ladder has a mass of 18.0 kg and its base is a distance of 2.30 m from the wall.A person of mass 70.0 kg climbs 2.50 m up the ladder.Assuming the ladder is to remain in place,what is the magnitude of the force exerted on the ladder by the wall?

A)249 N
B)150 N
C)224 N
D)100 N
E)300 N

Question 21

A light platform with a coordinate system drawn on it is supported at the center.A 5-kg mass is placed at .A 3-kg mass is placed at .Where should a 2-kg mass be placed such that the system is in equilibrium?

A)
B)
C)
D)
E)

Question 22

A 75-kg barbell is 1.0 m long and has its center of mass exactly in the middle of the barbell.A weightlifter holds it with his right hand 11 cm away from one end and his left hand 15 cm away from the other end.Find the force his right hand provides to the barbell.

A)81 N
B)350 N
C)370 N
D)390 N
E)500 N

Question 23

A 25-kg 10-m ladder is leaning against a frictionless wall with its base making an angle of 32 ^$\circ$ to the horizontal.What is the magnitude of the force exerted on the ladder by the ground?

A)314 N
B)675 N
C)245 N
D)462 N
E)543 N

Question 24

In building a house of cards,two cards are propped up against each other to form an inverted V.The length of each card is 88 mm and the mass of each card is 1.8 g.Both cards are tipped at an angle of 25 ^$\circ$ from vertical.Calculate the magnitude and direction of the friction force acting on the base of the card on the left required to keep the card structure from collapsing.

A)1.77 * 10^-2 N to right
B)8.83 * 10^-2 N to right
C)4.12 * 10^-3 N to right
D)1.77 * 10^-2 N to left
E)4.12 * 10^-3 N to left

Question 25

A SUV has a length of 4.4 m,a height of 1.5 m and a width of 1.6 m.What is the maximum speed the SUV could travel as it makes a turn of radius 71 m before it will begin to tip? Assume that the center of mass is in the geometric center of the car and that there is sufficient friction between the tires and the road to prevent skidding.

A)8.7 m/s
B)26 m/s
C)27 m/s
D)30 m/s
E)52 m/s

Question 26

A 55-kg diver stands at the far end of a 3.0-m long diving board,which has a mass of 32 kg.The diving board is supported at two places,with the first support at the end opposite the diver and the second support 65 cm away from that end.What is the direction and magnitude of the force that the second support applies to the diving board?

A)2.49 * 10³ N up
B)2.49 * 10³ N down
C)2.09 * 10³ N up
D)3.21 * 10³ N up
E)3.21 * 10³ N down

Question 27

A track is built whose height as a function of horizontal position x is given by (h and x,both in meters).If a marble is placed on this track,find the position closest to the axis where it will be in equilibrium.

A)0.29 m
B)-0.29 m
C)0.54 m
D)-0.54 m
E)1.3 m

Question 28

The 2-dimensional object of art shown in figure is held in display at a museum by support S and rope R.Support S is on the floor and rope R is attached to the ceiling.The coefficient of static friction between the object and support S is 0.5.If the angle, $\theta$ has its maximum value such that the object remains in static equilibrium on the support,what is the magnitude of the tension in the rope? The object's mass is 25 kg and the distances from object's center of mass,CM,to its contact points with the support and the rope are s = 35 cm and r = 55 cm,respectively.

A)154 N
B)119 N
C)245 N
D)95.7 N
E)194 N

Question 29

A diving board is 2.20 m long,has a mass of 5.20 kg and has a uniform density.There are supports holding it in place at one end (F1)and another 25.0 cm from the same end (F2).Find the support each of the support provides.Take upward forces to be positive.

A)Option A
B)Option B
C)Option C
D)Option D
E)Option E

Question 30

A track is built whose height as a function of horizontal position x is given by (h and x,both in meters).If a marble is placed on this track,find the position where it will be in a stable equilibrium.

A)0.29 m
B)-0.29 m
C)0.54 m
D)-0.54 m
E)1.3 m

Question 31

You wish to measure the strength of your biceps muscle by exerting a force on a test strap attached to a scale.When you pull on the strap,the scale moves and the movement measures the strength of your biceps.The strap is at 30 cm at the elbow and the biceps muscle is attached at a 5 cm from the pivot point.If the scale reads 20 N,the force exerted by the biceps muscle is

A)150 N.
B)120 N.
C)90 N.
D)75 N.
E)61 N.

Question 32

Two weights are hanging on a 60-cm long,100-g mass uniform wooden bar as shown in the figure.Is this system in equilibrium?

A)Yes
B)No
C)It cannot be determined.
D)It depends on value of normal force.

Question 33

A track is built whose height as a function of horizontal position x is given by (h and x,both in meters).If a marble is placed on this track,find the position closest to the axis where it will be in equilibrium.

A)0.29 m
B)0.53 m
C)1.3 m
D)1.9 m
E)There are no equilibrium points.

Question 34

Two weights are hanging on a 60-cm long,100-g mass uniform wooden bar as shown in the figure.Is this system in equilibrium?

A)Yes
B)No
C)It cannot be determined.
D)It depends on value of normal force.

Question 35

To crack a nut you exert equal and opposite forces of magnitude 25 N to the arms of a nut cracker.The distance between the nut and the pivot point is 2 cm and the distance between the nut and the free end of the nutcracker is 8 cm.The magnitude of the force experienced by the nut on the both side is

A)980 N.
B)350 N.
C)220 N.
D)120 N.
E)100 N.

Question 36

A track is built whose height as a function of horizontal position x is given by (h and x,both in meters).If a marble is placed on this track,find the position closest to the axis where it will be in equilibrium.

A)0.29 m
B)0.53 m
C)1.3 m
D)1.9 m
E)There are no equilibrium points.

Question 37

A thin 2-dimensional object with uniform mass density is in the shape of a square and has a mass of 2 kg.The sides of the square are 20 cm long each.The coordinate system is drawn with the origin at the center of the square.A point mass,m,of 200 g is placed at one corner of the square object and the assembly is held in equilibrium by positioning the support S at position (x,y)as shown in the drawing.Find the location of the support.

A)(-0.5 cm,-0.5 cm)
B)(-0.91 cm,-0.91 cm)
C)(-0.8 cm,-0.8 cm)
D)(-0.62 cm,-0.62 cm)
E)(-0.35 cm,-0.35 cm)

Question 38

A 5000-kg 200-m bridge is supported at both ends by pylons.A 1900-kg truck is 50 m from one end of the bridge.What force does the pylon nearest the truck exert on the bridge?

A)45,671 N
B)38,465 N
C)22,345 N
D)55,382 N
E)31,340 N

Question 39

One method of determining the location of the center of gravity of a person is to weigh the person as he/she lies on a board of negligible weight supported by two scales.In one example the height of the man is 190 cm;when he lies on the board,the left scale reads 450 N and the right scale reads 390 N.The center of gravity of the man relative to his feet on the right is

A)135 cm.
B)121 cm.
C)115 cm.
D)102 cm.
E)98 cm.

Question 40

Which of the following are in static equilibrium?

A)a pendulum at the top of its swing
B)a merry-go-round spinning at constant angular velocity
C)a projectile at the top of it's trajectory with zero velocity
D)All are correct.
E)None are correct.

Question 41

A board with a length of 7.00 m and a mass of 50.0 kg is attached by a large bolt to a support at a distance of 3.00 m from one end.The board makes an angle of 30.0 ^$\circ$ with the horizontal,as shown in the figure.A mass of 220 kg is attached with a rope to one end of the board,and a second rope is attached at a right angle to the other end of the board.Find the magnitude of the force exerted on the board by the bolt.

A)1350 N
B)2650 N
C)3810 N
D)3880 N
E)8480 N

Question 42

A board,with a weight of 85 N and a length of 6.0 m,is supported by two vertical ropes,as shown in the figure.Rope A is connected to one end of the board and rope B is connected a distance of 1.5 m from the other end of the board.A box with a weight of 25 N is placed on the board with its center of mass 1.0 m from rope A. What is the tension in rope A on the left?

A)13 N
B)25 N
C)38 N
D)48 N

Question 43

Three children acrobats are standing still on a circular horizontal platform of radius 4 m suspended at the center.The origin of the xy - Cartesian coordinate system is in the center of the circular platform.A 30-kg child is located at (1 m,2 m),and a 40-kg child is located at (-1 m,- 2 m).Assuming the children stand still on their positions,where must a 20-kg child acrobat be located so that the center of mass of the system consisting of the three children is at the origin and the platform is balanced?

A)(-0.5 m,2 m)
B)(-0.5 m,-2 m)
C)(-0.5 m,1 m)
D)(-0.5 m,-1 m)
E)Equilibrium impossible in this configuration.

Question 44

A system is in a stable equilibrium if

A)after the system is disturbed slightly from its equilibrium position,it returns to its original position.
B)after the system is disturbed slightly from its equilibrium position,it moves farther away from its original position.
C)after the system is disturbed slightly,no torques or forces act in either toward or away from the original position.

Question 45

A ladder of uniform density,length L and weight W rests on a rough floor (µ_s = 0.45)and against a frictionless wall.The maximum value of the angle between the wall and the ladder to prevent slipping is

A)42 ^$\circ$ .
B)37 ^$\circ$ .
C)29 ^$\circ$ .
D)24 ^$\circ$ .
E)19 ^$\circ$ .

Question 46

A pivot is placed under a massless 100-cm pole at 50 cm from the ends.A 4-kg mass is hung 15 cm from the left end and a 3-kg mass is hung 45 cm from the left end.If the stick is to remain in rotational equilibrium,how far from the left end of the pole must a third 8-kg mass have be hung?

A)19.4 cm
B)24.4 cm
C)30.6 cm
D)69.4 cm
E)74.4 cm

Question 47

Three children acrobats are standing still on a circular horizontal platform of radius 4 m suspended at the center.The origin of the xy - Cartesian coordinate system is assumed to be in the center of the circular platform.A 30-kg child is located at (1 m,2 m),and a 40-kg child is located at (2 m,- 3 m).Assuming the children stand still on their positions,where must a 20-kg child acrobat be located so that the center of mass of the system consisting of the three children is at the origin and the platform is balanced?

A)(-0.5 m,2 m)
B)(0.5 m,-2 m)
C)(-0.5 m,1 m)
D)(0.5 m,1 m)
E)Equilibrium impossible in this configuration.

Question 48

The definition of neutral equilibrium of a system is

A)after the system is disturbed slightly from its equilibrium position,it returns to its original position.
B)after the system is disturbed slightly from its equilibrium position,it moves farther away from its original position.
C)after the system is disturbed slightly,no torques or forces act in either toward or away from the original position.
D)the system does not move when slightly disturbed.

Question 49

A meter stick of mass 150 g is pivoted at its center.A mass m₁ of 75.0 g is suspended 13.0 cm from the left end of the meter stick.How much mass m₂ must be suspended 69.0 cm from the left end of the meter stick to achieve rotational equilibrium?

A)19.4 g
B)56.3 g
C)98.2 g
D)146.g
E)38.5 g

Question 50

Your precocious,22-kg,six year old sister sits on a swing and asks you to give her an amplitude of 32 degrees for her swing path.In order to do this precisely,you pull her back so that the angle with the vertical that the swing chains make is 32 degrees,and then you let go.As you held her at 32 degrees,what horizontal force were you applying to her?

A)61 N
B)110 N
C)130 N
D)180 N

Question 51

A board,with a weight of 85 N and a length of 6.0 m,is supported by two vertical ropes,as shown in the figure.Rope A is connected to one end of the board and rope B is connected a distance of 1.5 m from the other end of the board.A box with a weight of 25 N is placed on the board with its center of mass 1.0 m from rope A. What is the tension in rope B on the right?

A)13 N
B)25 N
C)38 N
D)55 N
E) 62 N

Question 52

A see-saw will balance when the pivot is placed at the center of mass of the system.If a boy and his brother sit at distances 3L and L from the pivot,respectively,and the see-saw is balanced,what is the boy's mass if his brother's is 85 kg? Assume the see-saw board is uniform.

A)28 kg
B)64 kg
C)21 kg
D)57 kg

Question 53

Your friend Joe hangs from a horizontal bar by his two hands,with his arms each inclined 35 degrees from the vertical (so that his arms have an angle between them of 70 degrees.If his mass is 76 kg,what is the tension in each of his arms?

A)745 N
B)372 N
C)455 N
D)909 N
E)1090 N

Question 54

The distance between the front wheels and the back wheels of the professor's car is 4 m.The center of mass of the car is located 1 m from the front wheels.If the car has a mass of 1020 kg,what are the forces that the cars two front tires,F_f,and two rear tires,F_r,exert on the street,when the car is standing on a horizontal surface?

A)F_f = 510 N,F_r = 510 N
B)F_f = 1530 N,F_r = 510 N
C)F_f = 7500 N,F_r = 2500 N
D)F_f = 1020 N,F_r = 1020 N
E)F_f = 5000 N,F_r = 5000 N

Question 55

A system is in an unstable equilibrium if

A)after the system is disturbed slightly from its equilibrium position,it returns to its original position.
B)after the system is disturbed slightly from its equilibrium position,it moves farther away from its original position.
C)after the system is disturbed slightly,no torques or forces act in either toward or away from the original position.
D)the system does not move when slightly disturbed.

Question 56

An airplane flies on a level path with an aerobat standing 22 m along one wing away from the central axis of the airplane.If the aileron on the opposite wing has to provide an additional downward force of 770 N at 15 m from the central axis of the airplane body in order to keep the airplane flying on a level path,what is the mass of the aerobat?

A)54 kg
B)79 kg
C)120 kg
D)110 kg

Question 57

A mobile is constructed from a metal bar and two wooden blocks as shown in the figure.The metal bar has a mass of 2.0 kg and is 12 cm long.There is a 3.0-kg wooden block hanging from the left end of the metal bar and a string to support the mobile is tied to the metal bar at a distance of 3 cm from the left end.How large of a wooden block should be hung from the right end of the bar to keep the bar level?

A)0.33 kg
B)0.50 kg
C)1.0 kg
D)2.0 kg
E)3.0 kg

Question 58

A 75-kg box with a height of 90 cm and a width of 30 cm is at rest on a flat board attached to the bed of a pickup truck.The coefficient of static friction between the box and the board is 0.47.What s the maximum acceleration that the pickup truck can have without the box tipping over?

A)1.5 m/s²
B)3.3 m/s²
C)3.5 m/s²
D)4.6 m/s²
E)7.0 m/s²

Question 59

Which of the following arrangements of three masses (hanging off the horizontal rod)would result in a balanced mobile?

A)Option A
B)Option B
C)Option C
D)Option D
E)Option E

Question 60

Your precocious,22-kg,six year old sister sits asks you to give her an amplitude of 32 degrees for her swing path.In order to do this precisely,you pull her back so that the angle with the vertical that the swing chains make is 32 degrees,and then you let go.As you held her at 32 degrees,what is the tension force in each of the two the swing chains?

A)470 N
B)250 N
C)130 N
D)340 N
E)220 N