Deck 8: Extended Bodies at Rest

Question 1

In the figure,four point objects are placed as shown.Assume that all the numbers in the figure are accurate to two significant figures.What are the x and y coordinates of the center of mass of this arrangement?

A)(2.2 m, 2.6 m)
B)(2.2 m, 2.7 m)
C)(2.3 m, 2.6 m)
D)(2.3 m, 2.7 m)
E)(2.3 m, 2.8 m)

Answer 1

E

Question 2

A croquet mallet balances when suspended from its center of mass,as shown in the left part of the figure.If you cut the mallet into two pieces at its center of mass,as shown in the right part of the figure,how do the masses of the two pieces compare? (There could be more than one correct choice.)

A)The masses are equal.
B)The piece with the head of the mallet has the greater mass.
C)The piece with the head of the mallet has the smaller mass.
D)It is impossible to tell.

Answer 2

B,D

Question 3

If the sum of the external torques exerted on an object is zero,then the sum of the external forces exerted on it must also be zero.

Answer 3

False

Question 4

If the sum of both the external torques and the external forces exerted on an object is zero,then the object must be at rest.

Question 5

A 60.0-kg man stands at one end of a 20.0-kg uniform 10.0-m long board.How far from the man is the center of mass of the man-board system?

A)1.25 m
B)2.50 m
C)5.00 m
D)7.50 m
E)9.00 m

Question 6

Two equal-magnitude forces are exerted to a door at the doorknob.The first force is exerted perpendicular to the door,and the second force is exerted at 30° to the plane of the door.Which force exerts the greater torque about the door hinge?

A)the first force (exerted perpendicular to the door)
B)the second force (exerted at an angle)
C)Both forces exert equal non-zero torques.
D)Both forces exert zero torque.

Question 7

There must be equal amounts of mass on both sides of the center of mass of a system.

Question 8

If an object remains at rest,then the sum of both the external torques and the external forces exerted on the object must be zero.

Question 9

Three small objects are positioned at the following coordinates: the 3-0 kg object at (3.0 m,2.0 m); the 4.0-kg object at (0.0 m,-1.0 m); and the 5.0-kg object at (5.0 m,-7.0 m).What are the coordinates of the center of mass of this system?

Question 10

As shown in the figure,a given force is applied to a rod in several different ways.In which case is the torque about the pivot P due to this force the greatest?

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

Question 11

A 2.0-m rope is lying on a table.You pick up one end and start raising it vertically.How high above the table is the center of mass of the rope when half of the rope has lifted off the table?

A)0.25 m
B)0.50 m
C)0.75 m
D)1.0 m
E)1.5 m

Question 12

Three balls are moving along a straight line having the instantaneous positions shown in the figure.At that instant,find the location and velocity of the center of mass of this system.

Question 13

When a car is weighed,it is driven slowly on a horizontal floor over a scale that records a reading as the front wheels go over the scale,and then records a second reading as the rear wheels go over the scale.The weight of the car is equal to

A)the reading of the scale when it is under the front wheels.
B)the reading of the scale when it is under the rear wheels.
C)the average of the two readings.
D)the sum of the two readings .
E)the difference of the two readings.

Question 14

The center of mass of a two-particle system is at the origin.One particle is located at (3.0 m,0.0 m)and has a mass of 2.0 kg.The other particle has a mass of 3.0 kg.What is the location of the 3.0-kg particle?

A)(-3.0 m, 0.0 m)
B)(-2.0 m, 0.0 m)
C)(2.0 m, 0.0 m)
D)(3.0 m, 0.0 m)

Question 15

Three small objects are positioned as follows: the 2.0-kg object at (0.0 m,0.0 m),the 2.0-kg object at (2.0 m,0.0 m),and the 4.0-kg object at (2.0 m,1.0 m).Determine the coordinates of the center of mass of this system.

A)(0.50 m, 1.5 m)
B)(1.5 m, 0.50 m)
C)(2.5 m, 1.5 m)
D)(2.5 m, 0.50 m)

Question 16

Three objects are located in the x-y plane as follows: a 6 kg-object is at (0 m,0 m),a mass of 4 kg is at (3 m,0 m),and a 2 kg-object is at (0 m,3 m).Where is the center of mass of the system?

A)(1 m, 2 m)
B)(2 m, 1 m)
C)(1 m, 1 m)
D)(1 m, 0.5 m)
E)(0.5 m, 1 m)

Question 17

If the sum of the external forces exerted on an object is zero,then the sum of the external torques exerted on it must also be zero.

Question 18

A 30-kg child stands at one end of a floating 20-kg canoe that is 5.0-m long and initially at rest in the water.The child then slowly walks to the other end of the canoe.How far does the canoe move in the water,assuming water friction is negligible?

A)1.0 m
B)2.0 m
C)3.0 m
D)4.0 m
E)5.0 m

Question 19

Two forces produce equal torques on a door about the door hinge.The first force is exerted at the midpoint of the door; the second force is applied at the doorknob.Both forces are exerted perpendicular to the door.Which force has a greater magnitude?

A)the first force (at the midpoint)
B)the second force (at the doorknob)
C)The two forces are equal.

Question 20

Five forces are exerted on a rod that is free to pivot at point P,as shown in the figure.Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

A)force A
B)force B
C)force C
D)force D
E)force E

Question 21

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N ∙ m.What is the angle (less than 90°)between the wrench handle and the direction of the exerted force?

A)30°
B)24°
C)36°
D)42°

Question 22

An 82-kg diver stands at the edge of a light 5.0-m diving board,which is supported by two vertical pillars that are 1.6 m apart,as shown in the figure.Find the magnitude and direction of the force exerted by each pillar.

Question 23

An irregularly shaped object that is 10 m long is placed with each end on a scale.If the scale on the right reads while the scale on the left reads how far from the left end is the center of mass of this object?

A)5.7 m
B)7.4 m
C)4.3 m
D)14 m

Question 24

A 15-kg child is sitting on a playground teeter-totter,1.5 m from the pivot.What is the magnitude of the minimum force,applied 0.30 m on the other side of the pivot,that is needed to make the child lift off the ground?

A)75 N
B)740 N
C)23 N
D)44 N
E)66 N

Question 25

A man in a gym is holding an 8.0-kg object at arm's length,a distance of 0.55 m from his shoulder joint.What is the torque about his shoulder joint due to the object if his arm is held at 30° below the horizontal?

A)22 N ∙ m
B)2.2 N ∙ m
C)4.4 N ∙ m
D)13 N ∙ m
E)37 N ∙ m

Question 26

An object of 3.0-kg mass is located at (0.0 m,8.0 m),and an object of 1.0-kg mass is located at (12 m,0.0 m).You want to add a 4.0-kg object so that the center of mass of the three-object system will be at the origin.What should be the coordinates of the 4.0-kg object?

A)(-3.0 m, -6.0 m)
B)(-12 m, -8.0 m)
C)(3.0 m, 6.0 m)
D)(-6.0 m, -3.0 m)

Question 27

Consider the sun and its largest planet Jupiter.On the line joining them,how far from the center of the sun is their center mass? Is it within or outside the sun? (Jupiter-sun distance is 778 × 10⁶ km,diameter of the sun is 1.4 × 10⁶ km,the sun is 1000 times as massive as Jupiter)

Question 28

As shown in the figure,a uniform rectangular crate 0.40 m wide and 1.0 m tall sits on a horizontal surface.The crate weighs 460 N,and its center of mass is at its geometric center.A horizontal force of magnitude F is exerted at a distance h above the floor.Friction at the floor is great enough to prevent the crate from sliding.If what minimum value of F is required to make the crate start to tip over?

Question 29

As shown in the figure,a 10.0 m long bar is attached by a frictionless hinge to a wall and held horizontal by a light rope that makes an angle θ = 49° with the bar.The bar is uniform and weighs What distance x from the hinge should a 10.0 kg object be suspended for the tension in the rope to be 177 N?

Question 30

An 82-kg painter stands on a long horizontal board 1.55 m from one end.This 27-kg board is uniform,5.5 m long,and supported at each end by vertical posts.
(a)What is the magnitude of the total force provided by both posts?
(b)With what force does the post that is closest to the painter push upward on the board?

Question 31

Three objects of masses 1.0 kg,2.0 kg,and 3.0 kg,are located at (0.0 m,0.0 m),(1.0 m,1.0 m),and (2.0 m,-2.0 m),respectively.What is the location of the center of mass of this system?

A)(1.3 m, 0.67 m)
B)(1.3 m, -0.67 m)
C)(-1.3 m, 0.67 m)
D)(-1.3 m, -0.67 m)

Question 32

A meter stick balances at the 50.0-cm mark.If a 50.0-g object is placed at the 90.0-cm mark,the stick balances at the 61.3-cm mark.What is the mass of the meter stick?

A)127 g
B)178 g
C)89.7 g
D)32.6 g
E)73.4 g

Question 33

A force of 17 N is exerted to the end of a 0.63-m long torque wrench at an angle 45° from a line joining the pivot point to the handle.What is the magnitude of the torque about the pivot point produced by this force?

A)7.6 N ∙ m
B)10.7 N ∙ m
C)12.0 N ∙ m
D)9.7 N ∙ m

Question 34

A uniform 1200-N piece of medical apparatus that is 3.5 m long is suspended horizontally by two vertical wires at its ends.A small but dense 550-N object is placed on the apparatus 2.0 m from one end,as shown in the figure.What are the forces,A and B,that the two wires exert on the beam?

A)A = 880 N, B = 880 N
B)A = 840 N, B = 910 N
C)A = 9000 N, B = 8200 N
D)A = 910 N, B = 840 N
E)A = 8200 N, B = 9000 N

Question 35

A 15-kg child is sitting on a playground teeter-totter,1.5 m from the pivot.What is the minimum distance,on the other side of the pivot,such that a 220-N force will make the child lift off the ground?

A)1.0 m
B)1.5 m
C)0.10 m
D)9.8 m
E)2.4 m

Question 36

The figure shows a person's foot.In that figure,the Achilles tendon exerts a force of magnitude F = 720 N.What is the magnitude of the torque that this force produces about the ankle joint?

A)12 N ∙ m
B)16 N ∙ m
C)21 N ∙ m
D)26 N ∙ m
E)36 N ∙ m

Question 37

The lug nuts on a car wheel require tightening to a torque of 90 N ∙ m.If a 30-cm long wrench is used,what is the magnitude of the minimum force required using the wrench?

A)300 N
B)150 N
C)30 N
D)15 N

Question 38

A uniform ladder 12 meters long rests against a vertical frictionless wall,as shown in the figure.The ladder weighs 400 N and makes an angle θ = 51° with the floor.A man weighing 874 N climbs slowly up the ladder.When he is 78 m from the bottom of the ladder,it just starts to slip.What is the coefficient of static friction between the floor and the ladder?

Question 39

A man in a gym is holding an 8.0-kg object at arm's length,a distance of 0.55 m from his shoulder joint.What is the torque about his shoulder joint due to the object if his arm is horizontal?

A)0.24 N ∙ m
B)4.4 N ∙ m
C)43 N ∙ m
D)15 N ∙ m
E)0 N ∙ m

Question 40

A 1.0-g bead is at (-2.0 cm,2.0 cm),a 2.0-g bead is at (2.0 cm,-4.0 cm),and a 3.0-g bead is at (2.0 cm,0.0 cm).What are the coordinates of the center of mass of this system of beads?

Question 41

A mobile is shown in the figure.The horizontal supports have negligible mass.Assume that all the numbers given in the figure are accurate to two significant figures.What mass M is required to balance the mobile?

A)18 g
B)30 g
C)36 g
D)60 g
E)90 g

Question 42

A uniform rod weighs 40 N and is 1.0 m long.It is hinged to a wall at the left end,and held in a horizontal position at the right end by a vertical string of negligible weight,as shown in the figure.What is the magnitude of the torque due to the string about a horizontal axis that passes through the hinge and is perpendicular to the rod? The hinge is very small with negligible friction.

A)40 N ∙ m
B)10 N ∙ m
C)5.0 N ∙ m
D)20 N ∙ m
E)30 N ∙ m

Question 43

A 3.00-m-long 200-N ladder,leans against a smooth vertical wall with its base on a horizontal rough floor,a distance of 1.00 m away from the wall.The ladder is not completely uniform,so its center of gravity is 1.20 m from its base.What force of friction must the floor exert on the base of the ladder to prevent the ladder from sliding down?

A)93.3 N
B)130 N
C)28.3 N
D)102 N
E)150 N

Question 44

A 40-kg uniform ladder that is 5.0 m long is placed against a smooth wall at a height of h = 4.0 m,as shown in the figure.The base of the ladder rests on a rough horizontal surface whose coefficient of static friction with the ladder is 0.40.An 80-kg bucket is suspended from the top rung of the ladder,just at the wall.What is the magnitude of the force that the ladder exerts on the wall?

A)740 N
B)1300 N
C)980 N
D)900 N
E)1100 N

Question 45

A store's sign has a mass of 20 kg and is 3.0 m long.It is uniform,so its center of gravity is at the center of the sign.It is supported horizontally by a small loose bolt attached to the wall at one end and by a wire at the other end,as shown in the figure.What is the force that the wire exerts on the sign?

A)460 N
B)230 N
C)120 N
D)200 N
E)300 N

Question 46

The mobile shown in the figure is perfectly balanced,and the horizontal supports have insignificant masses.What must be the masses of the suspended objects m₁,m₂,and m₃ to maintain balance?

Question 47

A 320-g ball and a 400-g ball are attached to the two ends of a string that goes over a pulley with a radius of 8.7 cm.Because of friction in its axle,the pulley does not begin to rotate.What is the magnitude of the frictional torque at the axle of the pulley if the system remains at rest when the balls are released?

A)0.068 N ∙ m
B)0.61 N ∙ m
C)0.079 N ∙ m
D)0.063 N ∙ m
E)0.00070 N ∙ m

Question 48

A 100-kg nonuniform boom that is 6.0 m long is loosely pinned at the pivot at P.A 600-kg concrete block is suspended from the end of the boom at A,as shown in the figure.The boom forms a 30° angle above the horizontal,and is supported by a 4.0-m cable between points D and B.Point B is 4.0 m from P,and point D is 4.0 m above P.The center of mass of the boom is at point C,which is 2.0 m from P.Assume that all the quantities shown in the figure are accurate to two significant figures.What is the force that the cable connected between points B and D exerts on the boom?

A)9300 N
B)8400 N
C)8100 N
D)7500 N
E)6900 N

Question 49

A 5.00-m-long 200-N uniform ladder, rests against a smooth vertical wall with its base on a horizontal rough floor,a distance of 1.20 m away from the wall.The coefficient of static friction between the ladder and the floor is 0.200.How far up the ladder,measured along the ladder,can a 600-N person climb before the ladder begins to slip?

A)1.50 m
B)1.26 m
C)1.05 m
D)3.95 m
E)4.56 m

Question 50

A store's sign has a mass of 20 kg and is 3.0 m long.It is uniform,so its center of gravity is at the center of the sign.It is supported horizontally by a small loose bolt attached to the wall at one end and by a wire at the other end,as shown in the figure.What is the magnitude of the net force that the bolt exerts on the sign?

A)460 N
B)230 N
C)200 N
D)120 N
E)300 N

Question 51

A light board that is 10 m long is supported by two sawhorses,one at one end of the board and a second at the midpoint.A 40-N object is placed between the two sawhorses,3.0 m from the end and 2.0 m from the center.What magnitude forces do the sawhorses exert on the board?

Question 52

An athlete holds a 7.5-kg shot put in his hand with his lower arm horizontal,as shown in the figure.His lower arm has a mass of 2.8 kg and its center of gravity (or center of mass)is 12 cm from the elbow-joint pivot.How much force must the extensor muscle (which is _M in the figure)in the upper arm exert on the lower arm?

A)100 N
B)500 N
C)1000 N
D)1500 N

Question 53

In the figure,a uniform 200-N ladder 10 m in length leans against a perfectly smooth wall.A 600-N firefighter climbs a distance x up the ladder.The coefficient of static friction between the ladder and the floor is 0.50.What is the maximum value of x for which the ladder will not slip?

A)3.9 m
B)5.0 m
C)6.0 m
D)6.3 m
E)8.4 m

Question 54

A uniform 40-N board supports two children weighing 500 N and 350 N.If the support is at the center of the board and the 500-N child is 1.5 m from its center,how far is the 350-N child from the center?

A)1.1 m
B)1.5 m
C)2.1 m
D)2.7 m

Question 55

To determine the location of the center of mass of a car,the car is driven over a scale on a horizontal floor.When the front wheels are over the scale,the weight recorded by the scale is 5800 N,and when the rear wheels are over the scale,the scale reads 6500 N.The distance between the front and rear wheels is measured to be 3.20 m.How far behind the front wheels is the center of mass located?

A)0.845 m
B)1.50 m
C)1.59 m
D)1.69 m
E)1.72 m

Question 56

A 10-m uniform beam weighing 100 N is supported by two vertical ropes at its ends.If a 400-N person sits at a point 2.0 m from the left end of the beam,what is the force that each rope exerts on the beam?

Question 57

A light board that is 10 m long is supported by two sawhorses,one at one end of the board and a second at the midpoint.A 40-N object is placed between the two sawhorses,3.0 m from the end and 2.0 m from the center.A second,15-N object,is placed on the supported end.What magnitude forces do the sawhorses exert on the board?

Question 58

A 120-kg refrigerator that is 2.0 m tall and 85 cm wide has its center of mass at its geometrical center.You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator.The coefficient of static friction between the floor and the refrigerator is 0.30.Depending on where you push,the refrigerator may start to tip over before it starts to slide along the floor.What is the highest distance above the floor that you can push the refrigerator so that it will not tip before it begins to slide?

A)0.71 m
B)1.0 m
C)1.2 m
D)1.4 m
E)1.6 m

Question 59

A child is trying to stack two uniform bricks,each 24 cm long,so they will protrude as far as possible over the edge of a table without tipping over,as shown in the figure.What is the maximum possible overhang distance d?

A)10 cm
B)12 cm
C)14 cm
D)16 cm
E)18 cm