Question 1

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.

Accepted Answer

A) True 
 B)False  False

Question 2

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.

Accepted Answer

A) True 
 B)False  True

Question 3

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.

Accepted Answer

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) 
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) B

Question 4

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.)

Accepted Answer

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. 
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.

Question 5

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 $h = 0.69 \mathrm {~m}$ what minimum value of F is required to make the crate start to tip over?

Accepted Answer

The answer of As shown in the figure,a uniform rectangular...

Question 6

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?

Accepted Answer

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

Question 7

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 $\overrightarrow { \mathrm { F } }$ M in the figure)in the upper arm exert on the lower arm?

Accepted Answer

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

Question 8

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?

Accepted Answer

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 
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 9

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.

Accepted Answer

A) True 
 B)False

Question 10

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?

Accepted Answer

The answer of An 82-kg painter stands on a long...

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?

Accepted Answer

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

Question 12

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?

Accepted Answer

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

Question 13

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?

Accepted Answer

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

Question 14

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.

Accepted Answer

7.00 m to the right

Question 15

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?

Accepted Answer

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) 
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 16

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?

Accepted Answer

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) 
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 17

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?

Accepted Answer

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

Question 18

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?

Accepted Answer

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

Question 19

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?

Accepted Answer

m₁ = 1 g, m

Question 20

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.

Accepted Answer

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

Exam 8: Extended Bodies at Rest

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.

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.

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 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.)

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?

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.

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 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 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?

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.

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?

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 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?

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?

Introduction

Kinematics: Motion in One Dimension

Newtonian Mechanics

Applying Newtons Laws

Circular Motion

Impulse and Linear Momentum

Work and Energy

Rotational Motion

Gases

Static Fluids

Fluids in Motion

First Law of Thermodynamics

Second Law of Thermodynamics

Electric Charge force and Energy

The Electric Field

Dc Circuits

Magnetism

Electromagnetic Induction

Vibrational Motion

Mechanical Waves

Reflection and Refraction

Mirrors and Lenses

Wave Optics

Electromagnetic Waves

Special Relativity

Quantum Optics

Atomic Physics

Nuclear Physics

Particle Physics

Filters

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?