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)

Accepted Answer

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.

Accepted Answer

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.

Accepted Answer

The sum of the external torques being zero only ensures that the object is not experiencing any angular acceleration; it does not necessarily mean that the sum of the external forces is zero, as these forces could still cause linear acceleration if they are not balanced.

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.

Accepted Answer

An object can be in uniform motion (constant velocity) as well, as both conditions (zero external torques and forces) imply no change in the object's state of motion, according to Newton's first law of motion.

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

Accepted Answer

The answer of A 60.0-kg man stands at one end...

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.

Accepted Answer

The first force exerts a greater torque because torque is maximized when the force is applied perpendicular to the lever arm (in this case, the door), as torque is calculated by the product of the force magnitude and the lever arm length times the sine of the angle between the force direction and the lever arm. The sine of 90° (perpendicular) is 1, resulting in maximum torque, whereas the sine of 30° is less than 1, resulting in less torque.

Question 7

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

Accepted Answer

The center of mass is determined by the distribution of mass in a system, not by the amount of mass on each side. The center of mass will be closer to the side with more mass and farther away from the side with less mass, but there is no requirement for equal amounts of mass on both sides.

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.

Accepted Answer

This statement is a restatement of the first condition of equilibrium, which states that the sum of forces and torques acting on an object at rest must be zero. If the sum of torques was not zero, the object would begin to rotate, while if the sum of forces was not zero, the object would begin to accelerate in the direction of the net force.

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?

Accepted Answer

The answer of Three small objects are positioned at the...

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? $1 .$

$2 .$
 
$3 .$

$4 .$

$5 .$

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

Accepted Answer

The answer of As shown in the figure,a given force...

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

Accepted Answer

When half of the rope is lifted off the table, the center of mass of the lifted portion is at the midpoint of that half, which is 0.5 m from the end being lifted. Since this is half the rope, the midpoint is 0.25 m from the table.

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.

Accepted Answer

The answer of Three balls are moving along a straight...

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.

Accepted Answer

The weight of the car is the total weight distributed across all wheels, so it is the sum of the readings when the front wheels and then the rear wheels are on the scale.

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)

Accepted Answer

The center of mass formula for a two-particle system is:

r_cm = (m1r1 + m2r2) / (m1 + m2)

Given that the center of mass is at the origin, we can write:

(m1r1 + m2r2) / (m1 + m2) = 0

Substituting the values:

(2.0 kg)(3.0 m) + (3.0 kg)(r2) = 0

6.0 + 3r2 = 0

r2 = -2.0 m

Therefore, the location of the 3.0 kg particle is (-2.0 m, 0.0 m), which corresponds to choice B.

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)

Accepted Answer

The center of mass (COM) of a system can be found using the formula $x_{\text{COM}} = \frac{\sum m_ix_i}{\sum m_i}$ and $y_{\text{COM}} = \frac{\sum m_iy_i}{\sum m_i}$ for the x and y coordinates respectively. For the given system, $x_{\text{COM}} = \frac{(2.0 \times 0.0) + (2.0 \times 2.0) + (4.0 \times 2.0)}{2.0 + 2.0 + 4.0} = \frac{0 + 4 + 8}{8} = 1.5 \, \text{m}$ and $y_{\text{COM}} = \frac{(2.0 \times 0.0) + (2.0 \times 0.0) + (4.0 \times 1.0)}{2.0 + 2.0 + 4.0} = \frac{0 + 0 + 4}{8} = 0.5 \, \text{m}$. Therefore, the coordinates of the center of mass are (1.5 m, 0.5 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)

Accepted Answer

The answer of Three objects are located in the x-y...

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.

Accepted Answer

The sum of external forces being zero implies no linear acceleration, but torques depend on the point of application and can still cause rotational motion.

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

Accepted Answer

According to the principle of conservation of momentum, when the child starts moving towards the other end, the total momentum of the system (child and canoe) must remain constant. Since the initial momentum is zero, the final momentum must also be zero. This means that the canoe must move in the opposite direction to compensate for the child's motion.

The child moves from one end to the other end, covering a distance of 5.0 m. Since the canoe is initially at rest, the center of mass of the system (child and canoe) is at rest. When the child moves to the other end, the center of mass of the system is displaced by a distance of 2.5 m (half the length of the canoe), towards the end where the child started. In order to maintain the center of mass of the system at rest, the canoe must move 2.5 m in the opposite direction.

Therefore, the canoe moves a total distance of 2.5 m + 0.5 m (the initial distance between the child and the end of the canoe) = 3.0 m in the water.

Hence, the correct choice is C) 3.0 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.

Accepted Answer

Since torque is the product of force and the perpendicular distance from the pivot point (torque = force x distance), and both forces produce equal torques, the force applied closer to the hinge (at the midpoint) must be greater to compensate for the shorter distance compared to the force applied at the doorknob.

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

Accepted Answer

The answer of Five forces are exerted on a rod...

Quiz 8: Extended Bodies at Rest

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 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.)

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.

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 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?

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?

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

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 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?

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? $1 .$ $2 .$ $3 .$ $4 .$ $5 .$

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?

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.

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

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?

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.

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?

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.

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?

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?

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.)

Quiz 8: Extended Bodies at Rest

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 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.)

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.

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 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?

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?

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

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 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?

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? 1.1 .1. 2.2 .2. 3.3 .3. 4.4 .4. 5.5 .5.

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?

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.

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

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?

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.

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?

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.

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?

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?

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.)

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? $1 .$ $2 .$ $3 .$ $4 .$ $5 .$