Question 1

A net torque applied to a rigid object always tends to produce:
A)linear acceleration
B)rotational equilibrium
C)angular acceleration
D)rotational inertia
E)none of these

Accepted Answer

A net torque applied to a rigid object always tends to produce angular acceleration, which causes the object to rotate. This is because torque is a measure of the force that causes an object to rotate around an axis, and the resulting acceleration is proportional to the torque and inversely proportional to the object's moment of inertia. Linear acceleration refers to changes in linear velocity, and rotational equilibrium means that the object is not rotating. Rotational inertia is a property of the object that determines how difficult it is to change its rotational motion. Therefore, the correct answer is C (angular acceleration).

Question 2

For an object in equilibrium the sum of the torques acting on it vanishes only if each torque is calculated about:
A)the center of mass
B)the center of gravity
C)the geometrical center
D)the point of application of the force
E)the same point

Accepted Answer

For an object to be in equilibrium, the sum of the torques must be zero, but this condition holds true regardless of the point about which the torques are calculated, as long as all torques are calculated about the same point. This principle is a consequence of the rotational equilibrium condition in physics.

Question 3

A cylinder placed so it can roll on a horizontal table top, with its center of gravity above its geometrical center, is:
A)in stable equilibrium
B)in unstable equilibrium
C)in neutral equilibrium
D)not in equilibrium
E)none of the above

Accepted Answer

The cylinder is in unstable equilibrium. Any small displacement from its equilibrium position will lead to a net force that will cause it to continue to roll in that direction.

Question 4

Three identical uniform rods are each acted on by two or more forces, all perpendicular to the rods.Which of the rods could be in static equilibrium if an additional force is applied at the center of mass of the rod? 
A)Only 1
B)Only 2
C)Only 3
D)Only 1 and 2
E)All three

Accepted Answer

The answer of Three identical uniform rods are each acted...

Question 5

Which of the following is in static equilibrium?
A)a rock resting on the ground
B)a rock sliding at constant velocity across a frictionless surface
C)a rock rotating in place on a frictionless surface
D)a rock rotating at a constant rate as it slides at constant velocity across a frictionless surface
E)a rock falling off a cliff

Accepted Answer

A rock resting on the ground is in static equilibrium because it is not moving and remains at rest.

Question 6

The center of gravity coincides with the center of mass:
A)always
B)never
C)if the center of mass is at the geometrical center of the body
D)if the acceleration due to gravity is uniform over the body
E)if the body has a uniform distribution of mass

Accepted Answer

The center of gravity coincides with the center of mass when the acceleration due to gravity is uniform over the body, ensuring that the weight distribution is uniform and thus aligning the center of gravity with the center of mass.

Question 7

A massless meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark.A force  is applied perpendicularly to the end of the stick at 0 cm, as shown.A second force  (not shown)is applied perpendicularly at the 60-cm mark.The forces are in the plane of the table top.If the stick does not move, the force exerted by the pivot on the stick: 
A)must be zero
B)must be in the same direction as  and have magnitude

C)must be directed opposite to  and have magnitude

D)must be in the same direction as  and have magnitude

E)must be directed opposite to  and have magnitude

Accepted Answer

Since the meter stick is not moving, the net torque acting on it is zero. Thus, the torque due to the force applied at 0cm must be equal and opposite to the torque due to the force applied at 60cm. The torque due to a force is given by the product of the force and the distance between the force and the pivot point. Let x be the force applied at 0cm and y be the force applied at 60cm. Then we have:

x(80cm) = y(20cm)
y = 4x

So the force applied at 60cm is four times the force applied at 0cm. Since the force applied at 0cm is perpendicular to the meter stick and passes through the pivot point, it does not produce any torque about the pivot point, and thus the pivot exerts no force on that end of the stick. However, the force applied at 60cm produces a clockwise torque about the pivot point, and thus the pivot exerts a counterclockwise force on that end of the stick. This force must be in the same direction as the force applied at 60cm, and its magnitude must be equal and opposite to the torque due to that force. Therefore, the answer is B – the pivot exerts a force in the same direction as the force applied at 60cm, with magnitude 4x (where x is the force applied at 0cm).

Question 8

A picture can be hung on a wall in three different ways, as shown.The tension in the string is: 
A)least in I
B)greatest in I
C)greatest in II
D)least in III
E)greatest in III

Accepted Answer

The answer of A picture can be hung on a...

Question 9

A massless meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark.A force  is applied perpendicularly to the end of the stick at 0 cm, as shown.A second force  (not shown)is applied perpendicularly to the stick at the 100-cm end of the stick.The forces are in the plane of the table top.If the stick does not move, the force exerted by the pivot on the stick: 
A)must be zero
B)must be in the same direction as  and have magnitude

C)must be directed opposite to  and have magnitude

D)must be in the same direction as  and have magnitude

E)must be directed opposite to  and have magnitude

Accepted Answer

The answer of A massless meter stick on a horizontal...

Question 10

The location of which of the following points within an object might depend on the orientation of the object?
A)Its center of mass
B)Its center of gravity
C)Its geometrical center
D)Its center of momentum
E)None of the above

Accepted Answer

The center of gravity depends on the orientation of the object because it is the point where the gravitational force can be considered to act, and this can change with the object's orientation in a non-uniform gravitational field.

Question 11

A 5.1-kg mass is located at the origin, and a 2.3-kg mass is located at x = 4.9 cm.Assuming g is constant, what is the location of the center of mass x_com, and the location of the center of gravity x_cog, of the two masses? A)x_com = 1.5 cm, x_cog = 3.4 cm B)x_com = 3.4 cm, x_cog = 1.5 cm C)x_com = 1.5 cm, x_cog = 1.5 cm D)x_com = 3.4 cm, x_cog = 3.4 cm E)x_com = 1.5 cm, x_cog = 0 cm

Accepted Answer

The center of mass (x_com) is calculated using the formula: (m1*x1 + m2*x2) / (m1 + m2). Substituting the given values, x_com = (5.1*0 + 2.3*4.9) / (5.1 + 2.3) = 1.5 cm. Since g is constant, the center of gravity (x_cog) is the same as the center of mass, so x_cog = 1.5 cm.

Question 12

Which of the following is NOT in equilibrium?
A)a rock resting on the ground
B)a rock sliding at constant velocity across a frictionless surface
C)a rock rotating in place on a frictionless surface
D)a rock rotating at a constant rate as it slides at constant velocity across a frictionless surface
E)a rock falling off a cliff

Accepted Answer

Equilibrium means the object has a net force of zero and is either at rest or moving with constant velocity. A rock falling off a cliff is not in equilibrium as it is accelerating due to gravity. Choices A, B, C, and D are all situations where the rock is in equilibrium.

Question 13

To determine if a rigid body is in equilibrium the vector sum of the gravitational forces acting on the particles of the body can be replaced by a single force acting at:
A)the center of mass
B)the geometrical center
C)the center of gravity
D)a point on the boundary
E)none of the above

Accepted Answer

The answer of To determine if a rigid body is...

Question 14

A picture P of weight W is hung by two strings as shown.The magnitude of the tension force of each string is T.The total upward pull of the strings on the picture is: 
A)2W cos $\theta$
B)T sin $\theta$
C)T cos $\theta$
D)2T sin$\theta$
E)2T cos$\theta$

Accepted Answer

The answer of A picture P of weight W is...

Question 15

The conditions that the sum of forces and the sum of the torques both vanish:
A)hold for every solid body in equilibrium
B)hold only for elastic solid bodies in equilibrium
C)hold for every solid body
D)are always sufficient to calculate the forces on a solid object in equilibrium
E)are sufficient to calculate the forces on a solid object in equilibrium only if the object is elastic

Accepted Answer

The conditions that the sum of forces and the sum of the torques both vanish, also known as static equilibrium, hold for every solid body in equilibrium, regardless of whether it is elastic or not. These conditions are necessary for a solid object to be in a state of rest or constant velocity. However, they do not alone provide sufficient information to calculate the forces on a solid object. Additional information, such as the object's mass and acceleration, is needed to calculate the individual forces.

Question 16

A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in ________ equilibrium with respect to rotation about the edge and in ________ equilibrium with respect to rotation about a horizontal axis that is perpendicular to the edge.
A)stable, stable
B)stable, unstable
C)unstable, stable
D)unstable, unstable
E)unstable, neutral

Accepted Answer

The cube is in unstable equilibrium with respect to rotation about the edge because any small disturbance will cause it to tip over. It is in stable equilibrium with respect to rotation about a horizontal axis perpendicular to the edge because the center of gravity is at the lowest point relative to this axis.

Question 17

A 160-N child sits on a light swing and is pulled back and held with a horizontal force of 100 N.The magnitude of the tension force of each of the two supporting ropes is:
A)60 N
B)94 N
C)120 N
D)190 N
E)260 N

Accepted Answer

The force acting on the swing is the tension force in each of the supporting ropes, which must balance the weight of the child and the horizontal force of 100 N pulling the swing back.

To find the tension force in each rope, we can use the equation:

Tension force = (weight of child + horizontal force)/2

Tension force = (160 N + 100 N)/2

Tension force = 260 N/2

Tension force = 130 N

However, this is the tension force in each rope combined. To find the tension force in each individual rope, we need to divide by 2:

Tension force in each rope = 130 N/2

Tension force in each rope = 65 N

Therefore, the correct answer is B) 94 N, which is the closest choice to the calculated tension force of 65 N.

Question 18

For a body to be equilibrium under the combined action of several forces:
A)all the forces must be applied at the same point
B)all of the forces are composed of pairs of equal and opposite forces
C)any two of these forces must be balanced by a third force
D)the sum of the torques about any point must equal zero
E)the lines of action of all the forces must pass through the center of gravity of the body

Accepted Answer

The condition for a body to be in equilibrium under the combined action of several forces is that the sum of the torques about any point must equal zero. This means that the clockwise torques must be balanced by anticlockwise torques, and vice versa. This condition ensures that the body does not rotate under the applied forces. Choices A, B, C, and E are incorrect because they do not fully capture the necessary conditions for equilibrium.

Question 19

For a body to be equilibrium under the combined action of several forces:
A)all the forces must be applied at the same point
B)all of the forces are composed of pairs of equal and opposite forces
C)the sum of the components of all the forces in any direction must equal zero
D)any two of these forces must be balanced by a third force
E)the lines of action of all the forces must pass through the center of gravity of the body

Accepted Answer

The condition for a body to be in equilibrium under the combined action of several forces is that the sum of the components of all the forces in any direction must equal zero. This means that the net force acting in any direction is zero and the body will not accelerate in that direction. Option A is incorrect because the forces can be applied at different points. Option B is incorrect because the forces may not be equal and opposite. Option D is incorrect because any two forces can be balanced by a third force or more. Option E is incorrect because the lines of action of the forces may not pass through the center of gravity of the body.

Question 20

A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its geometrical center, is:
A)in stable equilibrium
B)in unstable equilibrium
C)in neutral equilibrium
D)not in equilibrium
E)none of the above

Accepted Answer

A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its geometrical center, is in stable equilibrium. This is because any small displacement from its equilibrium position will result in a restoring torque that will bring the cylinder back to its initial position.

Quiz 12: Equilibrium and Elasticity

A net torque applied to a rigid object always tends to produce:

For an object in equilibrium the sum of the torques acting on it vanishes only if each torque is calculated about:

A cylinder placed so it can roll on a horizontal table top, with its center of gravity above its geometrical center, is:

Three identical uniform rods are each acted on by two or more forces, all perpendicular to the rods.Which of the rods could be in static equilibrium if an additional force is applied at the center of mass of the rod?

Which of the following is in static equilibrium?

The center of gravity coincides with the center of mass:

A picture can be hung on a wall in three different ways, as shown.The tension in the string is:

The location of which of the following points within an object might depend on the orientation of the object?

A 5.1-kg mass is located at the origin, and a 2.3-kg mass is located at x = 4.9 cm.Assuming g is constant, what is the location of the center of mass x_com, and the location of the center of gravity x_cog, of the two masses?

Which of the following is NOT in equilibrium?

To determine if a rigid body is in equilibrium the vector sum of the gravitational forces acting on the particles of the body can be replaced by a single force acting at:

The conditions that the sum of forces and the sum of the torques both vanish:

A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in equilibrium with respect to rotation about the edge and in equilibrium with respect to rotation about a horizontal axis that is perpendicular to the edge.

A 160-N child sits on a light swing and is pulled back and held with a horizontal force of 100 N.The magnitude of the tension force of each of the two supporting ropes is:

For a body to be equilibrium under the combined action of several forces:

For a body to be equilibrium under the combined action of several forces:

A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its geometrical center, is:

Quiz 12: Equilibrium and Elasticity

A net torque applied to a rigid object always tends to produce:

For an object in equilibrium the sum of the torques acting on it vanishes only if each torque is calculated about:

A cylinder placed so it can roll on a horizontal table top, with its center of gravity above its geometrical center, is:

Three identical uniform rods are each acted on by two or more forces, all perpendicular to the rods.Which of the rods could be in static equilibrium if an additional force is applied at the center of mass of the rod?

Which of the following is in static equilibrium?

The center of gravity coincides with the center of mass:

A picture can be hung on a wall in three different ways, as shown.The tension in the string is:

The location of which of the following points within an object might depend on the orientation of the object?

A 5.1-kg mass is located at the origin, and a 2.3-kg mass is located at x = 4.9 cm.Assuming g is constant, what is the location of the center of mass xcom, and the location of the center of gravity xcog, of the two masses?

Which of the following is NOT in equilibrium?

To determine if a rigid body is in equilibrium the vector sum of the gravitational forces acting on the particles of the body can be replaced by a single force acting at:

A picture P of weight W is hung by two strings as shown.The magnitude of the tension force of each string is T.The total upward pull of the strings on the picture is:

The conditions that the sum of forces and the sum of the torques both vanish:

A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in ________ equilibrium with respect to rotation about the edge and in ________ equilibrium with respect to rotation about a horizontal axis that is perpendicular to the edge.

A 160-N child sits on a light swing and is pulled back and held with a horizontal force of 100 N.The magnitude of the tension force of each of the two supporting ropes is:

For a body to be equilibrium under the combined action of several forces:

For a body to be equilibrium under the combined action of several forces:

A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its geometrical center, is:

A 5.1-kg mass is located at the origin, and a 2.3-kg mass is located at x = 4.9 cm.Assuming g is constant, what is the location of the center of mass x_com, and the location of the center of gravity x_cog, of the two masses?

A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in equilibrium with respect to rotation about the edge and in equilibrium with respect to rotation about a horizontal axis that is perpendicular to the edge.