Mastering Physics Set 4 Midterm #1 Answers
What property of objects is best measured by their capacitance?
the ability to conduct electric current
the ability to distort an external electrostatic field
the ability to store charge (CORRECT ANSWER)
Consider an air-filled charged capacitor. How can its capacitance be increased?
Increase the charge on the capacitor.
Decrease the charge on the capacitor.
Increase the spacing between the plates of the capacitor.
Decrease the spacing between the plates of the capacitor.(CORRECT ANSWER)
Increase the length of the wires leading to the capacitor plates.
Consider a charged parallel-plate capacitor. How can its capacitance be halved?
Check all that apply.Double the charge.
Double the plate area.
Double the plate separation.(CORRECT ANSWER)
Halve the charge.
Halve the plate area.(CORRECT ANSWER)
Halve the plate separation.
Consider a charged parallel-plate capacitor. Which combination of changes would quadruple its capacitance?
Double the charge and double the plate area.
Double the charge and double the plate separation.
Halve the charge and double the plate separation.
Halve the charge and double the plate area.
Halve the plate separation and double the plate area.(CORRECT ANSWER)
Double the plate separation and halve the plate area.
If the potential of plate 1 is V, then, in equilibrium, what are the potentials of plates 3 and 6? Assume that the negative terminal of the battery is at zero potential.
V and V
2V and 3V
V and 0(CORRECT ANSWER)
V2 and V3
If the charge of the first capacitor (the one with capacitance C) is Q, then what are the charges of the second and third capacitors?
2Q and 3Q(CORRECT ANSWER)
Q2 and Q3
Q and Q
0 and 0
Qtot = 6C
Suppose we consider the system of the three capacitors as a single “equivalent” capacitor. Given the charges of the three individual capacitors calculated in the previous part, find the total charge Qtot for this equivalent capacitor.
ANSWER : Express your answer in terms of V and C.
Ceq = 6C
Using the value of Qtot, find the equivalent capacitance Ceq for this combination of capacitors.
ANSWER : Express your answer in terms of C.
What are the charges on plates 3 and 6?
+Q and +Q
−Q and −Q
+Q and −Q(CORRECT ANSWER)
−Q and +Q
0 and +Q
0 and −Q
If the voltage across the first capacitor (the one with capacitance C) is ΔV1, then what are the voltages across the second and third capacitors?
2ΔV1 and 3ΔV1
1/2ΔV1 and 1/3ΔV1(CORRECT ANSWER)
ΔV1 and ΔV1
0 and ΔV1
ΔV1 = 6ΔV11
Find the voltage ΔV1 across the first capacitor.
ANSWER: Express your answer in terms of ΔV.
Q = CΔV1
Find the charge Q on the first capacitor.
ANSWER: Express your answer in terms of C and ΔV1.
Ceq = 6C/11
Using the value of Q just calculated, find the equivalent capacitance Ceq for this combination of capacitors in series.
ANSWER: Express your answer in terms of C.
The four capacitors shown in the diagram are neither all in series nor all in parallel. You can, however, identify portions of the arrangement that are either in series or parallel, as described in the following statements. Which of these statements are correct for this problem?
Check all that apply.C4 is in series with C1 and C2.
C3 is in series with C4.
C3 is in parallel with C1 and C2.(CORRECT ANSWER)
C1 is in series with C2.(CORRECT ANSWER)
Ceq = 14.4 μF
What is the equivalent capacitance Ceq of the entire combination?
Express your answer in microfarads to three significant figures.(CORRECT ANSWER)
Ceq must be less than C4.
Suppose that you are given another network of the same form as the one analyzed in Part B, but with different values for the individual capacitances. How would you expect the equivalent capacitance Ceq to compare to the values of each individual capacitor in the network? Choose the statement below that is true regardless of the actual values for the individual capacitors.
Ceq must be less than C3.
The value of Ceq is not bounded by the value of any individual capacitance in the network.
Ceq must be less than C4.(CORRECT ANSWER)
Ceq must be less than C1+C2 .
Suppose two parallel-plate capacitors have the same charge Q, but the area of capacitor 1 is A and the area of capacitor 2 is 2A.
If the spacing between the plates, d, is the same in both capacitors, and the voltage across capacitor 1 is V, what is the voltage across capacitor 2?V/2
V
2V
4V
V/2(CORRECT ANSWER)
Suppose two parallel-plate capacitors have the same charge Q, but the area of capacitor 1 is A and the area of capacitor 2 is 2A.
If the spacing between the plates in capacitor 1 is d, what should the spacing between the plates in capacitor 2 be to make the capacitance of the two capacitors equal?d/2
d
2d(CORRECT ANSWER)
4d
2d
CA = 2.59 μF
Find the equivalent capacitance CA of the network of capacitors.
Express your answer in microfarads.(CORRECT ANSWER)
CB = 2.54 μF
Two capacitors of capacitance C5 = 6.00 μF and C6 = 3.00 μF are added to the network, as shown in the diagram.(Figure 2) Find the equivalent capacitance CB of the new network of capacitors.
Express your answer in microfarads.(CORRECT ANSWER)
Ur = U/K
Find Ur, the the energy dissipated in the resistor.
Express your answer in terms of U and other given quantities.(CORRECT ANSWER)
Ur = KU
Consider the same situation as in the previous part, except that the charging battery remains connected while the dielectric is inserted.(Figure 2) The battery is then disconnected and the capacitor is discharged. For this situation, what is Ur, the energy dissipated in the resistor?
Express your answer in terms of U and other given quantities.(CORRECT ANSWER)
A spherical capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 10.0 centimeters, and the separation between the spheres is 1.50 centimeters. The magnitude of the charge on each sphere is 3.30 nanocoulomb.
What is the magnitude of the potential difference ΔV between the two spheres?
ΔV = 38.7 V(CORRECT ANSWER)
A spherical capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 10.0 centimeters, and the separation between the spheres is 1.50 centimeters. The magnitude of the charge on each sphere is 3.30 nanocoulomb.
What is the electric-field energy stored in the capacitor?
6.38×10^−8 J(CORRECT ANSWER)
An air-filled parallel-plate capacitor has plate area A and plate separation d. The capacitor is connected to a battery that creates a constant voltage V.
Find the energy U0 stored in the capacitor.Express your answer in terms of A, d, V, and ϵ0.
U0 = 1/2(ϵ0A/d)V^2(CORRECT ANSWER)
An air-filled parallel-plate capacitor has plate area A and plate separation d. The capacitor is connected to a battery that creates a constant voltage V.
The capacitor is now disconnected from the battery, and the plates of the capacitor are then slowly pulled apart until the separation reaches 3d. Find the new energy U1 of the capacitor after this process.
Express your answer in terms of A, d, V, and ϵ0.
U1 = 3ϵ0(AV^2)/2d(CORRECT ANSWER)
An air-filled parallel-plate capacitor has plate area A and plate separation d. The capacitor is connected to a battery that creates a constant voltage V.
The capacitor is now reconnected to the battery, and the plate separation is restored to d. A dielectric plate is slowly moved into the capacitor until the entire space between the plates is filled. Find the energy U2 of the dielectric-filled capacitor. The capacitor remains connected to the battery. The dielectric constant is K.
Express your answer in terms of A, d, V, K, and ϵ0.
U2 = 1/2(V^2)(Kϵ0A/d)(CORRECT ANSWER)
A=2cm^2 C=8nF >A=2cm^2 C=4nF > A=1cm^2 C=1nF >A=4cm^2 C=2nF > A=4cm^2 C=1nF = A=8cm^2 C=2nF
Rank the following capacitors on the basis of the dielectric constant of the material between the plates.(CORRECT ANSWER)
A=2cm^2 C=8nF >A=2cm^2 C=4nF > A=4cm^2 C=2nF = A=8cm^2 C=2nF > A=1cm^2 C=1nF = A=4cm^2 C=1nF
Rank the capacitors on the basis of the charge stored on the positive plate.(CORRECT ANSWER)
A downward force of magnitude 5 N is exerted on the book by the force of
the table
gravity(CORRECT ANSWER)
Inertia
5N/ book
An upward force of magnitude _____ is exerted on the _____ by the table.
5N/ book(CORRECT ANSWER)
no
Do the downward force in Part A (gravity) and the upward force in Part B (upward force of magnitude 5N exerted on the book on the table) constitute a 3rd law pair?
no(CORRECT ANSWER)
The reaction to the force in Part B (upward force of magnitude 5N exerted on the book on the table) is a force of magnitude _____, exerted on the _____ by the _____. Its direction is _____.
5 N / table / book / downward(CORRECT ANSWER)
Which of Newton’s laws could we have used to predict that the forces in Parts A (gravity) and B (upward force of magnitude 5N exerted on the book on the table) are equal and opposite?
Check all that apply.Newton’s 1st law(CORRECT ANSWER)
Newton’s 2nd law(CORRECT ANSWER)
Newton’s 3rd law
Which of Newton’s laws could we have used to predict that the forces in Parts B (upward force of magnitude 5N exerted on the book on the table) and E (force of magnitude 5N exerted on the table by the book downward) are equal and opposite?
Check all that apply.Newton’s 1st law
Newton’s 2nd law
Newton’s 3rd law (CORRECT ANSWER)
First, consider a book resting on a horizontal table.
Which object exerts a downward force on the book?
the book itself
the earth(CORRECT ANSWER)
the surface of the table
First, consider a book resting on a horizontal table.
The downward force acting on the book is __________.
a contact force
a long-range force(CORRECT ANSWER)
What is the downward force acting on the book called?tension
normal force(CORRECT ANSWER)
weight
friction
the surface of the table
First, consider a book resting on a horizontal table
Which object exerts an upward force on the book?
the book itself
the earth
the surface of the table(CORRECT ANSWER)
First, consider a book resting on a horizontal table.
The upward force acting on the book is __________.a contact force(CORRECT ANSWER)
a long-range force
First, consider a book resting on a horizontal table.
What is the upward force acting on the book called?tension
normal force(CORRECT ANSWER)
weight
friction
A string is attached to a heavy block. The string is used to pull the block to the right along a rough horizontal table.
Which object exerts a force on the block that is directed toward the right?the block itself
the earth
the surface of the table
the string(CORRECT ANSWER)
A string is attached to a heavy block. The string is used to pull the block to the right along a rough horizontal table.
The force acting on the block and directed to the right is __________.a contact force(CORRECT ANSWER)
a long-range force
A string is attached to a heavy block. The string is used to pull the block to the right along a rough horizontal table.
What is the force acting on the block and directed to the right called?
tension(CORRECT ANSWER)
normal force
weight
friction
A string is attached to a heavy block. The string is used to pull the block to the right along a rough horizontal table.
Which object exerts a force on the block that is directed toward the left?the block itself
the earth
the surface of the table(CORRECT ANSWER)
the string
A string is attached to a heavy block. The string is used to pull the block to the right along a rough horizontal table.
The force acting on the block and directed to the left is __________.
a contact force(CORRECT ANSWER)
a long-range force
A string is attached to a heavy block. The string is used to pull the block to the right along a rough horizontal table.
What is the force acting on the block and directed to the left called?tension
normal force
weight
friction(CORRECT ANSWER)
The same block is placed on the same rough table. However, this time, the string is disconnected and the block is given a quick push to the right. The block slides to the right and eventually stops. The following questions refer to the motion of the block after it is pushed but before it stops.
How many forces are acting on the block in the horizontal direction?0
1(CORRECT ANSWER)
2
3
The same block is placed on the same rough table. However, this time, the string is disconnected and the block is given a quick push to the right. The block slides to the right and eventually stops. The following questions refer to the motion of the block after it is pushed but before it stops.
What is the force acting on the block that is directed to the left called?
tension
normal force
weight
friction(CORRECT ANSWER)
What is the direction of the net force acting on the object at position A?
upward
downward
to the left
to the right
The net force is zero.(CORRECT ANSWER)
What is the direction of the net force acting on the object at position B?
upward
downward
to the left(CORRECT ANSWER)
to the right
The net force is zero.
What is the direction of the net force acting on the object at position C?
upward
downward(CORRECT ANSWER)
to the left
to the right
The net force is zero.
6
Which of these diagrams may possibly correspond to the situation at point A on the motion diagram?
ANSWER : 6
3,5
Which of these diagrams may possibly correspond to the situation at point B on the motion diagram?
ANSWER :3,5
Which of these diagrams may possibly correspond to the situation at point C on the motion diagram?
ANSWER :2,4
Which of these diagrams correspond to a situation where the moving object (not necessarily the one shown in the motion diagram) is changing its velocity?
ANSWER :1,2,3,4,5
Consider the following situations:
A car is moving along a straight road at a constant speed.(CORRECT ANSWER)
A car is moving along a straight road while slowing down.
A car is moving along a straight road while speeding up.
A hockey puck slides along a horizontal icy (frictionless) surface.(CORRECT ANSWER)
A hockey puck slides along a rough concrete surface.
A cockroach is speeding up from rest.
A rock is thrown horizontally; air resistance is negligible.
A rock is thrown horizontally; air resistance is substantial.
A rock is dropped vertically; air resistance is negligible.
A rock is dropped vertically; air resistance is substantial.Which of these situations describe the motion shown in the motion diagram at point A?
Consider the following situations:
A car is moving along a straight road at a constant speed.
A car is moving along a straight road while slowing down.(CORRECT ANSWER)
A car is moving along a straight road while speeding up.
A hockey puck slides along a horizontal icy (frictionless) surface.
A hockey puck slides along a rough concrete surface.(CORRECT ANSWER)
A cockroach is speeding up from rest.
A rock is thrown horizontally; air resistance is negligible.
A rock is thrown horizontally; air resistance is substantial.
A rock is dropped vertically; air resistance is negligible.
A rock is dropped vertically; air resistance is substantial.Which of these situations describe the motion shown in the motion diagram at point B?
Consider the following situations:
A car is moving along a straight road at a constant speed.
A car is moving along a straight road while slowing down.
A car is moving along a straight road while speeding up.
A hockey puck slides along a horizontal icy (frictionless) surface.
A hockey puck slides along a rough concrete surface.
A cockroach is speeding up from rest.
A rock is thrown horizontally; air resistance is negligible.(CORRECT ANSWER)
A rock is thrown horizontally; air resistance is substantial.
A rock is dropped vertically; air resistance is negligible.
A rock is dropped vertically; air resistance is substantial.
An object cannot remain at rest unless which of the following holds?
The net force acting on it is zero.(CORRECT ANSWER)
The net force acting on it is constant and nonzero.
There are no forces at all acting on it.
There is only one force acting on it.
If a block is moving to the left at a constant velocity, what can one conclude?
There is exactly one force applied to the block.
The net force applied to the block is directed to the left.
The net force applied to the block is zero.(CORRECT ANSWER)
There must be no forces at all applied to the block.
It A block of mass 2kg is acted upon by two forces: 3N (directed to the left) and 4N (directed to the right). What can you say about the block’s motion?
It must be moving to the left.
It must be moving to the right.
It must be at rest.
It could be moving to the left, moving to the right, or be instantaneously at rest.(CORRECT ANSWER)
A massive block is being pulled along a horizontal frictionless surface by a constant horizontal force. The block must be __________.
continuously changing direction
moving at constant velocity
moving with a constant nonzero acceleration(CORRECT ANSWER)
moving with continuously increasing acceleration
cannot have a magnitude equal to 5N
Two forces, of magnitude 4N and 10N, are applied to an object. The relative direction of the forces is unknown. The net force acting on the object __________.
Check all that apply.
cannot have a magnitude equal to 5N(CORRECT ANSWER)
cannot have a magnitude equal to 10N
cannot have the same direction as the force with magnitude 10N
must have a magnitude greater than 10N
B
D
Every force has one and only one 3rd law pair force.
true(CORRECT ANSWER)
false
The two forces in each pair act in opposite directions.
true(CORRECT ANSWER)
false
The two forces in each pair can either both act on the same body or they can act on different bodies.
true
false(CORRECT ANSWER)
The two forces in each pair may have different physical origins (for instance, one of the forces could be due to gravity, and its pair force could be due to friction or electric charge).
true
false(CORRECT ANSWER)
The two forces of a 3rd law pair always act on different bodies.
true(CORRECT ANSWER)
false
Given that two bodies interact via some force, the accelerations of these two bodies have the same magnitude but opposite directions. (Assume no other forces act on either body.)
true
false(CORRECT ANSWER)
.
According to Newton’s 3rd law, the force on the (smaller) moon due to the (larger) earth is
greater in magnitude and antiparallel to the force on the earth due to the moon.(CORRECT ANSWER)
greater in magnitude and parallel to the force on the earth due to the moon.
equal in magnitude but antiparallel to the force on the earth due to the moon.
equal in magnitude and parallel to the force on the earth due to the moon.
smaller in magnitude and antiparallel to the force on the earth due to the moon.