Notes

Question 1
(1 points)
[This question is will be counted as a BONUS QUESTION - it will not count against you if you miss it, but will add to your score if you get it correct!] (but note that this type of question on this topic is considered fair game for the final exam.]







(#139796) {Torque}



Which of the following arrangements is least effective in tightening the nut?

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Select the correct answer
None
B
C
D
A
No answer submitted
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Question 2
(1 points)

(#665748) {Torque}



A
3
0
30
�
�
cm wrench is used to loosen a bolt with a force applied
0
.
3
0.3
�
m from the bolt. It takes
6
0
60
�
N to loosen the bolt when the force is applied perpendicular to the wrench. How much force would it take if the force was applied at a
3
0
30 degree angle from perpendicular?

Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g. 0.23, -2, 1e6, 5.23e-8

Enter answer here
Strategy

A known force is applied at perpendicular to the long axis of a wrench, a known distance from the point of rotation of the wrench in order to turn a bolt. We are asked to determine the magnitude of the force necessary to turn the bolt if the force is applied at the same location, but at 30 degrees relative to the perpendicular. This problem can be solved using scaling that involves a trigonometric function (sine). Alternatively, the problem can be solved by first working out the torque necessary to turn the bolt using the information for the perpendicular force, and then use that torque value to determine the necessary force to be applied at the stated angle.



Extra Hint : Be careful about what angle you use in the torque equation. Check how the angle is stated in the torque definition and compare it to how the angle is defined in this problem statement.


Question 3
(1 points)
[This question is will be counted as a BONUS QUESTION - it will not count against you if you miss it, but will add to your score if you get it correct!] (but note that this type of question on this topic is considered fair game for the final exam.]







(#138954) {Moment of Inertia}



Two different types of frisbees are shown below, a solid disk and a hoop. Both have the same mass and outer radius. Which of the following statements is true?

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Select the correct answer
The disk frisbee has a larger moment of inertia than the hoop frisbee because it has more surface area
The hoop frisbee has a larger moment of inertia than the disk frisbee because it has less surface area
The hoop frisbee has a larger moment of inertia than the disk frisbee because its mass is more concentrated away from the center of rotation.
The disk frisbee has a larger moment of inertia than the hoop frisbee because its mass is more concentrated toward the center of rotation.
No answer submitted
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Question 4
(1 points)

(#468234) {Moment of Inertia}



The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer can exert a force of
1
.
9
6
×
1
0
3

N
1.96×10
​3
​​ N with an effective perpendicular lever arm of
3
.
1
5

c
m
3.15 cm, producing an angular acceleration of the forearm of
1
0
3

r
a
d
/
s
2
103 rad/s
​2
​​ . What is the moment of inertia of the boxer’s forearm?



[Note: the perpendicular lever arm is defined as
�
⊥
=
�
�
�
�
(
�
)
r
​⊥
​​ =rsin(θ); it incorporates both the distance from the joint to the insertion point of the muscle group (by way of tendons) to the bone as well as the angle of the insertion]



Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g. 0.23, -2, 1e6, 5.23e-8

Enter answer here

k
g
⋅
m
2
kg⋅m
​2
​​
No answer submitted
0 of 5 checks used

Question 5
(1 points)
[This question is will be counted as a BONUS QUESTION - it will not count against you if you miss it, but will add to your score if you get it correct!] (but note that this type of question on this topic is considered fair game for the final exam.]







(#078493) {Moment of Inertia}



In fast-pitch softball, a pitcher swings her arm starting from straight overhead, swinging the ball in a semi-circle, and releasing the 0.195 kg ball at the bottom of the swing. If a pitcher's arm has a length of 0.841 m and mass of 11.5 kg, and the ball goes from initially at rest to a tangential speed of 32.6 m/s before release, what average torque must the pitcher apply to the ball? Model the pitcher's arm as a uniform thin rod swung about one end, and make sure you don't forget the mass of the softball (but you can ignore its shape; i.e., treat it like a point mass). Hint: you will need to make use of the equations of circular motion for constant angular acceleration.

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Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g. 0.23, -2, 1e6, 5.23e-8

Enter answer here
kg m
2
​2
​​ s
−
2
​−2
​​
No answer submitted
0 of 5 checks used

Question 6
(1 points)

(#705769) {Rotational Kinetic Energy}



A spinning object doubles its angular speed after two rotations. The final rotational kinetic energy is ...

Select the correct answer
2 times the original angular energy
1/2 times the original angular energy
equal to the original angular energy
1/4 times the original angular energy
4 times the original angular energy
No answer submitted
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Question 7
(1 points)
[This question is will be counted as a BONUS QUESTION - it will not count against you if you miss it, but will add to your score if you get it correct!] (but note that this type of question on this topic is considered fair game for the final exam.]








(#520084) {Rotational Kinetic Energy}



You want to race a hoop,
�
ℎ
�
�
�
=
�
�
2
I
​hoop
​​ =MR
​2
​​ , a solid sphere,
�
�
�
�
�
�
�
�
ℎ
�
�
�
=
2
5
�
�
2
I
​solidsphere
​​ =
​5
​
​2
​​ MR
​2
​​ and a solid cylinder,
�
�
�
�
�
�
�
�
�
�
�
�
�
�
=
1
2
�
�
2
I
​solidcylinder
​​ =
​2
​
​1
​​ MR
​2
​​ down a ramp. Each object has the same mass and radius. Predict which object will win the race. Assume all three objects roll without slipping.

Select the correct answer
All three objects will tie.
The solid cylinder will win.
The hoop will win.
The solid sphere will win.
It's impossible to tell.
No answer submitted
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Question 8
(1 points)

(#761691) {Rotational Kinetic Energy}



The net work done in accelerating a suspended wheel (hanging by its axle from a string) from rest to an angular speed of
5
0
50 rev/ min is
�
=
5
9
0
0
W=5900
�
J. What is the moment of inertia of the wheel?

Select the correct answer
430.4
k
g
⋅
m
2
kg⋅m
​2
​​
118.1
k
g
⋅
m
2
kg⋅m
​2
​​
4916
k
g
⋅
m
2
kg⋅m
​2
​​
1054
k
g
⋅
m
2
kg⋅m
​2
​​
2.362
k
g
⋅
m
2
kg⋅m
​2
​​
No answer submitted
0 of 3 checks used

Question 9
(1 points)
[This question is will be counted as a BONUS QUESTION - it will not count against you if you miss it, but will add to your score if you get it correct!] (but note that this type of question on this topic is considered fair game for the final exam.]







(#177525) {Rotational Kinetic Energy}



A hollow sphere (
�
�
�
�
=
2
3
�
�
2
I
​COM
​​ =
​3
​
​2
​​ MR
​2
​​ ) of mass 0.865 kg and radius 0.239 m rolls without slipping at a speed of 9.83 m/s toward an inclined plane, which is tilted
�
θ = 18.7 degrees above horizontal. The ball rolls up the incline plane, again without slipping. How far does the ball go up the plane (
�
L) before it comes to a momentary stop? Assume there is negligible loss due to any friction in this process.

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Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g. 0.23, -2, 1e6, 5.23e-8

Enter answer here
meters
No answer submitted
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Question 10
(1 points)

(#209132) {Conservation of Angular Momentum}



A skater spins at an initial angular velocity of
�
�
=
1
2
w
​i
​​ =12 rad/s with her arms outstretched. The skater then lowers her arms and thereby decreasing her moment of inertia by a factor of
7
7. What is the skater's angular velocity?

Select the correct answer
588
rad/s
0.58
rad/s
19
rad/s
84
rad/s
1.7
rad/s
No answer submitted
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Question 11
(1 points)
[This question is will be counted as a BONUS QUESTION - it will not count against you if you miss it, but will add to your score if you get it correct!] (but note that this type of question on this topic is considered fair game for the final exam.]







(#656176) {Conservation of Angular Momentum}



Three children are riding on the edge of a merry-go-round that is a solid disk with a mass of 108 kg and a radius of 1.55 m. The merry-go-round is initially spinning at 10.2 revolutions/minute. The children have masses of 29.0 kg, 33.9 kg and 34.2 kg. If the child who has a mass of 33.9 kg moves to the center of the merry-go-round, what is the new angular velocity in revolutions/minute? Neglect any friction between the moving and stationary parts of the merry-go-round, and treat the children as point masses.

Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g. 0.23, -2, 1e6, 5.23e-8

Enter answer here
revolutions/minute
No answer submitted
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Question 12
(1 points)

(#691739) {Rotational Equilibrium}



A bar is acted upon by equal magnitude forces at different points along its length. The center of the bar is the center of mass (labeled with a
⊗
⊗). In which of the following cases would there be a net acceleration and a net angular acceleration?

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Select the correct answer
None of these
C
B
All of these
D
A
No answer submitted
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Question 13
(1 points)
[This question is will be counted as a BONUS QUESTION - it will not count against you if you miss it, but will add to your score if you get it correct!] (but note that this type of question on this topic is considered fair game for the final exam.]







Two children push on opposite sides of a door during play. Both push horizontally and perpendicular to the door. One child pushes with a force of 20.0 N at a distance of 0.766 m from the hinges, and the second child pushes at a distance of 0.329 m. What force must the second child exert to keep the door from moving? Assume friction is negligible.

Select the correct answer
46.6
N
38.7
N
19.7
N
23.0
N
28.3
N
No answer submitted
0 of 3 checks used

Question 14
(1 points)
[This question is will be counted as a BONUS QUESTION - it will not count against you if you miss it, but will add to your score if you get it correct!] (but note that this type of question on this topic is considered fair game for the final exam.]






A 82.7-kg person stands on their toes by exerting an upward force through the Achilles tendon, as in the figure shown below. Calculate the force at the pivot,
�
�
F
​p
​​ , of the simplified lever system shown—that force is representative of forces in the ankle joint. [Assume that the lower leg and foot are oriented such that both the force of the Achilles tendon (
�
⃗
�
​F
​⃗
​​
​A
​​ ) and the normal force (
�
⃗
​N
​⃗
​​ , equal in magnitude to the person's weight) act perpendicular to the horizontal lever arm that represents the foot.]

Image size: SMLMax



Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g. 0.23, -2, 1e6, 5.23e-8

Enter answer here
Newtons
No answer submitted
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Question 15
(1 points)

A uniform ladder of mass
�
=
4
0
m=40 kg and length
�
=
1
0
l=10 m is leaned against a frictionless wall. A person with mass
�
=
8
0
�
�
M=80kg stands on the ladder at a distance
�
=
7
x=7 m from the bottom, as measured along the ladder. The ladder makes a
3
0
∘
30
​∘
​​ degree angle with the floor. The floor is not frictionless and the ladder does not move. What is the normal force that the wall exerts on the ladder?

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Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g. 0.23, -2, 1e6, 5.23e-8

Enter answer here
N
No answer submitted
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Question 16
This question contains multiple parts. Make sure to read all the instructions and answer each part.
[This question is will be counted as a BONUS QUESTION - it will not count against you if you miss it, but will add to your score if you get it correct!] (but note that this type of question on this topic is considered fair game for the final exam.]







When picking up an object from the ground, it is generally recommended that you "lift with your legs" - that is, raise and lower yourself by bending your knees but keeping your upper body upright. If instead, you "lift with your back" by bending at the hip so that your upper body is angled, then you put a great deal more stress on your spine and back muscles. Consider a person who is "lifting with their back" such that they are bent at the hip with their upper body is parallel to the ground (i.e., their spine is oriented horizontally). Let us calculate the tension in the back muscles and the compression on the spine in this situation. We will model the spine and upper body as a horizontal rigid rod or uniform density with a length of 50.0 cm and a mass of 40.0 kg. Assume that the person attempts to lift an object with their arms, which we will model as attached at the far end of the rod. Support of the back in this position is provided primarily by the erector spinalis muscle which we will model as being attached at one end to the spine at a point 33.0 cm from the hip at an angle of 10 degrees; the other end of the muscle is attached to the lower body below the hip.



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Part a
(1 points)
The object being lifted has a mass of 15.4 kg. Calculate the tension,
�
T , in the back muscle for this scenario.



Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g. 0.23, -2, 1e6, 5.23e-8

Enter answer here
N
No answer submitted
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Part b
(1 points)
For lifting a 15.4 kg object, calculate the compressive reaction force,
�
�
F
​V
​​ , that is transmitted to the pivot point of the spine (at the level of the hips) by the vertebrae of the lower back.

Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g. 0.23, -2, 1e6, 5.23e-8

Enter answer here
N
No answer submitted
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Part c
(1 points)
Determine how many times more stress in put on the spine by lifting the 15.4 kg object in this way by calculating the ratio of the compression on the spine in this scenario compared to the simple weight of the upper body plus the object (i.e., calculate the ratio:
�
�
�
�
.
�
.
+
�
�
�
�
​w
​u.b.
​​ +w
​obj
​​
​
​F
​V
​​
​​ .)



Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g. 0.23, -2, 1e6, 5.23e-8

Enter answer here
×
×
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