Notes

Question 34
This question contains multiple parts. Make sure to read all the instructions and answer each part.

(962255) {2D Inelastic Collisions}



A ceramic platter of mass,
�
=
6

k
g
m=6 kg, is dropped from rest onto a horizontal frictionless floor. Upon impact with the floor the plate breaks into three pieces which go sliding away from each other across the frictionless floor. [



Hint: Because the surface is frictionless, it does not impart any horizontal momentum to the plate or any of its pieces.]



Part a
(1 points)
The first piece has a mass of
3

k
g
3 kg and slides horizontally away from the impact site directly to the east at
3
m
/
s
3m/s. The second piece has a mass of
2

k
g
2 kg and slides away horizontally at 30 degrees south of due west with a velocity of
5
.
0
9

m
/
s
5.09 m/s. Assume that the positive x-axis points due east and the positive y-axis points due north. Using the concept of conservation of momentum, calculate the x-component of the velocity of the the third piece, which has a mass of
1

k
g
1 kg.



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m/s
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Part b
(1 points)
Calculate the y-component of the velocity of the the third piece.



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Part c
(1 points)
Calculate the angle at which the third piece slides away horizontally. Give your answer in degrees relative to the positive x-axis (which points due east).



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degrees
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Part d
(1 points)
Finally, calculate the magnitude of the velocity of the third piece.



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m/s
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Question 35
This question contains multiple parts. Make sure to read all the instructions and answer each part.

(408553) {2D Inelastic Collisions}



At an Independence Day celebration show, a large firework is shot from the ground and, in the first stage of its bursting pattern, splits into two unequal parts.

Image size: SMLMax



Part a
(1 points)
Assume that the firework has a mass of
�
0
=
0
.
3
0

k
g
m
​0
​​ =0.30 kg and is launched from a cannon at an angle of
�
0
=
3
6
.
1
∘
θ
​0
​​ =36.1
​∘
​​ with an initial velocity of
∣
�
0
∣
=
2
0

m
/
s
∣v
​0
​​ ∣=20 m/s. Just as the firework reaches its hight point in its trajectory, it explodes into two pieces. Immediately after the explosion, the first piece, with a mass of
�
1
=
0
.
2

k
g
m
​1
​​ =0.2 kg flies off at an angle
�
1
=
1
5
0
∘
θ
​1
​​ =150
​∘
​​ relative to the positive (forward) horizontal axis at a velocity of
∣
�
1
∣
=
5

m
/
s
∣v
​1
​​ ∣=5 m/s relative to the ground. Calculate the trajectory angle,
�
2
θ
​2
​​ of the second piece immediately after the explosion. Assume the second piece has a mass of
�
2
=
0
.
1

k
g
m
​2
​​ =0.1 kg, neglect the effect of air resistance, and report your result as an angle relative to the positive (forward) horizontal axis.

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degrees
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Part b
(1 points)
Calculate the magnitude of the velocity of the second firework piece immediately after the explosion.



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m/s
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Question 36
(1 points)

(650410) {2D Elastic Collisions}



In Rutherford's famous gold foil experiment, a small percentage of alpha particles (helium nuclei) sent into a sheet of gold foil were found to scatter at large angles, in some cases back toward the emitter. Assuming that this is the result of collisions between the helium nuclei and the gold nuclei (which are 50 times more massive than helium nuclei), what do you predict happened to the gold nuclei for the cases where the helium nuclei are backscattered at angles
9
0
∘
<
�
�
�
<
1
8
0
∘
90
​∘
​​ <θ
​He
​​ <180
​∘
​​ ?





Image size: SMLMax



Select the correct answer
Nothing; they are so much more massive that they wouldn't have moved
They are turned into thallium nuclei
They are scattered out of the foil into the opposite direction as the incoming beam of helium nuclei
They are scattered out of the foil into the same direction as the incoming beam of helium nuclei
They are deflected slightly away from the incoming beam of helium nuclei, but atomic binding forces keep the gold nuclei in the foil
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Question 37
(1 points)

(167196) {Elastic Collisions}



Two identical carts are placed on a frictionless track. Cart 1 is initially at rest while Cart 2 is moving to the right towards Cart 1. The two carts collide elastically. After the collision, which of the following is true?



I. Carts 1 and 2 are both at rest

II. Cart 2 stops and cart 1 moves to the right with speed equal to the original speed of cart 2

III. Cart 1 remains at rest and cart 2 bounces back with speed equal to its original speed

IV. Cart 1 moves to the right with a speed slightly less than the original speed of cart 2 and cart 2 moves to the right with a very small speed

Select the correct answer
I, II, and IV
III and IV
I
II and III
II
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Question 38
(1 points)

(861000) {Elastic Collisions}



In an elastic collision, which of these three quantities are conserved: mass, kinetic energy, and momentum?

Select the correct answer
Mass, kinetic energy, and momentum
Momentum
Mass and kinetic energy
Kinetic energy
Kinetic energy and momentum
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Question 39
(1 points)

(257603) {Elastic Collisions}



Two blocks with masses 0.472 kg (A) and 0.795 kg (B) sit on a frictionless surface. Between them is a spring with spring constant 29.9 N/m, which is not attached to either block The two blocks are pushed together, compressing the spring by 0.275 meter, after which the system is released from rest. What is the final speed of the block A? (Hint: you will need to use both conservation of energy and conservation of momentum to solve this problem).

Image size: SMLMax



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m/s
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Question 40
This question contains multiple parts. Make sure to read all the instructions and answer each part.

(299763) {Center of Mass}



Two patterns are cut out of a flat, uniform sheet of metal, as shown in the two figures below. Calculate the center of mass for each pattern with their lower left corners placed at the coordinate origin (
�
=
0
x=0,
�
=
0
y=0)



Image size: SMLMax



Part a
(1 points)
Calculate the x-coordinate of the center of mass,
�
�
�
x
​CM
​​ for Pattern (A)

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meters
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Part b
(1 points)
Calculate the y-coordinate of the center of mass,
�
�
�
y
​CM
​​ for Pattern (A)

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meters
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Part c
(1 points)
Calculate the x-coordinate of the center of mass,
�
�
�
x
​CM
​​ for Pattern (B)

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meters
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Part d
(1 points)
Calculate the y-coordinate of the center of mass,
�
�
�
y
​CM
​​ for Pattern (B)

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meters
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Question 41
(1 points)

(591737) {Center of Mass}



Which of the following statements is true about the projectile motion of systems?

Select the correct answer
The momentum of an object in flight is conserved during projectile motion.
The momentum of each part of a system is separately conserved during projectile motion
The center of mass motion of a system is unaffected even if the system breaks apart
It is not possible to predict the center of mass motion of the system if it breaks apart
The kinetic energy of a system increases, then decreases during projectile motion
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Question 42
(1 points)

(440110) {Center of Mass}



A fisherman of mass
�
=
7
0
.
9

k
g
m=70.9 kg is sitting in a canoe with mass
�
=
1
4
0

k
g
M=140 kg on a warm summer day. The canoe has length
�
=
6
.
5
9

m
L=6.59 m and he is sitting 1 meter from the end of the canoe. After several hours of not catching anything, he decides to try his luck from the other end of the boat, so he gets up and walks over to the other end and sits back down 1 meter from the other end of the canoe. Assuming that the water applies no frictional force on the canoe, what is the (magnitude of the) distance the canoe has traveled in this process?



Note: You may also assume that the canoe is perfectly symmetric in its shape and mass distribution, and be sure to account for the fact that the fisherman moves a distance of 2 meters less than the full boat length.

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m
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Question 43
(1 points)

(470332) {Center of Mass}



A cannonball of mass 29.8 kg is shot into the air at an angle of 45 degrees with respect to horizontal. At the top of its ballistic trajectory, the cannonball suddenly explodes into two separate pieces, a smaller piece this is 1/3 the original mass, and a larger piece that is 2/3 the original mass. The smaller piece ends up retracing its original trajectory and landing right back at the spot where the cannonball was originally launched, 24.8 seconds after it was launched. How far from the launch site does the larger piece travel? You can neglect the effects of air resistance. (Hint: to use momentum in this problem, you'll want to go back and review your ballistic motion equations from week 2).

Image size: SMLMax



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meters
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Question 44
(1 points)

(886915) {Center of Mass}



A bullet of mass 10.0 gram moving at a velocity of 354 m/s toward the right strikes an orange of mass 90.0 gram. The bullet passes through the orange and in the process pulls out 10.0 grams of orange innards. Assuming that this collision is elastic (i.e., that no kinetic energy is lost), what is the velocity of the rest of the remaining 80 grams of orange? Take rightward motion to be positive and leftward motion to be negative.



Hint: It is easiest to do this problem if you first shift to the center of mass frame of the orange & bullet, determine the velocities of both objects after the collision in that frame, and then shift back to the "lab" frame.



Image size: SMLMax



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m/s
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Question 45
This question contains multiple parts. Make sure to read all the instructions and answer each part.

(633294) {Center of Mass}



Consider the collision of a 1500-kg car traveling east at 20.0 m/s (44.7 mph) with a 2000-kg truck traveling north at 25 m/s (55.9 mph). The cars lock together in such a way as to prevent them from separating or rotating significantly. One second before the collision, the car is located at position
(
�
,
�
)
=
(
−
2
0
,
0
)

m
(x,y)=(−20,0) m and the truck is located at position
(
�
,
�
)
=
(
0
,
−
2
5
)

m
(x,y)=(0,−25) m.

Part a
(1 points)
Calculate the x-coordinate of the center of mass of the two-automobile system,
�
�
�
x
​CM
​​ , one second before the collision.



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meters
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Part b
(1 points)
Calculate the y-coordinate of the center of mass of the two-automobile system,
�
�
�
x
​CM
​​ , one second before the collision.



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meters
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Part c
(1 points)
Calculate the magnitude of the velocity of the center of mass of the two-automobile system,
�
�
�
v
​CM
​​ , one second before the collision.



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m/s
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Part d
(1 points)
Calculate the direction of the velocity of the center of mass of the two-automobile system,
�
�
�
v
​CM
​​ one second before the collision. (Give you answer in degrees relative to the positive x-axis which points to the east.)

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degrees
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Part e
(1 points)
Calculate the magnitude of the velocity of the center of mass of the two-automobile system,
�
�
�
v
​CM
​​ , immediately after the collision.



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m/s
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Part f
(1 points)
Calculate the direction of the velocity of the center of mass of the two-automobile system,
�
�
�
v
​CM
​​ immediately after the collision. (Give you answer in degrees relative to the positive x-axis which points to the east.)



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degrees
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