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Solutions to Momentum Classwork and Homework
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Warped Warm-UpPicture if you will...a frog sitting on a frictionless lilypad. This frog has been a bad frog, experimenting with steroids and human growth hormone to improve his tongue speed. On this day he shoots his tongue out with such an incredible velocity that it rips loose and keeps going. If the tongue's velocity is 140 m/s and it's mass is .2 kg, and the frog recoils at 24 m/s. What is the frog's mass?
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8 kg 20 kg
Before After
8 kg 20 kgV=? 2.6 m/s
What do you ask for when you are all out of mentum?_______________What do you ask for when you are all out of mentum?_______________
6 slugs m
Before After
1.4 ft/s 44 ft/sm6 slugs
3. A 76 kg astronaut floats near her capsule, unable to reach it as she has run out of fuel for her jet pack. In desperation she throws a 0.04 kg wrench at 18 m/s oppositely to the direction she wishes to go. What is her newly acquired speed?
Ʃpi = Ʃpf0 = (8 kg)V + (20 kg)(2.6 m/s)V = 6.5 m/s
Ʃpi = Ʃpf0 = (6 slug)(1.4 ft/s) + m(44 ft/s)m = .19 slugs
Ʃpi = Ʃpf0 = (.04 kg)(18 m/s) + (76 kg)VV = .0095 m/s
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c) Is this collision elastic or inelastic?
d) Is energy conserved in this collision? If not, where did it go?
Followup Q's
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#1LA
T
E
R
4 m/s
V=?
θ = ?
6 m/s5 kg
3 kg
8 kg
Pythagorize it!
Trig it!
2D Mo or not 2D Mo...
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LA
T
E
R
5 m/s
300 m/s V=?
θ = ?
.03kg
4kg
#2
Solution is just like #1. Answer...V = 5.4 m/s, θ = 65o
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#3 LA
T
E
R
V=?
V'=?
33o
6 ft/s2 slug
1.5 slug
3.5 slug
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3kg
LA
T
E
R3 m/s
6 m/s V=?
θ = ?2kg2kg
3kg36o
#4
Pythagorize and Trig it...
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LA
T
E
R
V=?
5.7 m/s
V=6.8 m/s
θ = ?
65o
#5
1.4 kg
.55 kg8.8 m/s
.55 kg
1.4 kg
It's done like #4...answer is V = 4.02 m/s and θ = 54.6o
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WHO SAID 2D MO?1. 62.5 m/s @ 35.8o2. 59o Below Horizontal3. 25.7 m/s @ 46o4. 5.86 m/s @ 31.4o
WHO SAID 2D MO?
2D Moe
You sank my battleship.
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Horizontal: Σpxi = Σpxf(50)(80) ‑ (30)(90cos25o) = (50)Vx ‑ (30)(40cos35 o)
Vx = 50.7 m/s
Vertical: Σpyi = Σpyf0‑(30)(90sin25o) = ‑(50)Vy + (30)(40sin35o)
Vy = 36.6 m/s
Pythagorize it and trig it... V = 62.5 m/s and θ =35.8 o
50kg
30kg
50kg
30kg
80 m/s
90 m/s
40 m/s
θ
V
25o35o#1
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Horizontal: Σpxi = Σpxf(.3)(730) + 0 = (.3)(530) + (1.1)Vx
Vx = 54.5 ft/s
Vertical: Σpyi = Σpyf0‑(1.1)(91) = 0 + (1.1)V y
Vy = 91 ft/s
Use tangent function ... θ =59 o below horizon
#2
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Horizontal: Σpxi = Σpxf(60)(5) + 0 = (60)(4cos18 o) + (4)Vx
Vx = 17.9 m/s
Vertical: Σpyi = Σpyf0 + 0 = (60)(4sin18o) + (4)Vy Vy = 18.5 m/s
Pythagorize it and trig it...V = 25.7 m/s and θ =46o
60 kg
4kg
60 kg
4kg
5 m/s
4 m/s
θ
V
18o#3
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5 kg
3 kg
8 m/s
θ
Horizontal: Σpxi = Σpxf(8)(5) ‑ (3)(9cos20o) = (5)Vx ‑ (3)(4cos30o)
Vx = 5.0 m/s
Vertical: Σpyi = Σpyf0 ‑(3)(9sin20 o) = (5)Vy +(3)(4sin30 o)
Vy = 3.05 m/s
Pythagorize it and trig it...V = 5.86 m/s and θ =31.4 o
9 m/s20o
5 kg
3 kg4 m/s
30o
V
#4
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#1
#2
#3
Don't Be a Dummy!
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#6
#5
#4
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20o
9 m/s
8 m/s
3 kg
5 kg
30o
4 m/s
3 kg
5 kgθ = ?
V = ?
LA
T
E
R
Two slices of space toast collide elastically in outer space. Neglect gravity and friction. a.) Find the unknown angle and velocity.b.) If the slices are in contact for .1 sec during the collision, what is the average vertical force exerted on the 3 kg slice during the collision. (Hint: Impulse Momentum Theorem)
Deja Space Toast Deluxe
ANSWER: a) 5.8 m/s @31o below horizon b) 152 N
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25 N
1 slug200 m/s
20o
V10 m/s θ
The disembodied head of Sir Isaac Newton (weight = 25 N on Erf) is shot into outer space by Wayne's punkin chunker and collides inelastically with a giant space slug (mass = 1 slug). a. What is the final speed and direction of Issac's disembodied head with the slug stuck to it with slug mucous? b. What impulse did Issac's head receive during the collision?
ANSWER: a) 22 m/s @28o below horizonb) 453 Ns or kgm/s
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20o
9 m/s
8 m/s
3 kg
5 kg
30o
4 m/s
3 kg
5 kgθ = ?
V = ?
LA
T
E
R
Two slices of space toast collide elastically in outer space. Neglect gravity and friction. a.) Find the unknown angle and velocity.b.) If the slices are in contact for .1 sec during the collision, what is the average vertical force exerted on the 3 kg slice during the collision. (Hint: Impulse Momentum Theorem)
Deja Space Toast Deluxe
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25 N
1 slug200 m/s
20o
V10 m/s θ
The disembodied head of Sir Isaac Newton (weight = 25 N on Erf) is shot into outer space by Wayne's punkin chunker and collides inelastically with a giant space slug (mass = 1 slug). a. What is the final speed and direction of Issac's disembodied head with the slug stuck to it with slug mucous? b. What impulse did Issac's head receive during the collision?
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Horizontal: Σpxi = Σpxf(.003)(.06cos40o) + 0 = (.003)(.03cos25o) + (.002)Vx
Vx = .028 ft/sVertical: Σpyi = Σpyf
(.003)(.06sin40o) + 0 = (.002)Vy ‑ (.003)(.03sin25o)
Vy = .077 ft/sPythagorize it and trig it...V = .082 ft/s and θ = 70 o
(.06ft/s)cos40o
Vx
(.03ft/s)cos25o
(.06ft/s)sin40o
(.03ft/s)sin25o
Vy
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a) Σpxi = Σpxf(84.3 kg)(6 m/s) + 0 = (84.3 kg)Vf + (1.6 kg)(13.5 m/s)
Vf = 5.74 m/s
* Conversion... 5.8 slugs = 84.3 kg
b) I = Δp = pf pi = (1.6 kg)(13.5 m/s) 0 = 21.6 Ns
c) Mr. B receives an equal but opposite Impulse of 21.6 Ns
d)
e) The pin receives an equal but opposite average force of +1440N