Question

Momentum & Energy Conceptuals!
Answers not given, sorry.
---
SOLVED QUESTIONS.
32) How many joules of potential energy does a 1 kg book gain when it is tossed across the room at a speed of 2 m/s? How much energy is imparted to the wall it accidentally encounters?
33) Which has the greater kinetic energy - a car traveling at 30 km/h or a half-as-heavy car traveling at 60 km/h?
---
UNSOLVED.
@AllTehMaffs, help please (below)! T-T
40) If a moving object doubles its speed, how much more momentum does it have? How much more energy?
58) Consider the swinging balls apparatus. If two balls are lifted and released, momentum is conserved as two balls pop out the other side with the same speed. Can you explain why this never happens (Is this a typo? I Googled it and it said something about one ball popping out).

Answer 1

What do ya think 32 a) is?

Answer 2

A) would be... uh 2 joules?

Answer 3

What kind of energy is it asking for?

Answer 4

Joules? c:
I believe it's kinetic...

Answer 5

Like, directly, what does the question ask about the energy? Does it ask for the potential energy of the book or the kinetic energy of the book?

Answer 6

Nope. Doesn't say

Answer 7

32) "How many joules of potential energy does....."

Answer 8

OH. that.
Well, yes; but I thought that was a typo for "kinetic"/

Answer 9

That's a pretty big typo.... :P

Answer 10

You can never be faulted for answering a question as written - you can always be faulted for incorrectly inferring something not there.

Answer 11

My answer is 2 joules of kinetic due to conservation of momenta \[PE_0 + \cancel{KE_0}^0 = KE_f + \cancel{PE_f}^0\]Well, it's happened before (e.g. km/s when it should have been m/s)...

Answer 12

First, that's conservation of energy. Second, it doesn't apply here because it doesn't say any which way the books is being thrown. If it's being thrown horizontally, then there is no change in height, therefore no change in potential energy - ergo, what can you absolutely know about the potential energy of the book with the given info? (it's a trick question)

Answer 13

Sorry, I meant energy LOL
o.o what?

Answer 14

What can you absolutely know about the potential energy of the book with the given information?

Answer 15

It's 0?

Answer 16

For the book one, there is zero change in potential energy, correct. ^^

Answer 17

Part b is not zero, however.

Answer 18

\[PE_0=0,~KE_f=?\]
Eh... how do I solve o_o;;

Answer 19

You do know K though, you wrote it before.

Answer 20

It's what you originally thought the energy of the book was.

Answer 21

... I forgot...

Answer 22

The thread didn't forget :/

Answer 23

2 Joules?

Answer 24

Maybe - prove it to me. How did you get that before?

Answer 25

aka - What's the formula for Kinetic Energy?

Answer 26

I got 2 joules from conservation of energy...

Answer 27

\[KE_{i \ book}=\frac{1}{2}mv^2 = \frac{1}{2}(1kg)(4m^2/s^2)=2J\]
So if that's all the energy that the book has to start, and when it hits the wall it has zero velocity
\[KE_{f \ book} = \frac{1}{2}mv^2=\frac{1}{2}(1kg)(0m^s/s^2) = 0J\]
Then CoE
\[E_i=E_f\]
\[KE_{i \ book} = KE_{f \ book} + W_{NC \ wall}\]
where WNC is the Non-Conservative Work done by the wall to stop the book - aka, the amount of energy that is imparted to the wall. Therefor, how much energy is imparted to the wall when the book hits it?

Answer 28

?????

Answer 29

Isn't it 2m/s?

Answer 30

\[ v=2m/s\]
\[v^2 = 4 m^2/s^2\]
and energy is in joules, so the energy imparted to the wall is also in units of joules

Answer 31

Ooookay.... got that

Answer 32

And so you know that the book has 2 Joules of energy via kinetic energy when thrown.

When it hits the wall, what happens to the book's velocity?

Answer 33

2 J transferred to the wall

Answer 34

Bingo ^^

Answer 35

The book's velocity goes to zero, and the energy that the book loses is imparted to the wall.

Answer 36

Okay.
Is #33 "both have the same KE"?

Answer 37

Plug em both into
\[K_1 = \frac{1}{2}m_1v_1^2\]
\[K_2=\frac{1}{2}m_2v_2^2\]
\[K_1 \overset{?}{=} K_2\]

Answer 38

How did you do that last equals sign?
Also, I did do that and ended up getting the same KE.

Answer 39

Then you made an error, unfortunately, and it's magic!! ^^

Answer 40

1. what?
2. -_-

Answer 41

1) you did it wrong. try it again.
2) \overset{?}{=}

Answer 42

1. okay
2. thanks

---
car 1\[\frac{1}{2}mv^2=\frac{1}{2}m\times \frac{30km\times 10^3m\times 1h}{1h\times 1km\times 3600s}\approx 4.17\times m\]

Answer 43

you didn't actually square that velocity

Answer 44

oh I forgot to type that in.

Answer 45

... WAIT

Answer 46

car 1: 69.9m
car 2: 278m

Answer 47

What's this m business?

Answer 48

you're not measuring distance

Answer 49

It's mass.
Also, can momenta cancel (and can energy cancel)?

Answer 50

you're not using momentum, so I don't understand that, nor do I understand can "energy cancel" :/

Answer 51

Also, if you're just not going to actually put the mass in, the coefficient needs actual units. Otherwise that's in units of mass

Answer 52

Oh, no it's another question: "Can momenta cancel? Can energies cancel?"
Well, I don't have a given mass...

Answer 53

you have a relationship between them (and sorry, I thought that they were given - the other things still need units though!)

\[m_1=m\]
\[m_2=m/2\]

You can also do that with the velocities
\[v_1 = v = 30km/h\]
\[v_2 = 2v = 60km/h\]

\[K_1 =\frac{m_1v_1^2 }{2}=\frac{mv^2}{2}\]
\[K_2 = \frac{m_2v_2^2}{2} = \frac{(m/2)(2v)^2}{2} = mv^2\]
\[K_2 = 2K_1\]

Answer 54

Also, can you think of an example of momenta canceling?

How about energies canceling?

Answer 55

Nope. o.o

Answer 56

What happens if two balls of equal mass travel towards each other at equal velocities and inelastically collide, leaving them stuck together and still?

Answer 57

zero energy

Answer 58

and momentum

Answer 59

p1=-p2
\[p_1 + p_2 = -p_2+p_2 = 0\]

The energies don't specifically cancel though - the energy just changes form. there's sound and heat and light and whatnot from the collision, so only the momentum cancel each other.

Answer 60

Ah, right... so energies do NOT cancel.

Answer 61

@AllTehMaffs I solved for the kinetic energies and they're still the same? #32

Answer 62

I just showed that they're not equal - Car 2 has twice as much kinetic energy as car 1. It's the long post like 10 comments up.

Answer 63

and you mean 33 right?

Answer 64

oops yeah
Also... if a moving object doubles its speed, how much IMPULSE does it have? In the previous question (asking for momentum and energy) I got double the momentum and 4x the energy.

Answer 65

@AllTehMaffs I looked and couldn't find the long post...

Answer 66

It's the one that ends with
\[K_2=2K_2\] - you didn't get that one? :/ :(

Answer 67

derp,
\[K_2 = 2K_1\]

Answer 68

I got it but I can't turn the information in my work into that...

Answer 69

So you should use either
\[m_1=m
\\ m_2 = m/2\]
or
\[m_1 = 2m
\\ m_2 = m\]
Then for the v's
\[v_1 = v = 30km/h = \frac{25}{3}m/s\]
\[ v_2 = 2v = 2(30 km/h) = 2\left(\frac{25}{3} m/s\right)\]
Then plug the values into each expression
\[K_1 = \frac{m_1v_1^2}{2}\]
\[K_2 = \frac{m_2v_2^2}{2}\]
and compare them ^_^


Remember that
\[(ab)^2 = a^2b^2\]
ie
\[(2a)^2 = 4(a^2)\]

Answer 70

okeys :p

Answer 71

40)
Just like before, you can define
\[v_1=v
\\ v_2 = 2v\]
Then compare
\[ p_1 \ \text{vs} \ p_2\]
and
\[K_1 \ \text{vs} \ K_2\]

58) Needs a picture or more detail. What *is the "swinging balls apparatus?" - cannot infer anything based on given info....

Answer 72

Also, waaaay up above, you mentioned that you found the energy of the book with conservation of energy, and I said "that doesn't apply here." I meant that the way you had written the equation was not the correct method for the problem.
\[E_i = E_f\]
was true, but there wasn't any potential energy to speak of, so saying that the initial and final potential energies were different was incorrect. Conservation of energy still applied, however, it was just that the wall ate up the energy that was imparted to the book by the thrower. ^_^

Answer 73

okey

Answer 74

ԅ(≖ ω ≖ԅ)

Answer 75

o.o?! @♪Chibiterasu

Answer 76

How goes energy?

Answer 77

It goes fine (as soon as I have enough time to finish the rest).
@AllTehMaffs The "swinging ball apparatus" is a Newton's cradle.