Question

A 1.6 Kg cart moving at 6.0 m/s [E] collides with a 1.2 Kg cart moving at 3.0 m/s [W]. The head-on collision is completely elastic and is cushioned by a spring.

a) Find the velocity of the two carts when the spring is at maximum compression.

Answer 1

can you tell me the properties of a completely elastic collision?

Answer 2

no loss of kinetic energy?

Answer 3

wait let me say it more properly

Answer 4

an elastic collision is where 100% potential energy is converted into kinetic energy. It's where negative forces don't subtract energy from the conversion of potential to kinetic energy in the forms of heat, force of friction, air resistance etc

Answer 5

how wrong am i ?

Answer 6

ermm, you sure these bodies have potential energy?

Answer 7

......um wait.

Answer 8

i mean they are moving with some magnitude of force in the opposite directions.... if that counts.

Answer 9

i meant they're moving with some velocity if that counts

Answer 10

Look, in ideal conditions and body on 0 altitude and not attached to any elastic bodies like spring etc are considered having no potential energy

Answer 11

"i meant they're moving with some velocity if that counts" ----> thats kinetic energy

Answer 12

oh sheet.

Answer 13

dw.

Answer 14

so, the definition for elastic collision will be ----> an elastic collision is where 100% energy of the bodies before collision is equal to the energy of the bodies after collision. It's where negative forces don't subtract energy from the conversion of potential to kinetic energy in the forms of heat, force of friction, air resistance etc. OR IN SIMPLE WORDS : THE ENERGY OF THE BODIES REMAINS CONSERVED THROUGHOUT THE COLLISION.

Answer 15

gime me a few seconds to digest that.....

Answer 16

np :P

Answer 17

so are you saying no loss of energy in the collion?

Answer 18

collision*

Answer 19

exactly

Answer 20

so 100% potential energy converts into 100% kinetic energy?

Answer 21

So are we going to use the following formula?
P_initial = P_Final

Answer 22

m_1*v_1_o + m_2*v_2_o = m_1*v_1_f + m_2*v_2_f

Answer 23

What equation do i use to solve this monster? :)

Answer 24

nah nah no potential energy here. Kinetic energy before collision is equal to kinetic energy after collision

Answer 25

i found something useful ....wait le me post plz : )

Answer 26

m_1*v_1_o + m_2*v_2_o = m_1*v_1_f + m_2*v_2_f that is the momentum equation. i was coming to that later.

Answer 27

oh ok ...

Answer 28

ok, sorry i was afk for a bit

Answer 29

wait i need to go blow my nose. 1 second. :)

Answer 30

back

Answer 31

sorry that applied to the spring question we did earlier.

Answer 32

i think we are using P_T_o = P_T_f

Answer 33

first i think we have to find how fast the two carts are moving.

Answer 34

i think this is it.

Answer 35

umm no.

Answer 36

hold on a sec

Answer 37

ok :)

Answer 38

ok so, when there is an elastic collision between two bodies, Total energy and Momentum are conserved. So after the collision both the bodies will have different velocities.

Answer 39

v3 and v4 are unknown

Answer 40

ok got it

Answer 41

so there are two equations:

Answer 42

wait... is the last one 1/2 m_2v_3^2?

Answer 43

oh nvm.....i get it now.. one second plz.... let me take this in..

Answer 44

so you basically took out all the 1/2 from both sides of the equation... i see

Answer 45

wait did you also take out the v^2 from both sides?

Answer 46

ok so what are we solving the equation in terms of?

Answer 47

no no.
they are different equations.

Answer 48

you have two unknowns v3 and v4, and you have two equations to solve them

Answer 49

is your solution based on this following equation...??

Answer 50

like one by one ? for each variable?

Answer 51

\(\color{#0cbb34}{\text{Originally Posted by}}\) @GlockParrot69
like one by one ? for each variable?
\(\color{#0cbb34}{\text{End of Quote}}\)
yes

Answer 52

oh ok thats what i was thinking.....

Answer 53

ok before i go any further... im dealing with the energy conservation right? Solving the V_3 and V_4?

Answer 54

youre dealing with both energy and momentum conservation. Since both the bodies have different speeds after collision, you have two unknown values. So to find the values of those you need two different equations. One comes from energy conservation and the other from momentum conservtion

Answer 55

nice! which one do i need to solve first?

Answer 56

why dont you just rewrite equation 2 by putting in all the values you have

Answer 57

yes sir!!

Answer 58

ok so i divided both sides by m_1 and i got

V_3 = V_1 + V_2 minus V_4 am i wrong ?

Answer 59

just plug in the values in eq 2

Answer 60

you dont need to do that.\(\color{#0cbb34}{\text{Originally Posted by}}\) @GlockParrot69
ok so i divided both sides by m_1 and i got

V_3 = V_1 + V_2 minus V_4 am i wrong ?
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 61

holyyyy sheet. i read the question wrong. I AM SO SORRY. DAMN :(

Answer 62

SORRY SORRY

Answer 63

AAAAWWW :'(

Answer 64

it's k :)

Answer 65

A 1.6 Kg cart moving at 6.0 m/s [E] collides with a 1.2 Kg cart moving at 3.0 m/s [W]. The head-on collision is completely elastic and is cushioned by a spring.

Answer 66

So you were right. there is potential energy( I didnt see the spring)

Answer 67

yeah.

A) Find the velocity of the two carts when the spring is at max compression.

Answer 68

\(\color{#0cbb34}{\text{Originally Posted by}}\) @GlockParrot69
i think this is it.
\(\color{#0cbb34}{\text{End of Quote}}\)
This looks correct

Answer 69

^yes, i am so sorry. completely overlooked the spring thingy. im so sleepy ;-;

Answer 70

Aww... are you from india ?

Answer 71

just help ne with this question. plz :) i've been struggling for the longest time with this question.

Answer 72

yes howd you guess that?

Answer 73

idk maybe bcuz of the time difference!! lol

Answer 74

all i know is that when it's day here, it's night in india lol

Answer 75

So it's P_To = P_Tf?

Answer 76

lol, okay then. just post the rest of the question. i have to wake up early tmrw.

Answer 77

yup thats right.

Answer 78

A 1.6 Kg cart moving at 6.0 m/s [E] collides with a 1.2 Kg cart moving at 3.0 m/s [W]. The head-on collision is completely elastic and is cushioned by a spring.

a) Find the velocity of the two carts when the spring is at maximum compression

Answer 79

K so first do i solve for the velocities of the two carts?

Answer 80

so, when the spring is in max compression, both bodies move together ie. they have the same speed. So you use conservation of momentum

Answer 81

just plug in the values and solve for vf

Answer 82

yes sir!

Answer 83

ok THANKS YOU SO MUCH FOR YOUR HELP AND TIME!! GOD BLESS YOU!! LOVE INDIA. STAY CUTE :) <3

Answer 84

HAHA no problem. Loved helping you. youre a very patient student and smart too. :) take care :))

Answer 85

ill go sleep now! :)

Answer 86

Thanks you SIR. Can say the same for you too.

Answer 87

Good NIGHT!! SWEET DREAMS!

Answer 88

have a bice day. see ya later! :)

Answer 89

see you 2! :)P