Question

I WILL give a Medal for the best response!

A 2.00-kg object traveling east at 20.0 m/s collides with a 3.00-kg object traveling west at 10.0 m/s. After the collision, the 2.00-kg object has a velocity 5.00 m/s to the west. How much kinetic energy was lost during the collision?

The correct answer is supposed to be 458 J.

How can I solve this problem? I already tried using conservation of momentum, and conservation of energy, but I'm not getting the right answer. Am I supposed to be using calculus to solve this problem?

Any help would be greatly appreciated!

Answer 1

Hi

Answer 2

I believe I have your solution. Still care for it?

Answer 3

It's okay. I was able to solve it with help from someone in the Physics study area.

Thank you though!

Answer 4

I gave you a medal anyway because you were the only one to answer! :)

Answer 5

Lol, sorry, I have your solution...one sec.

Answer 6

Mass of the firstbody, M1 = 2 kg

Mass of the secondbody, M2 = 3 kg

Velocity of thefirst body before collision, U1 = 20 m/s

Velocity of thesecond body before collision, U2 = - 10 m/s ( '-' representWest )

Velocity of thefirst body after collision, V1 = - 5 m/s

Velocity of thesecond body after collision = V2

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From the lawof conservation of momentum,

Totalmomentum after collision = Total momentum before collision

M1 V1 + M2 V2 = M1 U1 + M2 U2

2 * - 5 + 3 V2 = 2 * 20 + 3 * - 10

- 10 + 3 V2 = 40 - 30

- 10 + 3 V2 = 10

3 V2 = 20

Velocity of the second body after collision, V2 = 6.67 m/s

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Total kinetic energy before collision, E1 = ( 1/2 ) M1 U12 + ( 1/2 ) M2 U2 2

= 0.5 [ 2 * 20 2 + 3 * ( -10 ) 2 ]

= 0.5 * 1100

= 550 J

Total kinetic energyafter collision, E2 = ( 1/2 ) M1 V1 2 + ( 1/2 ) M2V2 2

= 0.5 [ 2 * ( - 5 ) 2 + 3 * ( 6.67 )2 ]

= 0.5 * 183.47

= 91.73 J

Loss of kinetic energy during the collision, ΔE = E1 - E2

= 550 - 91.73

= 458.27 J

Anyways, hope that made sense. Good luck!

Answer 7

This is very good! Thank you!