Calculating Speed and Kinetic Energy in a Car Collision

[RachelT]

first post so here goes: this question isn't hard but i can't seem to get the answer i should have.

'a car of mass 1050kg runs into the back of car b which is stationary with mass 1200kg. car A was moving at 50mph immediately before impact. after impact, the vehicles are locked together'

calculate the speed at which the 2 vehicles move immediately after collision and the amount of kinetic energy lost in the collision. what has happened to this energy?

any help appreciated. thank you!

Edit: I had an answer of 18.65ms-1 for the speed of the coalesced vehicles. My KE lost was 132559.3J.

 

[lewando]

18.65m/s does not look right. Please check this (and show your steps).

 

[Filip Larsen]

Your answers does not look correct.

The first question can be found directly from the conservation of linear momentum of the two cars before and after the impact. Since the initial speed is given in mph I would recommend that you answer using this unit too, even if you use m/s in your calculations.

The second question can be found directly from considering the kinetic energy of the two cars. Since your answer is not far off, it may be that you got the equations right and only made a slip with the calculator or something. If you need to know you can show your calculations here. When you answer this I recommend that you think about how many digit of precision is needed (hint: use kJ as unit and round to a suitable number of decimals).

 

[sophiecentaur]

This may be a daft question but did you do the mph / ms^-1 conversion right? Without showing your workings, It's hard to rule out anything.

 

[RachelT]

yes thank you sophiecentaur. I have now converted and have a velocity of 10.26m/s. using this answer for the next part I had an energy loss of 105,637.96J. Can you tell me if these answers are correct. If not I will keep plugging away. Thanks for your time :-)

 

[Filip Larsen]

Your speed looks almost correct (you probably use a conversion factor different from 1 mph = 0.4474 m/s), but your energy does not. If you write up how you arrive at that number we can point out what or where the mistake is.

 

[CWatters]

just for info, using google to do the conversion I get 10.43m/s or 23.33mph

 

[RachelT]

Tried again and got total energy loss of 137995.2 J. Is this right?

 

[Filip Larsen]

Tried again and got total energy loss of 137995.2 J. Is this right?

Very close to what I get. The difference is probably because you either use a different conversion factor for changing mph to m/s, or because you round off intermediate results before you (re-)enter them on your calculator. Remember to round off your final answers to a suitable number of significant digits using an appropriate unit - settling for four significant number, for instance, the number you wrote above could be written up as 138.0 kJ.