Conservation of energy problem

Oct 2017
8
0


If the speed of a 62 kg skier at P is 1.5 m/s, and the conversion from potential energy to kinetic energy as she skies down the hill is 65% efficient, then her speed at point Q will be _ m/s and _ kJ of energy will have been lost due to friction.

I found the speed and it was 11.57 m/s. However, I don't get the same answer as the answer key says for the kJ of energy lost due to friction. The answer was 2.6 kJ, but I keep getting 3.6 kJ. What I did was I did epi+eki= ekf + epf + heat. Isolated heat to find the energy lost due to friction. I used the speed, 11.57m/s for the ekf. I still keep getting 3.6kJ and not 2.6 at all.
 

ChipB

PHF Helper
Jun 2010
2,367
292
Morristown, NJ USA
I get 2.6 KJ, but I don't agree that the final velocity is 11.57 m/s. Please show us how you arrived at that. I get a final velocity of 12.45 m/s, from:

\(\displaystyle \Delta PE \times 0.65 = \Delta KE\)

\(\displaystyle m g (15m -3m) (0.65) = \frac 1 2 m (v_2^2 - v_1^2)\)
 
Apr 2015
1,089
252
Somerset, England
change of PE = g x mass x change of elevation = 9.81*62*(15 -3) Joules = 7298.64J

35% of this is lost

7298.64 * 0.35 = 2.554J or 2.6 kJ

65% of the lost PE ends up as increased KE.

The skier starts off 0.5 *62 * 1.5 * 1.5 J of KE = 69.75J and gains 7298.64*0.65 J = 4744.12J of KE

Thus she has a total of 4813.87J of KE.

This corresponds to a velocity of sqrt (4813.87/31) = 12.46 m/sc

Edit I see I cross posted with Chip.

:)
 
Oct 2017
8
0
I did 0.65= ((.5*62*vf^2) + (62*9.8*3))/((.5*62*1.5^2) +(62*9.8*15)). Isolated vf to get 11.57.
 
Apr 2015
1,089
252
Somerset, England
I did 0.65= ((.5*62*vf^2) + (62*9.8*3))/((.5*62*1.5^2) +(62*9.8*15)). Isolated vf to get 11.57.
I can't tell from that reply whether you have realised your mistake or not?
 
Apr 2015
1,089
252
Somerset, England
65% of the lost PE ends up as increased KE.
I see I misphrased this line, which should have read

65% of the change in PE ends up as increased KE.

sorry.
 
Oct 2017
8
0
I saw that both you did it a different way, but I dont understand why you'd do it that way.
 
Apr 2015
1,089
252
Somerset, England
I saw that both you did it a different way, but I dont understand why you'd do it that way.
Actually both of us did it basically the same way.

Have you understood where you went wrong yet?

Hint this is not correct reasoning

I did 0.65= ((.5*62*vf^2) + (62*9.8*3))/((.5*62*1.5^2) +(62*9.8*15)). Isolated vf to get 11.57.