# Conservation of energy problem

#### Latinized 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
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:

$$\displaystyle \Delta PE \times 0.65 = \Delta KE$$

$$\displaystyle m g (15m -3m) (0.65) = \frac 1 2 m (v_2^2 - v_1^2)$$

#### studiot

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. #### Latinized

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.

#### studiot

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?

#### studiot

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.

#### Latinized

I saw that both you did it a different way, but I dont understand why you'd do it that way.

#### studiot

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.

#### THERMO Spoken Here

Past Problem

Hello Latinized,

Your problem is similar to one submitted to PHF some months past.
I solved it (as best I could). I reference it for your information.

Boy in a Wheelchair | THERMO Spoken Here!

Good Luck...
JP

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