# Mechanical equivalent of heat

kee23

## Homework Statement

A 5850kg truck decelerates uniformly from 85.0km/h to 50.0 km/h. if 95.0% of the energy reduction is converted into heat, how many kilocalories are produced?

## Homework Equations

kinetic energy (Ek)= 1/2mv2
1 Cal= 4.18J

## The Attempt at a Solution

So first I converted 85.0km/h and 50.0km/h to m/s. 85.0km/h=26.4m/s, 50.0km/h=13.9m/s.
Since 26.4m/s is initial velocity and 13.9m/s is final velocity, so the uniform velocity is v1-vo,: 13.9m/s-23.6m/s=-9.7m/s. (Although I'm not quite sure it's right)

Then
Ek=1/2mv2
.5*(5850kg)(-9.7m/s)2=2.75*105
(.95%)(2.75*105)=2.61*105
so I converted it to cal which 1 cal= 4.18J. so answer came 6.25*104cal. and it was incorrect. someone help me?

AtticusFinch
You just messed up the algebra. In particular this step:

.5*(5850kg)(-9.7m/s)2=2.75*105

You can't do that.

It should be:

0.5*(5850kg)*(26.4m/s)2 - 0.5*(5850kg)*(13.9m/s)2

kee23
hmm so speed not suppose to get subtracted?
sorry, my algebra is my most weakest spot.

AtticusFinch
Well the speeds are subtracted but you need to square them first before you subtract.

kee23
umm shouldn't final speed go first then initial speed go last on your solution?
how do you get the kcal part? I'm not sure what to do from there

Also I made mistake, initial speed should be 23.6m/s

AtticusFinch
Ok so firstly we are looking for a positive energy amount (they ask for energy produced) so we place the larger speed first.

The equation I gave you solves for the energy reduction of the truck in Joules. You need to figure out how much of that energy goes into heat and then convert from Joules to Kilocalories.

kee23
yay I got it. thank you.

AtticusFinch
No problem. Good job.