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.