# Mechanical equivalent of heat

• kee23
In summary, the conversation discusses a problem involving a 5850kg truck that decelerates uniformly from 85.0km/h to 50.0km/h. By using the equation for kinetic energy and converting units, it is determined that the energy reduction is 2.75*105 Joules. However, since only 95.0% of this energy is converted into heat, the final answer is 6.25*104 Kilocalories.
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?

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

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

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

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

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.

yay I got it. thank you.

No problem. Good job.

## 1. What is the mechanical equivalent of heat?

The mechanical equivalent of heat is a physical constant that relates the units of mechanical energy to the units of heat energy. It is represented by the symbol J and has a value of approximately 4.186 joules per calorie.

## 2. Who discovered the mechanical equivalent of heat?

The mechanical equivalent of heat was first discovered by the English physicist James Prescott Joule in the mid-19th century. He conducted a series of experiments to measure the relationship between mechanical work and heat energy.

## 3. How is the mechanical equivalent of heat determined?

The mechanical equivalent of heat is typically determined by measuring the amount of work done on a system and the resulting increase in temperature. This allows for the calculation of the mechanical energy required to produce a given amount of heat.

## 4. What is the significance of the mechanical equivalent of heat?

The mechanical equivalent of heat is significant because it helped to establish the concept of energy conservation and the relationship between different forms of energy. It also laid the foundation for the development of thermodynamics as a branch of physics.

## 5. How has our understanding of the mechanical equivalent of heat evolved over time?

Our understanding of the mechanical equivalent of heat has evolved over time as new discoveries and advancements have been made in the field of thermodynamics. The initial value of 4.186 joules per calorie has been refined and more precise measurements have been made, leading to a better understanding of the relationship between mechanical and heat energy.

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