How much energy is dissipated to stop a 3000 lb car travelling at 30 miles per hour?

Answer 1

For a start, stop using those silly imperial units of measure, they are obsolete and it is only stubborn conservatives who insist on using them. they will do you no good, and will only complicate understanding real world physics.

Here is a great site for unit conversion

http://www.davidson.com.au/tools/convert/default.asp

1lb = 0.4536 kg

3000 lb * 0.4536 = 1,360 kg

1mph = 1.6 km/h

30mph * 1.6 = 48 km/h

so you question should be:

How much energy is dissipated to stop a 1.3 t car travelling at 48 km/h

First you need to convert the velocity of the object into something useful, that is the SI standard for velocity m/s (meters per second)

1 m/s = 3.6 km/h (60 seconds * 60 minutes)/1000

1 / 3.6km/h = 0.277 (to convert km/h into m/s multiply by this amount)

48 km/h * 0.277 = 13.333 m/s

so we roughly have a 1300 kg mass travelling at 13 m/s.

The formula for converting Mass and Velocity to Kinetic Energy is

Ek = 1/2 MV^2 (Energy Kinetic [Joules] = 1/2 Mass * Velocity Squared)

so

1/2 * 1300 kg * (13 m/s * 13 m/s) = 109,850 J or roughly 110 kJ

So Your Answer is 110 kJ (Kilo Joules)

Now what can be done with that energy to compare it to a real life scenario ?

---- we could light a light bulb with it :

lets say a 100 watt incandescent globe.

1 watt for one second = 1 joule.

110 kJ = 110,000 watt seconds

110kj / 100w = 1100 seconds.

1100 seconds / 60 seconds = 18.33 minutes.

so the energy dissipated to stop a 1.3t car travelling at 48 km/h is enough energy to light a 100 watt light bulb for 18 minutes.

---- we could heat water with it :

Lets say we want to boil water.

4.184 Joules will heat 1 gram of water by 1°C.

to boil water to need to bring it to 100°C.

(110 kJ / 4.184) / 100°C = 262.90 grams = 263ml of water.

a typical small cup of coffee is 275ml

so the energy dissipated to stop a 1.3t car travelling at 48 km/h is almost enough energy to boil enough water for a small cup of coffee.

---- compare this energy to a 600ml bottle of coca cola.

a 600ml bottle of coca cola contains 1080 kJ of energy. this is almost enough to get our 1.3t car travelling from stop to 48 km/h 10 times !

of course all of these examples assume a perfect world with no friction, wind resistance, thermal loss, and other in-efficiencies so the figures will be a little less that ideal.