# Calculating Mass of a Car with KE of 1*10^6 J

• Lovely

#### Lovely

O.K . What is 1*10(6power)J mean. Do I further need to break this down in order to work the problem.
Problem: A car travleling 25 km/hour has Kinetic energy of 1*10(6power)J.
What is the mass of the car?
I've converted k/h to m/s

Lovely said:
O.K . What is 1*10(6power)J mean. Do I further need to break this down in order to work the problem.
Problem: A car travleling 25 km/hour has Kinetic energy of 1*10(6power)J.
What is the mass of the car?
I've converted k/h to m/s

Do you know what mass is in terms of velocity and energy?

Doug

Mathechyst said:
Do you know what mass is in terms of velocity and energy?

Doug
If I'm looking for mass am I suppose to know?

Lovely said:
If I'm looking for mass am I suppose to know?
No I do not know what mass is in terms of velocity and energy

$$KE=\frac{1}{2}mv^2$$. So, if $$KE = 10^6$$, and $$v=25km/h$$ or $$~6.9m/s...$$
10000000/.5(6.9)^2=416666kg? Thats almost 300X the average mass of a car

Edited: Oops on Calculations, Thanks Mathechyst

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DirtyDan said:
$$KE=\frac{1}{2}mv^2$$. So, if $$KE = 10^6$$, and $$v=25...$$
10000000/(312.5)=3200kg

It doesn't look like you accounted for the fact that the velocity is given in $km/hr$.

Yeah, I've been editing it lol.. But now look, I checked it a couple of times. Is it meant to come out with non-sensical numbers?

DirtyDan said:
Yeah, I've been editing it lol.. But now look, I checked it a couple of times. Is it meant to come out with non-sensical numbers?

Since we're giving out the answer, we should show how it is solved:
$$m=\frac{2K}{v^2}=\frac{2\cdot1\cdot10^6 kg\cdot{m^2}}{s^2}\cdot\frac{hr^2}{25^2 km^2}\cdot\frac{3600^2 s^2}{hr^2}\cdot\frac{km^2}{1000^2 m^2}=\frac{2\cdot3600^2}{25^2}kg=41472kg$$
Hmm. A 45.6 ton car. Still, it looks right to me. Let's do a back of the envelope calculation to see what we come up with. Suppose we have a 1000 kg (2200 lb) car going 25 km/hr.

$$\frac{mv^2}{2}=\frac{1000kg}{1}\cdot\frac{25^2 km^2}{hr^2}\cdot\frac{1000^2 m^2}{km^2}\cdot\frac{hr^2}{3600^2 s^2}=\frac{1000\cdot25^2\cdot1000^2 kg\cdot{m^2}}{s^2}=48225.3J$$

Yes, I would say a million joules at 25km/hr is a bit much.

Doug

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Mathechyst said:
Since we're giving out the answer, we should show how it is solved:
$$m=\frac{2K}{v^2}=\frac{2\cdot1\cdot10^6 kg\cdot{m^2}}{s^2}\cdot\frac{hr^2}{25^2 km^2}\cdot\frac{3600^2 s^2}{hr^2}\cdot\frac{km^2}{1000^2 m^2}=\frac{2\cdot3600^2}{25^2}kg=41472kg$$
Hmm. A $9\frac{1}{2}$ ton car. Still, it looks right to me.

Doug
O.K Mathechyst I got completed lost. I didn't see were you converted k/m into m/s. I'm sorry but i guess I'm missing the whole concept

Lovely said:
O.K Mathechyst I got completed lost. I didn't see were you converted k/m into m/s. I'm sorry but i guess I'm missing the whole concept

I find it easier to include the units conversion along with the rest of the solution. It's just a matter of multiplying by 1. For example, to convert km/hr to km/s you multiply the km/hr by the number of hours in a second, namely 1/3600.

$$\frac{25 km}{hr}\cdot\frac{hr}{3600 s}=\frac{25 km}{3600 s}=\frac{1 km}{144 s}$$

Notice how the $hr$ units cancel? That's what you want to do. Cancel out the units you don't want and replace them with the units you do want. Now to convert km/s to m/s you just multiply km/s by the number of meters in a kilometer, so:

$$\frac{1 km}{144 s}\cdot\frac{1000 m}{km}=\frac{1000 m}{144 s}=6.94\frac{m}{s}$$

See how the $km[/tex] units cancelled? Doug Mathechyst said: I find it easier to include the units conversion along with the rest of the solution. It's just a matter of multiplying by 1. For example, to convert km/hr to km/s you multiply the km/hr by the number of hours in a second, namely 1/3600. $$\frac{25 km}{hr}\cdot\frac{hr}{3600 s}=\frac{25 km}{3600 s}=\frac{1 km}{144 s}$$ Notice how the [itex]hr$ units cancel? That's what you want to do. Cancel out the units you don't want and replace them with the units you do want. Now to convert km/s to m/s you just multiply km/s by the number of meters in a kilometer, so:

$$\frac{1 km}{144 s}\cdot\frac{1000 m}{km}=\frac{1000 m}{144 s}=6.94\frac{m}{s}$$

See how the [itex]km[/tex] units cancelled?

Doug
Thanks for the help. I have completed the activity. I appreciate you.
:rofl: