# Ratio of Power between Two Cars

• Balsam
In summary: I would check the answer assuming these are the same car ... the answer should be 1:4 ... it's good to check your work.BTW ... the shortcut is a good way to find the answer quickly ... the long way is good when you need to show your work.
Balsam

## Homework Statement

A Grand Prix race car accelerates to twice the speed of the car in sample problem 1, in the same amount of time. Calculate the ratio of the power needed by the Grand Prix car to the power needed by the car in sample problem 1.
Given: initial speed of car=0m/s,

final speed of car in sample problem 1=22.7m/s, so speed of Grand Prix car will be 2(22.7)=55.6m/s,

time=7.7s

h=0, so there's no gravitational potential energy, only kinetic energy.

power in sample problem 1=55kW=55000W

## Homework Equations

W=ΔEg=1/2mvf^2-1/2mvi^2,

After finding W, use P=W/t to solve for power and then write what the ratio between the power is

## The Attempt at a Solution

I don't know how to solve this because we're not given the mass of the Grand Prix car. I can't think of a way to solve this problem.

My guess is that you're supposed to assume the mass of both cars is the same, and the question only asks for the ratio of power, so the common mass term would drop out of the ratio.

Other assumptions are also involved. For example, is the acceleration constant, so that the maximum power only occurs at the end of the time period, or is the power constant, which requires infinite friction at the start, or is it some combination of the two.

What is the source of the relevant equations? There are alternative equations that could be used.

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rcgldr said:
My guess is that you're supposed to assume the mass of both cars is the same, and the question only asks for the ratio of power, so the common mass term would drop out of the ratio.

Other assumptions are also involved. For example, is the acceleration constant, so that the maximum power only occurs at the end of the time period, or is the power constant, which requires infinite friction at the start, or is it some combination of the two.

What is the source of the relevant equations? There are alternative equations that could be used.
I tried doing that, but I got the wrong answer. The answer is 1:4

Considering the iplied level ... you are probably finding the ratio of average power, properly given:
$$\bar P =\frac{\Delta E}{\Delta t}$$
... adjust your strategy: it is best practise do the algebra before you use numbers ... so work entirely in variables. Make sure you use a different variable for the things that are different.
i.e. ##\bar P_1## would be the average power of the 1st car (the one in sample problem 1 say) and ##v_1## would be it's final speed.
This will allow you to eliminate the variables that have the same value without having to know what they are.

I take it you are given the mass of the car in sample problem 1, but not problem 2 ... you may assume that the grand prix car has the same mass (or near enough) or you can look up the regulation weight of a grand prix car and use that. Make sure you list your assumptions.

I have a feeling that you are expected to use a shortcut here ... but since you didn't spot it, you should go through the long way.

Balsam said:
I tried doing that, but I got the wrong answer. The answer is 1:4
That answer suggests the shortcut I mentioned above... it is correct for assuming the cars are equal mass.

Since you tried that, it means you did something wrong in your maths.

Simon Bridge said:
Considering the iplied level ... you are probably finding the ratio of average power, properly given:
$$\bar P =\frac{\Delta E}{\Delta t}$$
... adjust your strategy: it is best practise do the algebra before you use numbers ... so work entirely in variables. Make sure you use a different variable for the things that are different.
i.e. ##\bar P_1## would be the average power of the 1st car (the one in sample problem 1 say) and ##v_1## would be it's final speed.
This will allow you to eliminate the variables that have the same value without having to know what they are.

I take it you are given the mass of the car in sample problem 1, but not problem 2 ... you may assume that the grand prix car has the same mass (or near enough) or you can look up the regulation weight of a grand prix car and use that. Make sure you list your assumptions.

I have a feeling that you are expected to use a shortcut here ... but since you didn't spot it, you should go through the long way.

I tried assuming that the masses of both cars are the same (1100 kg), but I got the wrong answer. The correct answer is 1:4

See post #5 (above yours). Our posts crossed.
1:4 is the correct answer if the cars have the same mass.

Simon Bridge said:
See post #5 (above yours). Our posts crossed.
1:4 is the correct answer if the cars have the same mass.

I did Em=Eg=.5(1000)(55.6)^2. Em=1700248--plug that in for W: P=W/t. P=1700248/7.7=220811.4268.

That would make the ratio between the cars 220811.4268:55000, which is wrong

So the car in problem 1 reached 27.8m/s then? You definitely did something wrong ... maybe the probelm 1 power calc is wrong or there is a calculator button-press error somewhere?

Do what I suggested and do the algebra first.
If car 1 reaches speed ##v_1## in time ##T## then car 2 reaches speed ##v_2=2v_1## in time ##T## and the power ratio is given by:

$$\frac{\bar P_2}{\bar P_1} = \frac{\frac{1}{2T}mv_2^2}{\frac{1}{2T}mv_1^2} = \cdots$$ ... and simplify.

Last edited:
Em=Eg=.5(1000)(55.6)^2. Em=1700248
But: 0.5*1000*(55.6)^2 = 1545680 ... check your arithmetic.

I tried this and I got the right answer because I ended up recalculating the power for the sample problem, which gave me a non-rounded value. The problem was that the sample problem in the book only writes the rounded value and that was what I used. Thanks !

Simon Bridge
Continuing the algebra from post #9 ... the ##\frac{1}{2T}m## terms divide out leaving:
$$\frac{\bar P_2}{\bar P_1} = \frac{v_2^2}{v_1^2} = \frac{(2v_1)^2}{v_1^2} = 4$$ so the ratio is: ##\bar P_1:\bar P_2 = 1:4##

The shortcut is to realize that, since power depends on the square of the speed, doubling the speed will quadruple the power.
Now you don't need to do so much maths in future. ;)

Aside: the regulation minimum weight for a grand prix car is 750kg ... most actual cars weight less than this and the teams add additional weights to meet the regs, so ##m_2 = 3m_1/4## is reasonable... this means that the correct ratio should be 1:3 instead of 1:4... can you see how that is calculated without having to crunch all the numbers?

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Simon Bridge said:
Continuing the algebra from post #9 ... the ##\frac{1}{2T}m## terms divide out leaving:
$$\frac{\bar P_2}{\bar P_1} = \frac{v_2^2}{v_1^2} = \frac{(2v_1)^2}{v_1^2} = 4$$ so the ratio is: ##\bar P_1:\bar P_2 = 1:4##

The shortcut is to realize that, since power depends on the square of the speed, doubling the speed will quadruple the power.
Now you don't need to do so much maths in future. ;)

Aside: the regulation minimum weight for a grand prix car is 750kg ... most actual cars weight less than this and the teams add additional weights to meet the regs, so ##m_2 = 3m_1/4## is reasonable... this means that the correct ratio should be 1:3 instead of 1:4... can you see how that is calculated without having to crunch all the numbers?

Yeah, that makes sense. If you keep all other values the same but double the velocity, it'll result in a quadrupled power

Simon Bridge said:
Aside: the regulation minimum weight for a grand prix car is 750kg
Formula 1 2016 season minimum "weight" limit is 702kg with driver, but not including the 100 kg max fuel at the start of a race (Formula 1 cars do not refuel during a race). As a further aside, a few years ago FIA banned the usage of depleted uranium for ballast (based on a cost issue, about $2750 USA per kg, so for a team with 3 cars at up to 75kg of ballast per car, that would be$618,750 USA).

For those in the USA, grand prix is also used to refer to Indy Racing League cars, where the weight limit is 691kg, but without driver or fuel.

## 1. What is the ratio of power between two cars?

The ratio of power between two cars refers to the comparison of the maximum power output of one car to another. It is typically expressed as a decimal or a percentage.

## 2. How is the ratio of power between two cars calculated?

The ratio of power between two cars is calculated by dividing the maximum power output of one car by the maximum power output of the other car. This can be calculated using the horsepower or kilowatt ratings of the cars.

## 3. Why is the ratio of power between two cars important?

The ratio of power between two cars is important because it can provide insight into the relative performance of the cars. A higher ratio indicates that one car has a greater power advantage over the other, which can translate to better acceleration and overall speed.

## 4. Is the ratio of power between two cars the only factor that determines performance?

No, the ratio of power between two cars is not the only factor that determines performance. Other factors such as weight, aerodynamics, and transmission also play a significant role in a car's overall performance.

## 5. Can the ratio of power between two cars change?

Yes, the ratio of power between two cars can change. It can be affected by modifications such as engine tuning, adding turbochargers or superchargers, and upgrading the transmission. The ratio can also change over time as the cars' engines age and wear down.

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