Acceleration Disadvantage: Solving a Problem with a Go-Kart and Different Masses

[oblit]

Hi Guys,

I'm a newbie to this, so be gentle!

I'm trying to work out a (simple, but I can't do it!) problem regarding a theoretical acceleration disadvantage...

What is the disadvantage in acceleration when a go-kart with a 7.5HP engine is used to propel a 80kg mass to 10m/s, when compared to a 65kg mass? (assume kart mass is 110kg).

Any help & workings would be most appreciated!

Thanks.

 

[Kurdt]

Welcome to PF! You must make an attempt or discuss your ideas before you can receive any help on the forum. What principles do you think you need to answer this question.

 

[oblit]

Well, obviously F=ma is involved.

What I'm having difficulty with is calculating the "Force" of the engine from a power rating. This would be a lot easier question for me to solve if it was related to the thrust of a turbofan!

 

[Kurdt]

Horsepower is obviously a power rating. You might want to convert that to kilowatts. You can just type that into google and it will give you the conversion factor. Instantaneous power is force multiplied by velocity.

 

[oblit]

Okay, I've given it a go.

I calculate that to 10 m/s, the 80kg mass will accelerate at 2.9 m/s, while the 65kg mass will accelerate at 3.2 m/s, leaving a 0.3 m/s gap. This is assuming that I am correct in thinking that the motor will provide a forward force of 560N.

 

[Kurdt]

Ok probably got you to attack this from the wrong angle because I wasn't thinking about it properly. Power is also the rate of doing work and work is the change in kinetic energy. Since the kart is starting from rest the initial kinetic energy is 0. One can assume that the kart uses all its 7.5Hp to accelerate the kart from rest to its speed of 10m/s and find the time it takes to do that. Then one can work out the acceleration.

 

[oblit]

Right, 2nd attempt!

Work done by engine to accelerate 190kg total mass to 10 m/s = (190*10^2)/2 = 9500J

Work done by engine to accelerate 175kg total mass to 10 m/s = (175*10^2)/2 = 8500J

Using P=W/t & the total engine power as 5600W (can I do this?)

t for 190kg mass = 1.7 s (seems very fast!)
t for 175kg mass = 1.5 s (seems very fast!)


sooo...a 0.2s disadvantage to 10m/s?

 

[Kurdt]

That seems a better way of doing it.