Need help - Force required for accelerating vehicle

[Mew]

Hello,
I would need some guidance to calculate the force required to accelerate a vehicle up to a certain speed over given amount of time. This might seem simple but I am not sure if I am on the right track anymore. I did some online searching and I couldn't really understand it.

1. Homework Statement

The vehicle has a mass of 250 Kg and uses 4 rubber tires which have a rolling coefficient of 0.02.
The vehicle must reach 100 km/h 60 seconds after start from 0 km/h (stillstand) on a even plane.

We will ignore the effect of aerodynamic drag to keep things easy for starters.

Homework Equations

Fr=c*m
F=m*a

The Attempt at a Solution

I do not have a solution but I would say:

1) Calculate force required to overcome rolling resistance with given tires.
Fr=c*m
Fr=0.02*250 Kg
Fr=5 N

So the rolling resistance will be 5 N with tires of 0.02 coefficient ?

2) Calculate the force required to accelerate vehicle of 250 Kg to 100 km/h in 60 seconds from standstill on an even plane.
This is where I can't figure out the correct formula to use since I have to take into account the acceleration over a given period of time.

Your help will be greatly appreciated.
Brgds
Steven

 

[vela]

Hello,
I would need some guidance to calculate the force required to accelerate a vehicle up to a certain speed over given amount of time. This might seem simple but I am not sure if I am on the right track anymore. I did some online searching and I couldn't really understand it.

1. Homework Statement

The vehicle has a mass of 250 Kg and uses 4 rubber tires which have a rolling coefficient of 0.02.
The vehicle must reach 100 km/h 60 seconds after start from 0 km/h (stillstand) on a even plane.

We will ignore the effect of aerodynamic drag to keep things easy for starters.

Homework Equations

Fr=c*m
F=m*a

The Attempt at a Solution

I do not have a solution but I would say:

1) Calculate force required to overcome rolling resistance with given tires.
Fr=c*m
Fr=0.02*250 Kg
Fr=5 N

So the rolling resistance will be 5 N with tires of 0.02 coefficient ?

How'd you get an answer in Newtons from 0.02*250 kg?

2) Calculate the force required to accelerate vehicle of 250 Kg to 100 km/h in 60 seconds from standstill on an even plane.
This is where I can't figure out the correct formula to use since I have to take into account the acceleration over a given period of time.

You wrote the equation you need above: F = ma. What does F represent? (Hint: it's not the force you're looking for.) What's the acceleration of the car?

 

[RyanH42]

Here my idea (I need to claim that I am in high school my idea can be wrong)
Thing this way there's four tires each tire will cary quarter mass of car and so resistance force will depend it.5 N is true but I didnt understand that's the "total" resistance or one tire's resistance.The other thing use ##x=1/2at^2## equation it comes from differantiation.If you differantiate both side respect to t you get ##dx/dt=at## , ##v=at##.
Make km/h to m/sc then write down the equation then find a.If you interest my idea reply me and I can help you.

 

[dean barry]

You don't give the value for local gravity rate (g), you can use 9.81 (m/s)/s, it won't be far away
Id use SI units, so 100 km/h = 27.778 m/s
Assuming a constant accelerating force value makes the problem simpler and is probably what is implied in the question, its safe also to assume that the weight distribution is equal.
The net rolling resistance force (N) for all the tyres combined will be : 250 * g * 0.02
(you can split the weight if you like then calculate each wheel individually, then add the 4 results, but the answer will be the same)

A good starting point might be calculating the acceleration rate required from the given data (Newtons rules of motion), and then the force required to produce this rate of acceleration (as you stated, F = m*a)

 

[haruspex]

Fr=c*m

As vela has hinted, that equation is wrong. There's something missing.

The net rolling resistance force (N) for all the tyres combined will be :...

Vela's hint, and pointing out the incorrect quoted equation, should be enough as a first response. We should give the OP a chance to supply the right equation.

 

[Mew]

Thank you for your answers !

@vela
I am sure that I messed up the Fr=c*m equation. To have a result in Newton I need to account for the gravity of 9.81 m/s^2 present. Wiki calls the equation Fr=c*Fn where Fn is normal force.
I think this should be correct:

Fr = 0.02*(250 kg*9.81 m/s^2)
Fr = 0.02*(2452.5)
Fr = 49.05 N

I found a site that explains the F=m*a equation in an easier way and now I understand that I have to include acceleration in m/s^2 for the equation to work.
The required acceleration should then be calculated with this equation a = delta v / delta t , is this correct ? Your acceleration hint pointed me in the right way.

If this is correct it should be like this:

delta v = 100km/h converted to m/s = 27.77 m/s
delta t = 60 seconds

a = delta v / delta t
a = 27.77 m/s / 60 s
a = 0.4628 m/s^2

Now F=m*a makes sense too.

F = m * a
F = 250 kg * 0.4628 m/s^2
F = 115.70 N

Then the total force required to accelerate this vehicle will be 115.70 N + 49.05 N = 164.75 N

@RyanH42
I think the 5 N for the rolling resistance I calculated were wrong since I did not account for gravity.

@dean barry
Yes, weight distribution should be equal or as equal as possible, buts let's assume it is equal for the sake of simplicity.

 

[RyanH42]

I think the 5 N for the rolling resistance I calculated were wrong since I did not account for gravity.

You are right friction force is true its 49.05 N.
Your equations and idea is right you find the answer.