# Frictional force by tires

1. Jul 21, 2011

### kraigandrews

[1. The problem statement, all variables and given/known data

An SUV pulls a trailer carrying a boat. The mass of the SUV is 2460 kg and the mass of the boat and trailer is 490 kg. The SUV starts from rest (velocity = 0) and accelerates for 10 seconds to final velocity 12 m/s; i.e., a = 1.2 m/s2.

What is the frictional force exerted by the road on the tires of the SUV?

2. Relevant equations

F=ma

3. The attempt at a solution

so I used
.5mv^2=$\mu$mgd

d=.5at^2
d=60m

thus $\mu$=0.1223

so then Ff on the road by the tires =M_suv*0.1223=300.92 N, but this is not correct, where am I going wrong this seems so simple

2. Jul 21, 2011

### Pi-Bond

Why are you equating the kinetic energy and energy dissipated by friction? No kinetic energy is being dissipated by friction here. Use Newton's second law.

3. Jul 21, 2011

### kraigandrews

ok yeah I thought that was wrong, so then the net force on the SUV is 2950N, but I am confused as to where to go from here.

4. Jul 21, 2011

### Pi-Bond

Is this all the information you have? You can express the force on the SUV in terms of the frictional force and a forward force.

5. Jul 21, 2011

### kraigandrews

This is all the info I have yes. So could you nudge me in the right direction at least, because at the surface this seems simple so I think I'm over looking something.

6. Jul 21, 2011

### Pi-Bond

When the SUV obtains it's final velocity, all forces on it must be balanced. So you need to find the forces on the SUV.

7. Jul 21, 2011

### kraigandrews

so the forces needed here are just the forward force and frictional, so F=ma however how do you find the Forces with the info given, I would only think the net force can be found

8. Jul 21, 2011

### Pi-Bond

True, you need the forward force. I might be missing something here...let me think.

9. Jul 21, 2011

### Pi-Bond

Do you have to find the frictional force or the coefficient of friction?

EDIT: It seems your original method is correct. From conservation of energy-

0=(Kinetic Energy)+(Work due to friction)

I think you forgot a g when calculating the frictional force. Instead of taking that long route you could just have divided the kinetic energy by the distance. F=ma isn't really applicable since you lack knowledge of all forces.

Last edited: Jul 21, 2011