Calculating Frictional Force on Tires in SUV and Trailer System

[kraigandrews]

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Homework Statement

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?

Homework Equations

F=ma

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

 

[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.

 

[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.

 

[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.

 

[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.

 

[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.

 

[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

 

[Pi-Bond]

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

 

[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.