Understanding Newton's Third Law in Action: A Truck Pushing an SUV

[eglaud]

Homework Statement

A 2,300 kg truck pushes a 2,500 kg SUV, and they both move at 3.75 m/s². I am to find the force that the SUV exerts on the truck.

Homework Equations

F=ma

The Attempt at a Solution

I solved this problem already, it was just taking the acceleration I had found (3.75) and multiplying it by the mass of the SUV, 2,500 kg. My issue is why can't we use Newtons Third Law here, and say that the force of the truck pushing on the suv (2,300 * 3.75) is the same as the force of the suv pushing back onto the truck? Why does this not apply? Some simple clarification would be fantastic, thanks!

 

[andrewkirk]

Newton's Second Law F=ma tells us that the net force on the SUV is 2500 x 3.75. If no other forces are operating on the SUV - including that its motor is off and it is in Neutral - then that is the force exerted by the truck on the SUV.

Then Newton's Third Law tells us that the force exerted by the SUV on the truck is equal and opposite to that, ie -2500 x 3.75.

The amount 2300 x 3.75 doesn't come into any of that. 2300 x 3.75 is the net force on the truck, which we get from Newton's Second Law applied to the truck. that net force will most likely come from a gross force of (2500+2300) x 3.75 from the ground pushing the truck forwards (reaction against the truck's wheels pushing on the ground with the truck engine in operation), together with a force of -2500 x 3.75 which is the SUV pushing back on the truck.

 

[CWatters]

My issue is why can't we use Newtons Third Law here, and say that the force of the truck pushing on the suv (2,300 * 3.75) is the same as the force of the suv pushing back onto the truck? Why does this not apply? Some simple clarification would be fantastic, thanks!

Why do you think the force the truck can apply depends on the weight of the truck (2,300)? It depends on the power of the engine in the truck.

 

[Chestermiller]

Homework Statement

A 2,300 kg truck pushes a 2,500 kg SUV, and they both move at 3.75 m/s². I am to find the force that the SUV exerts on the truck.

Homework Equations

F=ma

The Attempt at a Solution

I solved this problem already, it was just taking the acceleration I had found (3.75) and multiplying it by the mass of the SUV, 2,500 kg. My issue is why can't we use Newtons Third Law here, and say that the force of the truck pushing on the suv (2,300 * 3.75) is the same as the force of the suv pushing back onto the truck? Why does this not apply? Some simple clarification would be fantastic, thanks!

Have you drawn separate free body diagrams on the truck and on the suv, or do you feel that you have advanced to the point where you no longer need to use free body diagrams?

 

[eglaud]

Newton's Second Law F=ma tells us that the net force on the SUV is 2500 x 3.75. If no other forces are operating on the SUV - including that its motor is off and it is in Neutral - then that is the force exerted by the truck on the SUV.

Then Newton's Third Law tells us that the force exerted by the SUV on the truck is equal and opposite to that, ie -2500 x 3.75.

The amount 2300 x 3.75 doesn't come into any of that. 2300 x 3.75 is the net force on the truck, which we get from Newton's Second Law applied to the truck. that net force will most likely come from a gross force of (2500+2300) x 3.75 from the ground pushing the truck forwards (reaction against the truck's wheels pushing on the ground with the truck engine in operation), together with a force of -2500 x 3.75 which is the SUV pushing back on the truck.

Thanks, this explains it perfectly!