How Do You Calculate Tension and Acceleration in a Truck and Trailer System?

[aznkid310]

Homework Statement

The 10-Mg truck hauls the 20-Mg trailer. If the unit starts from rest on a level road with a tractive force f of 20 kN between the driving wheels of the truck and the road, compute the tension T in the horizontal drawbar and the acceleration a of the rig.

Homework Equations

Did i do my sum of forces correctly? If so, I have two unknowns and one equation. The sum of forces in the y - direction would not help. Do i use constant acceleration formulas? If so, i can't seem to figure out which one to use.

The Attempt at a Solution

F_x = ma_x

ma_x = T - f
[(20+10)*10^3]*a_x = T - 20,000

 

[PhanthomJay]

Homework Statement

The 10-Mg truck hauls the 20-Mg trailer. If the unit starts from rest on a level road with a tractive force f of 20 kN between the driving wheels of the truck and the road, compute the tension T in the horizontal drawbar and the acceleration a of the rig.

Homework Equations

Did i do my sum of forces correctly? If so, I have two unknowns and one equation. The sum of forces in the y - direction would not help. Do i use constant acceleration formulas? If so, i can't seem to figure out which one to use.

The Attempt at a Solution

F_x = ma_x

ma_x = T - f
[(20+10)*10^3]*a_x = T - 20,000

You are not noting the net forces correctly. You have to examine the net external forces acting on the truck and trailer system by drawing a free body diagram of the system. Then break up the system into its component parts (truck only or trailer only), and examine the net forces acting on those parts using free body diagrams of those parts.
It is a good idea to first look at the truck-trailer system, which apparently you are attempting to do, having correctly noted that the mass of the system is 30,000 kg. But when you look at the system as a whole, what is the net external force acting on the system? You should note that the tension in the towbar is internal to the system, and will not show up in your determination of the net force in the x direction. The next step would be to look at a FBD of the trailer only. What net force acts on it? Are you familiar with free body diagrams?

 

[aznkid310]

I don't know how to draw a picture on the computer, so I'll try to explain my FBD. In the x-direction (for the trailer), there is the force by the truck in the (+) direction, the tractive force in the (-) direction, so:

ma = F_truck - f

It appears that I am missing something, but I am not sure what. If i only examine the trailer, then the tension becomes external correct?

 

[Redbelly98]

Trailer wheels are free-spinning, and exert no tractive force.

 

[PhanthomJay]

If i only examine the trailer, then the tension becomes external correct?

Yes, and that is the ONLY force acting on the trailer in the horizonatl direction. But before you look at the trailer, look at the entire truck-trailer system, and note that the ONLY force acting on the system is the tractive force (friction force between the tires and road that propels the truck-trailer forward in the +ive direction) of 20,000N. Solve for the acceleration, then go back to the trailer FBD to solve for the drawbar tension. Check your work by looking at a FBD of the truck only.