How to calculate tension in straight-line motion

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1. Oct 29, 2016

Peter Halsall

1. The problem statement, all variables and given/known data
A locomotive has a mass of 40 tonnes.
In one situation, the locomotive is pulling two trucks, each of mass 10 tonnes
Calculate the tension in the coupling pulling the two trucks behind the locomotive.
The coupling is positioned such that it is linking the locomotive and the first truck, which is linked to the second truck.
acceleration of system = 0.2 ms^-2
2. Relevant equations
F=ma

3. The attempt at a solution
Well tension is the amount of force being exerted by two objects on a mass in between these two objects. So would I calculate the force exerted by locomotive and then add that to the force exerted by the two trucks?

2. Oct 29, 2016

TomHart

What information do you need in order to calculate the force required to accelerate 20 tonnes at 0.2 m/s2?

3. Oct 29, 2016

Peter Halsall

The mass and the acceleration, but I don't really see what that's got to do with tension?

4. Oct 29, 2016

TomHart

Peter, your question caused me to really stop and think about what tension is - that I really didn't know the true meaning of it. I assumed it was the force exerted in either direction by some type of connecting/coupling device.

Based on what I have read this morning (part of which is from Wikipedia - see below), here is how I would answer - given as an example:
If there is a 10 kg mass hanging vertically from a string attached to the ceiling, the tension in the string will be (10 kg)(9.8 ms-2) = 98 N. And the force exerted on the weight by the string is 98 N upward. And the force exerted on the ceiling by the string is 98 N downward.

One of the key things that I read is that tension is a non-negative scalar quantity. So tension is not a force. But the numeric value and units are the same as the force that the coupling device exerts at its endpoints.

To any of the resident experts on this site, please feel welcome to share more insight on this or to correct me. Thank you.

From Wikipedia:
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In physics, tension describes the pulling force exerted by each end of a string, cable, chain, or similar one-dimensional continuous object, or by each end of a rod, truss member, or similar three-dimensional object. Tension is the opposite of compression.

In physics, although tension is not a force, it does have the units of force and can be measured in newtons (or sometimes pounds-force). The ends of a string or other object under tension will exert forces on the objects to which the string or rod is connected, in the direction of the string at the point of attachment. These forces due to tension are often called "tension forces". There are two basic possibilities for systems of objects held by strings:[1] either acceleration is zero and the system is therefore in equilibrium, or there is acceleration, and therefore a net force is present in the system.

Tension in a string is a non-negative scalar quantity. Zero tension is slack. A string or rope is often idealized as one dimension, having length but being massless with zero cross section. If there are no bends in the string, as occur with vibrations or pulleys, then tension is a constant along the string, equal to the magnitude of the forces applied by the ends of the string. By Newton's Third Law, these are the same forces exerted on the ends of the string by the objects to which the ends are attached. If the string curves around one or more pulleys, it will still have constant tension along its length in the idealized situation that the pulleys are massless and frictionless.
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