Two particles are connected by a rope and are moving in the same direction. What is gained by treating them as a single particle, and what happens to the tension?

Treating them as one particle gives a single equation of motion for the whole system, using the total mass . The tension disappears from it: it pulls one particle forwards and the other backwards with equal magnitude, so the two contributions cancel. That makes it the quickest route to the acceleration or to an external force; to find the tension itself, go back to one of the particles on its own.

A car tows a caravan with a tow bar, modelled as a light rod . When is the rod in tension and when is it in thrust?

A rod is in tension when it is being stretched, which happens while the car is accelerating and the rod has to drag the caravan along. It is in thrust , or compression, when it is being squashed, which happens while the car is braking and the caravan tends to catch up with the car and push against it. So the test is which way the caravan tends to move relative to the car: falling behind stretches the rod, catching up compresses it.

What can a rope do that a rod cannot, and what does that mean for the forces in it?

A rope can go slack . A rope only ever pulls, so it can only ever be in tension ; if it would ever need to push, it goes slack and the tension becomes zero. A rod can be in tension or in thrust, so it can push as well as pull and never goes slack.

For two connected particles, how many equations of motion can you write, and how many do you actually need?

Three are available: one for each particle on its own, and one for the two treated as a single system. Only two of them are independent, because the system equation is just the two separate equations added together, with the tension cancelling. So choose whichever two make the unknown you want easiest to reach, rather than writing all three and hoping.

A trailer is towed along level ground. There is no vertical motion, so is there any point in writing a vertical equation?

Yes: with no vertical motion the vertical resultant is zero , which still gives a usable equation. For the trailer that equation says the normal reaction equals the weight, and the normal reaction is exactly what you need if friction is involved later, since friction depends on it. No motion in a direction does not mean no information in that direction; it means the acceleration there is zero, which is a value like any other.

A LevelMathsCambridge (CIE)MechanicsFlashcardsForces & EquilibriumNewton's Second Law

Newton's Second Law (Cambridge (CIE) A Level Maths: Mechanics): Flashcards

Exam code: 9709

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FrontConnected Bodies (Ropes & Tow Bars)
Two particles are connected by a rope and are moving in the same direction. What is gained by treating them as a single particle, and what happens to the tension?
BackConnected Bodies (Ropes & Tow Bars)
Treating them as one particle gives a single equation of motion for the whole system, using the total mass.
The tension disappears from it: it pulls one particle forwards and the other backwards with equal magnitude, so the two contributions cancel.
That makes it the quickest route to the acceleration or to an external force; to find the tension itself, go back to one of the particles on its own.
BackConnected Bodies (Ropes & Tow Bars)
A rod is in tension when it is being stretched, which happens while the car is accelerating and the rod has to drag the caravan along.
It is in thrust, or compression, when it is being squashed, which happens while the car is braking and the caravan tends to catch up with the car and push against it.
So the test is which way the caravan tends to move relative to the car: falling behind stretches the rod, catching up compresses it.

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Cards in this collection (5)

Two particles are connected by a rope and are moving in the same direction. What is gained by treating them as a single particle, and what happens to the tension?
Treating them as one particle gives a single equation of motion for the whole system, using the total mass.
The tension disappears from it: it pulls one particle forwards and the other backwards with equal magnitude, so the two contributions cancel.
That makes it the quickest route to the acceleration or to an external force; to find the tension itself, go back to one of the particles on its own.
A car tows a caravan with a tow bar, modelled as a light rod. When is the rod in tension and when is it in thrust?
A rod is in tension when it is being stretched, which happens while the car is accelerating and the rod has to drag the caravan along.
It is in thrust, or compression, when it is being squashed, which happens while the car is braking and the caravan tends to catch up with the car and push against it.
So the test is which way the caravan tends to move relative to the car: falling behind stretches the rod, catching up compresses it.
What can a rope do that a rod cannot, and what does that mean for the forces in it?
A rope can go slack.
A rope only ever pulls, so it can only ever be in tension; if it would ever need to push, it goes slack and the tension becomes zero.
A rod can be in tension or in thrust, so it can push as well as pull and never goes slack.
For two connected particles, how many equations of motion can you write, and how many do you actually need?
Three are available: one for each particle on its own, and one for the two treated as a single system.
Only two of them are independent, because the system equation is just the two separate equations added together, with the tension cancelling.
So choose whichever two make the unknown you want easiest to reach, rather than writing all three and hoping.
A trailer is towed along level ground. There is no vertical motion, so is there any point in writing a vertical equation?
Yes: with no vertical motion the vertical resultant is zero, which still gives a usable equation.
For the trailer that equation says the normal reaction equals the weight, and the normal reaction is exactly what you need if friction is involved later, since friction depends on it.
No motion in a direction does not mean no information in that direction; it means the acceleration there is zero, which is a value like any other.

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