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My first question is I wonder why there's no opposite tension acting the towing cable in the diagram above since the two tugboats are dragging the supertanker. I thought if one obeject is dragging another object with a rope, there should be two equal but opposite tension acting on the rope since they are like 'opposing' each other right like the diagram below? Is there any misconception?

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My second question is do tensions always exist in pair (equal and opposite) between two objects connected by a rope if one object is dragged? If no, why (please provide me an example if possible)? If yes, what about an object pulled by a force using a rope, is it still two equal and opposite tensions acting on the rope?

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There is an equal and opposite tension that slows the tugboat. It isn't shown because the question is about the forces on the supertanker, and not the tugboats.

As to why forces always occur in equal and opposite pairs, physics does not provide any better answer than "because Newton's 3rd law says so". Physics says how the universe behaves, not why it does so. Questions about why a complex law is true can be answered in terms of deriving the complex law from simpler laws. But the simplest laws are just accepted as true because they have been verified by experiment.

For why tension is equal and opposite in a rope, see Why is the tension on both sides of an Atwood machine identical?

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I thought if one obeject is dragging another object with a rope, there should be two equal but opposite tension acting on the rope since they are like 'opposing' each other right like the diagram below? Is there any misconception?

Yes, but the equal and opposite forces acting on the ropes are the internal forces acting on the ropes.

The diagram below shows the ropes between the tanker and the tugs cut creating free body diagrams (FBDs) for the tanker, tugs and a section of the rope between them.

For the FBDs of the tanker and tugs the tension force acts as an external force. For the FBDs of the sections of rope, which are assumed to be light and inextensible, the tension forces are internal equal and opposite forces per Newton's 3rd law.

Hope this helps.

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