# How to calculate an object breaking point or force require to break it?

for example, i have a 10 ft rope that has a strength to hold 2000lbs.

when I attach the rope to an object of 1500lb and pull it toward me, (keep it simple with no friction apply) the rope should not be damaged

Now I wrap the rope around the object and have 2 persons identity with the same amount of force pulling toward to themselves. does each person share equal amount of 2000lbs ? which law of physics define this?

• Are you lifting the object, or dragging towards you? If you are dragging it then there isn't any force needed to do so since there is no friction. – John Alexiou Oct 22 '17 at 15:56

You have asked at least two different questions here. I will answer the one in the title of your post.

To solve for when the rope will break, you need to know three things: 1) the magnitude of the load, 2) the cross-sectional area of the rope, and 3) the yield strength of the rope material.

The yield strength is quoted in terms of pounds of load per square inch of area at the breaking point. So you solve for (magnitude of load)/(cross sectional area of rope). If this number is greater than the yield strength, the rope breaks.

It's really just newton's laws of motion. I guess principally the 3rd one "for every action there is an equal and opposite re-action." https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion

It depends how fast you accelerate the object, the force must be less than the tension limit in the strings or ropes at all times. (F=ma)

Friction is usually significant in terms of increasing tension, and should not be neglected.

You can gear up the force using pulleys, more details here, https://en.wikipedia.org/wiki/Pulley

• what if both persons pull the weight to the same direction ----> does newton 3rd law still applies? or say you have thin rope that stands 50g, and you place it on a ruler. each end hangs a 30g weight. will the rope break ? – Marc Jan 23 '17 at 9:57
• The tension in the rope (if you fix it to the object with a pulley) is the sum of the net force applied at each end. That is, if your ruler is fixed then 60g, it will break. However, when you pull the object towards you, it moves, the only force the rope needs to overcome is friction, which you asked to be neglected, i.e. = 0. In this case a cotton thread would not break. (I advise not to neglect friction.) The Mass or Weight of the object would be used directly if you hang the object from the rope/ropes; in your horizontal example it would play a role in generating friction. – JMLCarter Jan 23 '17 at 10:06
• To clarify the comment the cotton thread will of course break if you accelerate the system too fast, exceeding it's tension limit, i.e. $ma>T$ Although the question was kind of a static question. The same applies to the rope. – JMLCarter Jan 23 '17 at 10:24