Physics / mechanics help pls

coffeehound

Anyone good at mechanics problem solving please?  It's a simple situation but I don't know the answer.  

Suppose you have a weight, say 100 kg for a round number, and it is suspended by two ropes.  Now if those ropes were vertical, the weight on each would be 50 kg.  But what happens if the ropes are fixed at an angle like say 30º to the vertical?  I would guess they see a higher weight loading?  But how much more, if so?  

Mickey666

Where would any extra weight come from?

coffeehound

I was thinking of the edge case where if you tried to pull on the ropes to bring the load towards horizontal, you need to use increasing force.  So therefore the ropes must see a higher weight as you increase the angle?  

MattMattMattUK

The load on two the two ropes would still be 50 kg each, based on them both taking equal load, or split to a combined total of 100kg (eg 70/30, 60/40). A 100kg weight at rest will exert 100kg (980 Newtons) of downward pressure (in a simplified example, real world there are slight variables), other factors come into play in an engineering situation, but the mass does not change. 

pbartlett

Are you asking about the tension on the ropes? This will decrease as the weight moves around the angles until when the ropes are horizontal the tension in the ropes is zero

rdr

If the two ropes are are the same length and so the weight is evenly supported, the tension in each rope will be = (1/2)(Mg/cosϴ) N, where M= the hanging mass, g=  acceleration due to gravity (=9.8 m/s²), ϴ = between the rope and vertical.
for a 100kg mass and a 30° angle the tension in each rope will be 566 N. This is equivalent to the force produced by suspending a mass of 57.7 kg.

grumpycrab

pbartlett said:

when the ropes are horizontal the tension in the ropes is zero

what's keeping the weight up at this point?

Chino

rdr said:

This is equivalent to the force produced by suspending a mass of 57.7 kg.

Hadn't seen your post but I'd calculated the tension in each angled rope as being 2/SQRT(3) times greater than when the ropes are vertical, which agrees.

coffeehound

Thanks all, appreciate your quick responses.  The 'ropes' in this project are a chain of seven different components which I originally spec'd for the basic slung weight, before having a 'hold on!' moment this morning.  Will need to measure the actual angle with everything assembled and do the calcs to check that each item can cope with the increased equivalent weight.  ~15% uplift for a 30º angle is pretty significant.

pbartlett

grumpycrab said:

pbartlett said:

when the ropes are horizontal the tension in the ropes is zero

what's keeping the weight up at this point?

Not the rope

pbartlett

The ropes at 30deg will see a lower tension and so can be less spec'd - this is because some of the load will be taken by the additional force you need to stop the mass simply swinging down to vertical again. As rdr says, the tension in the ropes decreases as a function of cos(theta), which is 1 when the ropes are vertical (hence then support the full 100kg), to zero when they are horizontal - in that case the rope could be made of cotton as there is no tension in it.