How Do Angles and Forces Affect Equilibrium in Physics Scenarios?

[ryuu21]

Situation 1
A box is suspended from the ceiling by two ropes each at an equal angle lesser than 30 degrees with the horizontal.

Why is the tension of either rope greater than the weight of the box itself?

Situation 2

A bungee jumper momentarily comes to rest at the bottom of his dive before he springs back upward.

At the bottom of his jump, was he at a state of equilibrium? Why? or Why not?

P.S.
If these questions were already answered, which I'm guessing they already were, please point me in the right direction.

 

[stewartcs]

Situation 1
A box is suspended from the ceiling by two ropes each at an equal angle lesser than 30 degrees with the horizontal.

Why is the tension of either rope greater than the weight of the box itself?

Situation 2

A bungee jumper momentarily comes to rest at the bottom of his dive before he springs back upward.

At the bottom of his jump, was he at a state of equilibrium? Why? or Why not?

P.S.
If these questions were already answered, which I'm guessing they already were, please point me in the right direction.

You must make an attempt yourself before receiving help on this forum. What do you think intuitively?

CS

 

[ryuu21]

sorry, but I've been thinking about it...

Situation 1 Attempt
I really don't know what to answer but I've noticed that as the angle of both ropes change, the Tension also changes with it... I just can't get why the tension could be greater than the weight of the box itself.

Situation 2 Attempt
Well, the jumper couldn't be in the state of equilibrium coz the net force at that moment wouldn't be zero, because the tension of the bungee cord would be at a very high value.

 

[Feldoh]

If we have a box and w drop it, would you agree that the only force on that box is gravity? Would you also agree that the force of gravity is only downward (call -y direction)? But when we add in the ropes, notice the tension forces have both x and y components!

 

[stewartcs]

Situation 1 Attempt
I really don't know what to answer but I've noticed that as the angle of both ropes change, the Tension also changes with it... I just can't get why the tension could be greater than the weight of the box itself.

It is a bit counter intuitive at first. But remember, the weight of the box is only the vertical component of tension, not the resultant (i.e. vectoral sum). Thus when one adds the horizontal component in, the resultant force (i.e. the tension) is larger.

Does that help?

Situation 2 Attempt
Well, the jumper couldn't be in the state of equilibrium coz the net force at that moment wouldn't be zero, because the tension of the bungee cord would be at a very high value.

What does equilibrium mean in physics? That is to say, what are the three conditions required for an object to be in equilibrium?

CS

 

[ryuu21]

yeah thanks a lot...
for situation one...
So this means that I can't just change the y-axis value because that would alter the angle. So, the ropes need to increase both x and y-axis values to keep the angle and satisfy the y-axis requirement to lift the weight. Its the horizontal component that makes the resultant so big.

As for situation 2...
The first condition is that the the sum of all forces must be equal to zero. Second, there should be no acceleration. Third, the sum of all torque should be equal to zero.
I think my answer was wrong, because all the conditions have been satisfied. At the bottom of the jump, the weight of the jumper was inversely matched by the tension and there was certainly no acceleration at that moment. So, yes, the jumper was at the state of equlibrium at that moment. Was that correct?

 

[LowlyPion]

yeah thanks for situation one...
So this means that I can't just change the y-axis value because that would alter the angle. So, the ropes need to increase both x and y-axis values to keep the angle and satisfy the y-axis requirement to lift the weight. Its the horizontal component that makes the resultant so big.

You've almost got it, or you do and aren't expressing it clearly.

You are right that there are components of force in the tension of the lines. And you know that the vertical components MUST together equal the weight they are supporting ... or else it would be in motion. It's not, so ... If the tension in the lines are made up of vertical components that must add to equal the weight, then any other addition from any horizontal components must make it add to more.

Your thinking on the second part needs some work. If something is at equilibrium its motion is experiencing neither velocity nor acceleration. The Pyramids are at equilibrium. A bungee jumper is at equilibrium sitting in a chair.

Is a ball at the top of its flight at equilibrium?

 

[stewartcs]

As for situation 2...
The first condition is that the the sum of all forces must be equal to zero. Second, there should be no acceleration. Third, the sum of all torque should be equal to zero.
I think my answer was wrong, because all the conditions have been satisfied. At the bottom of the jump, the weight of the jumper was inversely matched by the tension and there was certainly no acceleration at that moment. So, yes, the jumper was at the state of equlibrium at that moment. Was that correct?

You're right on track. I think it is safe to assume the person jumped straight down, therefore there should be no horizontal components of force acting on the person - that's one requirement satisfied.

Next is the vertical requirement. At the bottom of the jump, right before the person changes direction, he is not in motion and the tension in the bungee cord equals his weight - that satisfies the second requirement.

The last requirement is just the torques. It should be obvious that since there are no moment arms involved in this example (again assuming he jumped straight down) that there are no torques about the person.

Thus the bungee jumper would be in equilibrium momentarily at the very bottom of his jump.

CS

 

[LowlyPion]

At the bottom of the jump, right before the person changes direction, he is not in motion and the tension in the bungee cord equals his weight -

I'm sorry this is not correct. The tension in the cord is greater than his weight. Merely because he slowed from descent to 0, doesn't mean that the tension diminished to just his weight. Otherwise he would simply stop at that point, suspended in space, if there was a net zero balance of forces on him.

When his motion ceases, the oscillations up and down cease, he will satisfy tension equilibrium, but not before.

 

[stewartcs]

I'm sorry this is not correct. The tension in the cord is greater than his weight. Merely because he slowed from descent to 0, doesn't mean that the tension diminished to just his weight. Otherwise he would simply stop at that point, suspended in space, if there was a net zero balance of forces on him.

When his motion ceases, the oscillations up and down cease, he will satisfy tension equilibrium, but not before.

Opps! Of course that is correct...For some reason I had the idea stuck in my head that he was already finished oscillating and was just hanging there in stable equilibrium. Nice catch LowlyPion!

CS