Work Check - Centripetal force - Finding Tension in a Rope

In summary: So the tension the vine exerts must be upwards (at the bottom of the swing). Note that if the man were just hanging at the bottom with no velocity, the tension would just equal his weight. Since he's swinging, the tension must be greater than his weight in order to produce a centripetal acceleration.T = 85(15.818) = 1344.53 = 1345 NRound off to 3 digits. (You don't have enough information to justify 4 digits.)In summary, to find the tension in the vine while a man with a mass of 85 kg swings on it with a length of 11m and speed of 8m/s
  • #1
Abood
14
3

Homework Statement


A man, with a mass of 85kg, swings from a vine with a length of 11m. If this speed at the bottom of the swing is 8m/s, what is the tension if g = 10m/s^2?
Given:
m (mass) = 85kg
r (radius) = 11m
V (speed) = 8m/s
g = 10m/s^2
T = ?

Homework Equations


Fc (centripetal force) = T (Tension)
F = ma (Newton's second law)
ac (centripetal acceleration) = v^2 / r
T = m*ac
w (angular velocity) = v/r

The Attempt at a Solution


Fc = T
Fc = ma
Fc = (m)(v^2/r)
Fc = (85)(8^2/11) = 494. 545 N
T = 494.545 N

I feel as though I am missing something really important but I don't know what. The g felt like it was just to throw me off. And some wording seems vague to me, like "at the bottom of the swing."
Would be nice if someone could check my work and if there are any issues, could tell me where they are.
 
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  • #2
Abood said:
I feel as though I am missing something really important but I don't know what.
Yes, you missed something important.

Abood said:
The g felt like it was just to throw me off.
No, you'll need it. Hint: What forces act on the person? (Note that Newton's 2nd law applies to the net force.)
 
  • #3
Doc Al said:
Yes, you missed something important.No, you'll need it. Hint: What forces act on the person? (Note that Newton's 2nd law applies to the net force.)
The 2 forces are gravity (weight) and the Normal force which acts as Tension here but I'm not sure how it should be used
 
  • #4
Abood said:
The 2 forces are gravity (weight) and the Normal force which acts as Tension here but I'm not sure how it should be used
The two forces are the weight and the tension in the vine. (I would not use the term normal force for the tension.)

Since the acceleration is centripetal, apply Newton's 2nd law: ΣF = ma (But make sure you include both forces.)

(Note that it's the net force in the radial direction that provides the centripetal force.)
 
  • #5
Doc Al said:
The two forces are the weight and the tension in the vine. (I would not use the term normal force for the tension.)

Since the acceleration is centripetal, apply Newton's 2nd law: ΣF = ma (But make sure you include both forces.)

(Note that it's the net force in the radial direction that provides the centripetal force.)
ac = 5.818 m/s^2
g = 10
Sum of a = 10 - 5.818 = 4.182 m/s^2 downwards
Net force = 85*4.182 = 355.47 N downwards
What confuses me is how the net force is downwards. Does that mean the weight is too much that the vine will snap?
 
  • #6
Abood said:
ac = 5.818 m/s^2
g = 10
Sum of a = 10 - 5.818 = 4.182 m/s^2 downwards
Net force = 85*4.182 = 355.47 N downwards
What confuses me is how the net force is downwards. Does that mean the weight is too much that the vine will snap?
The net force is upwards! It has to be, since the net force is what produces the centripetal acceleration, which is upwards.

Think this way:
What forces act on the person? Weight (downwards) and Tension (upwards)
What is the acceleration? (v^2)/r (upwards -- toward the center of the path)

Choose a sign convention: Let up = positive.
Now apply Newton's 2nd law:
ΣF = ma
T - mg = ma

You do the rest and solve for the tension (T).
 
  • #7
Doc Al said:
The net force is upwards! It has to be, since the net force is what produces the centripetal acceleration, which is upwards.

Think this way:
What forces act on the person? Weight (downwards) and Tension (upwards)
What is the acceleration? (v^2)/r (upwards -- toward the center of the path)

Choose a sign convention: Let up = positive.
Now apply Newton's 2nd law:
ΣF = ma
T - mg = ma

You do the rest and solve for the tension (T).
T = ma + mg = 80(5.818+10) = 1265.44 N
EDIT: I was wondering how come is Tension opposing the weight since the man is swinging and I didn't see anything say T was opposing W
 
  • #8
Abood said:
T = ma + mg = 80(5.818+10) = 1265.44 N
(1) The mass is 85 kg, not 80.
(2) Round off to some reasonable number of digits.

Abood said:
EDIT: I was wondering how come is Tension opposing the weight since the man is swinging and I didn't see anything say T was opposing W
Ropes (or vines) can only pull. So the tension the vine exerts must be upwards (at the bottom of the swing).

Note that if the man were just hanging at the bottom with no velocity, the tension would just equal his weight. Since he's swinging, the tension must be greater than his weight in order to produce a centripetal acceleration.
 
  • #9
Doc Al said:
(1) The mass is 85 kg, not 80.
(2) Round off to some reasonable number of digits.
Oh sorry, was just solving another problem with m = 80 kg.
T = 85(15.818) = 1344.53 = 1345 N
Doc Al said:
Ropes (or vines) can only pull. So the tension the vine exerts must be upwards (at the bottom of the swing).

Note that if the man were just hanging at the bottom with no velocity, the tension would just equal his weight. Since he's swinging, the tension must be greater than his weight in order to produce a centripetal acceleration.
Ok, now I get it!
Thank you very much for your help! It is very appreciated that you spared some time to check my work.
 

Related to Work Check - Centripetal force - Finding Tension in a Rope

1. What is centripetal force?

Centripetal force is the force that keeps an object moving in a circular path. It is directed towards the center of the circle and is necessary for the object to maintain its circular motion.

2. How is centripetal force related to tension in a rope?

In the context of a work check, the centripetal force is equal to the tension in the rope. This means that the tension in the rope is responsible for keeping the object moving in a circular path.

3. How do you calculate the tension in a rope in a work check?

The formula for calculating tension in a rope in a work check is T = (m*v^2)/r, where T is the tension, m is the mass of the object, v is the velocity, and r is the radius of the circle.

4. What are the units for tension in a rope?

The units for tension in a rope are typically in Newtons (N) in the SI system, or pounds (lbs) in the imperial system.

5. Can the tension in a rope ever be greater than the centripetal force?

No, in a work check, the tension in the rope is equal to the centripetal force. If the tension were to be greater than the centripetal force, the object would not be able to maintain its circular motion and would fly off in a straight line.

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