Work Check - Centripetal force - Finding Tension in a Rope

[Abood]

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.

 

[Doc Al]

I feel as though I am missing something really important but I don't know what.

Yes, you missed something important.

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.)

 

[Abood]

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

 

[Doc Al]

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.)

 

[Abood]

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?

 

[Doc Al]

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).

 

[Abood]

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

 

[Doc Al]

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.

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.

 

[Abood]

(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

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.