Pendulum and Centripetal Motion Question

In summary, the conversation discusses a solved question about calculating the speed of a pendulum at the bottom of its swing after being raised to a certain height. The relevant equations and attempt at a solution using the equation F_c=F_T+mg are mentioned, but the correct solution is found using conservation of energy.
  • #1
MaZnFLiP
17
0
[SOLVED] Pendulum and Centripetal Motion Question

Picture and FBD
Physics.jpg


The Problem/Question
Calculate the speed of a 2.0m length pendulum at the very bottom of the swing if you raise it a vertical height of 0.12m


Relevant equations

[tex] F_net = F_T + F_G = F_C = m(\frac{V^2}{r}) [/tex]

The attempt at a solution

Well, after looking over this problem, I think I'm doing something amazingly wrong.

Looking at My equations, I went from

[tex] F_C = F_T + mg [/tex]

to

[tex] m(\frac{V^2}{r}) = F_T + mg [/tex]

From there I got:

[tex] \frac {V^2}{r} = F_T + g [/tex] because the masses cancel.

Next:

[tex] V^2 = gr + F_T[/tex]

After finding [tex](-9.81\frac{m}{s}^2)(2.0m) = 19.62[/tex], I found the square root which was [tex] 4.429 \frac {m}{s}^2 [/tex]

The problem is that after looking at the answer sheet, The answer is supposed to be:

[tex]1.5\frac{m}{s}^2[/tex]

Could someone please help as to tell me where I went wrong?
 
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  • #2
Hi MaZnFLip,

MaZnFLiP said:
Picture and FBD
Physics.jpg


The Problem/Question
Calculate the speed of a 2.0m length pendulum at the very bottom of the swing if you raise it a vertical height of 0.12m


Relevant equations

[tex] F_net = F_T + F_G = F_C = m(\frac{V^2}{r}) [/tex]

The attempt at a solution

Well, after looking over this problem, I think I'm doing something amazingly wrong.

Looking at My equations, I went from

[tex] F_C = F_T + mg [/tex]

At the bottom of the swing, the equation would be [itex]F_c=F_T - mg[/itex], but everywhere else along the swing the tension is not in the opposite direction as the weight, and you would need some trig functions to take that effect into account. Also, you would need to take into account the tangential acceleration that is actually causing the mass to speed up.

Rather than that, I would suggest using conservation of energy for this problem. What does that give?
 
  • #3
Umm. The way I learned to use conservation of energy is converting PE since its higher up and when it goes all the way down it turns into KE so PE = KE. That means that MGH = 0.5mv^2 and since the masses cancel that would leave me with GH = 0.5v^2. Multiplying GH together would give me 1.1772. After dividing that with 0.5, I then get 2.3544. Finally, After getting the square root of that, I ended up getting 1.5m/s! Yes! Thank you so much!
 
  • #4
Sure, glad to help!
 

1. What is a pendulum and how does it work?

A pendulum is a weight suspended from a fixed point that is able to swing freely back and forth. It works due to the force of gravity and the principle of conservation of energy. As the pendulum swings, it continually converts potential energy into kinetic energy and back again.

2. What factors affect the motion of a pendulum?

The motion of a pendulum is affected by its length, mass, and the force of gravity. The longer the pendulum, the slower it swings; the heavier the weight, the faster it swings; and the stronger the force of gravity, the faster it swings.

3. What is centripetal motion and how does it differ from linear motion?

Centripetal motion is the circular motion of an object around a center point. Unlike linear motion, where an object moves in a straight line with a constant speed, centripetal motion involves a constant change in direction and a constant inward force towards the center.

4. How does centripetal force relate to centripetal motion?

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

5. Can a pendulum exhibit centripetal motion?

Yes, a pendulum can exhibit centripetal motion if it is attached to a rotating frame or if its motion is restricted to a circular path. In these cases, the force of gravity acts as the centripetal force, keeping the pendulum in its circular motion.

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