Finding Length of a Pendulum from Kinetic Energy

  • Thread starter Thread starter Dante Tufano
  • Start date Start date
  • Tags Tags
    Pendulum
AI Thread Summary
The discussion revolves around finding the length of a pendulum using its kinetic energy and potential energy. The user initially calculated the height from kinetic energy but struggled to connect it to the pendulum's length. They were guided to use the conservation of energy principle, equating maximum kinetic energy to potential energy at a height related to the angle θ. After recalculating, the user resolved their algebra mistake and found the correct values. The conversation emphasizes the importance of careful calculations in applying physics principles.
Dante Tufano
Messages
32
Reaction score
0
Okay, so here's the question:

The figure below shows the kinetic energy K of a simple pendulum versus its angle θ from the vertical. The pendulum bob has mass 0.320 kg. What is the length of the pendulum?

W0353-N.jpg


Equations: KE=(mv^2)/2
U=mgh
x(t)=xmcos(wt+phi)

I solved for the height by setting the max kinetic energy equal to the max potential energy, and got .004783, but I have no idea how to use the position equation to find the max velocity or what to do after that. Could I please get some guidance?
 
Physics news on Phys.org
when the pendulum is in it's mean position, you know that the KE is maximum.

So, find the velocity there. Then use the conservation of energy principle assuming that that the pendulum bob rises to a height L(1-cosθ). substituting v in that equation you get

L(1-cosθ) is equal some value. You know θ when KE becomes 0 from the graph.
substitute that.
 
Okay, so I solve for the velocity using the max kinetic energy and have a max velocity of .3062 m/s. I set L(1-cosθ) equal to (KEmax/mg) and solved for L using the θ value .1. However, I got the wrong answer, so can I get any more clues as to what I'm doing wrong?
 
Sorry, I made an algebra mistake! The values came out write after I punched them in again. Thanks a lot!
 
oh, haha
happy to help. :smile:
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

Simulating a Rotary Inverted Pendulum in Python
Replies
15
Views
1K
For a Pendulum: Knowing Acceleration Find Maximum Angle
Replies
26
Views
3K
I Lagrangian for pendulum
Replies
11
Views
2K
Differential Equation for a Pendulum
Replies
21
Views
2K
Rod w/ Pivot and Attached Mass Pendulum
Replies
4
Views
2K
Pendulum Conservation of Energy
Replies
31
Views
4K
Physics IA: Distance B/w Pendulum & Alum. Block, Finding Damping Coefficient
Replies
9
Views
2K
Work done on a conical pendulum
Replies
3
Views
2K
Show Energy Equality of Simple Pendulum with Equipartition
Replies
1
Views
1K
Maximum Kinetic Energy from a Physical Pendulum
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top