Physics project confusion (effects of length on a pendulum)

AI Thread Summary
The discussion revolves around designing a physics project to study centripetal acceleration using a pendulum and motion sensor while varying the pendulum's length. The professor suggests incorporating a force sensor, which raises questions about its necessity since the primary focus is on measuring velocity. Participants highlight the importance of considering both centripetal acceleration and gravitational force in the experiment. Clarifications are sought regarding the specifics of the force measurement and the experimental setup, including the height or angle of the pendulum bob. Overall, the project aims to explore the relationship between pendulum length and centripetal acceleration, potentially expanding beyond initial expectations.
dpatil
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Homework Statement
We are seeking to study the effects of length (or radius) of a pendulum on the centripetal acceleration.
Relevant Equations
Centripetal Acceleration= velocity^2/r
We are seeking to design a project where we use a simple pendulum and a motion sensor (that will give us velocity) in order to study centripetal acceleration by essentially changing the length of the pendulum for each trial. This felt simple enough, however our professor insists that we would also need a force sensor in order to do the experiment. I cannot understand why we would need force if all we are doing is swinging a pendulum through a motion sensor to study velocity^2/r where r is the length of the pendulum. How would force help us in this situation?
 
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Welcome, @dpatil ! :smile:

He may want to relate force or tension in the string (centripetal acceleration x mass of the pendulum) to the changes in the length of the pendulum.

Acceleration of gravity (always vertical) on the pendulum needs to be considered as well in combination with the centripetal acceleration (always radial).
 
Welcome to PF.

dpatil said:
How would force help us in this situation?
What are your thoughts so far on this? Did the professor say where they wanted the force(s) measured? Did they suggest a 1-D or 2-D force sensor?
 
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This doesn't have to do with the force measurement, but are you planning on raising the bob to the same height or the same angle? What are the expected results for ##\frac{v^2}{R}## at the lowest point of the swing in either case? That might be something to try and figure out and attempt to verify via measurement.
 
You say you don’t need a force sensor. Ok. Please post the description of the task as given to you and the experimental procedure you propose to follow. Then we will be in a better position to ascertain whether a force sensor is appropriate to use and how.
 
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Likes phinds and erobz
This is actually a very nice idea for an experiment that can go beyond "seeking to study the effects of length (or radius) of a pendulum on the centripetal acceleration." I will not say anything more lest I spoil it for someone.
 
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}...
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