Mass of a Pendulum on a Grandfather Clock

[twenty5]

Homework Statement

Can someone please revise my work? It's quite short )

Question:
A grandfather clock is designed to have a pendulum which swings a mass at the end of a chain in a horizontal circular motion. The pendulum is designed to swing at 15° off the vertical and to complete one revolution every 2.0 seconds. The chain is 1.0 metre long and the maximum tension in the chain is 2.0N

Length of string : 1m
angle at the top: 15°
1 Revolution = 2s
F_T : 2.0N

Homework Equations

F=mg

The Attempt at a Solution

I drew the FBD, which then I got:

2.0cos15° = F_T(y) = m (9.81)
did the algebra... and ended up with

m = 0.1969kg


I have a positive feeling that this is too little. Any thoughts? thanks! I'll be here all day haha

 

[tiny-tim]

hi twenty5!

I drew the FBD, which then I got:

2.0cos15° = F_T(y) = m (9.81)

no, you've tried to use ∑F = 0 in the vertical direction …

but there's a vertical acceleration, so you can't

in fact, there's no obvious direction in which the acceleration is zero …

you'll have to use ∑F = ma and https://www.physicsforums.com/library.php?do=view_item&itemid=27"

 

[twenty5]

m k thanks I'll see what I can come up with then I'll post my results thakns!

 

[twenty5]

deleted ~ found out this method was wrong. pleaswe look at my next post

 

[twenty5]

ok so what I am at now is:

F_c = mv² / rI got Velocity by getting the radius, and then getting the circumference from that. Circumference = 1.684m
We know that it takes 2 seconds for 1 revolution. So I used V = d/t V = 1.684 / 2 V = 0.842m/s
Now I'm left withF_c = m (0.842 )² / 0.268can I get some sort of push as to which way I should head now?

I'm looking for the mass. But the only formulae I know of that gives Force of centripetl is that one that I listed...

 

[tiny-tim]

hi twenty5!

… So I used V = d/t

no, that only works for constant speed

try using conservation of energy

 

[twenty5]

ah. okay thank you very much sir.