# Tension in the string and tangential accleration

## Homework Statement

A particle of mass m is whirled on the end of a string of length R. The motion is in vertical plane in Earth's gravitational field . The instantaneous speed is v when the string makes angle Ө with the horizontal. Find the tension T in the string and the tangential acceleration at this instant.

## The Attempt at a Solution

This is my classical mechanics homework problem.
T= Fc+W sin theta .
I have come up with this equation , is this correct . And how to find the tangential acceleration?

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mfb
Mentor
How did you come up with it, and what are Fc and W? The final answer should use R, v and Ө only.

Can you show me how ?

haruspex
Homework Helper
Gold Member
How did you come up with it, and what are Fc and W? The final answer should use R, v and Ө only.
m and g also.

haruspex
Homework Helper
Gold Member
Can you show me how ?
Express Fc in terms of m, g, r, v, Ө (you won't need all of them). There's a standard equation you should use (and which should have been listed in the Relevant Equations).
Express W similarly.
Be careful with signs. Define whether up or down is considered positive, and whether the value of g is taken to be positive or negative. (E.g. if up is positive, then you can write gravitational acceleration as g, taking a negative value, or as -g, taking a positive value.)

mfb
Mentor
Be careful with signs. Define whether up or down is considered positive, and whether the value of g is taken to be positive or negative. (E.g. if up is positive, then you can write gravitational acceleration as g, taking a negative value, or as -g, taking a positive value.)
It's not just signs, you should consider both contributions as vectors, not with their absolute values.
m and g also.
Right, of course.

It's not just signs, you should consider both contributions as vectors, not with their absolute values.Right, of course.
I am not getting it :(

mfb
Mentor
At least write down the equations you know that could be relevant here, and see if one of those has quantities that are given here.

Express Fc in terms of m, g, r, v, Ө (you won't need all of them). There's a standard equation you should use (and which should have been listed in the Relevant Equations).
Express W similarly.
Be careful with signs. Define whether up or down is considered positive, and whether the value of g is taken to be positive or negative. (E.g. if up is positive, then you can write gravitational acceleration as g, taking a negative value, or as -g, taking a positive value.)
And what is that relevant equation from which I should start my assumption?

haruspex
Homework Helper
Gold Member
And what is that relevant equation from which I should start my assumption?
The formula for centripetal acceleration.

The formula for centripetal acceleration.
mv^2/r , this one? So I should substitute value of Fc in T= Fc+W sin theta? I am sorry , if my silly questions are annoying you

haruspex