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A particle of mass m tied with a string of length l is released from a horizontal position . Find the velocity at lowest position

A particle of mass m tied with a string of length l is released from a horizontal position . Find the velocity at lowest position 

Grade:11

2 Answers

Arun
25750 Points
4 years ago
A particle of mass m attached to end of the string of length l is released from horizontal position. 
then, energy at horizontal position of particle = energy at lowest position of particle.
Let at lowest position speed of particle = v
now, mgl = 1/2 mv² 
v = √2gl 
now we should find speed of particle at highest position . Let v' be the speed of particle at highest position .
so, mg(2l) + 1/2mv'² = 1/2 mv² 
2mgl + 1/2mv² = 1/2mg(2gl) = mgl 
1/2mv² = -mgl 
v² = -2gl , here v is imaginary number .
means this situation is not possible . if we released particle from horizontal position , particle doesn't complete circle
 
Harsh
47 Points
4 years ago
As the particle is at horizontal position,let its height from the lowest position be h.
Applying conservation of energy on the system we get
Ke at horizontal position+pr wt horizontal position=
Ke at lower position+ pe at lower position.
Hence,
0+mgh=1/2mv²+0
mgh=1/2mv²
gh=1/2mv²
V=√2gh.

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