- #1
thebosonbreaker
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Homework Statement
A light elastic string of natural length 0.3m has one end fixed to a point on a ceiling. To the other end of the string is attached a particle of mass M. When the particle is hanging in equilibrium, the length of the string is 0.4m.
(a) Determine, in terms of M and g (take g = 9.8 ms-2), the modulus of elasticity of the string.
(b) A horizontal force is applied to the particle so that it is held in equilibrium with the string making an angle α with the downward vertical. The length of the string is now 0.45m. Find α, to the nearest degree.
Homework Equations
F = ke (Hooke's law)
Modulus of elasticity, λ = kL
The Attempt at a Solution
I have no problem with part (a).
I simply combine the two equations mentioned under "relevant equations" to give:
λ = FL/e = (tension * natural length) / extension = (Mg * 0.3) / 0.1 = 3Mg.
It is part (b) that I'm having trouble understanding.
I have attempted to consider the right-angled triangle formed between the string and the downwards vertical but I don't seem to be getting anywhere.
Could someone please help me by explaining how they would answer part (b)?
Thanks a lot in advance.