# Further mechanics

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#1
A particle P of mass m lies on a smooth inclined plane at an angle a to the horizontal, where tanα = 3/4 The particle is attached to one end of a light elastic string of natural length a and modulus of elasticity 3 mg. The other end of the string is attached to a fixed point O on the plane. The particle P is in equilibrium at the point A on the plane and the extension of the string is 2a/5.
The particle is now projected from A down a line of the greatest slope of the plane with speed V. It comes to an instantaneous rest after moving a distance 1a/5.
By using the principle of conservation of energy,
a) Find V in terms of a and g (6 marks) ( so far for this question I've tried to make the initial energy of the particle equal to the final energy of the particle, so I've made the E.P.E (initial)+ K.E(initial) +G.P.E(initial)= E.P.E (final)- i thought that there would only be E.P.E as it's at rest and i assume that you make the GPE equal to zero) Any help will be appreciated!
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7 months ago
#2
(Original post by Alana8989)
A particle P of mass m lies on a smooth inclined plane at an angle a to the horizontal, where tanα = 3/4 The particle is attached to one end of a light elastic string of natural length a and modulus of elasticity 3 mg. The other end of the string is attached to a fixed point O on the plane. The particle P is in equilibrium at the point A on the plane and the extension of the string is 2a/5.
The particle is now projected from A down a line of the greatest slope of the plane with speed V. It comes to an instantaneous rest after moving a distance 1a/5.
By using the principle of conservation of energy,
a) Find V in terms of a and g (6 marks) ( so far for this question I've tried to make the initial energy of the particle equal to the final energy of the particle, so I've made the E.P.E (initial)+ K.E(initial) +G.P.E(initial)= E.P.E (final)- i thought that there would only be E.P.E as it's at rest and i assume that you make the GPE equal to zero) Any help will be appreciated!
Sounds reasonable, depending what you mean by make the GPE equal to zero.

You can set the zero point anywhere when working out GPE, since you're almost invariable having to work out GPE (initial) - GPE (final), or the other way round. And it's the difference in height between the initial and final position that determines the change in GPE.

If you set the zero point for GPE to be the final position, then GPE(final) is zero.

If you still have problems, post working.
Last edited by ghostwalker; 7 months ago
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#3
(Original post by ghostwalker)
Sounds reasonably, depending what you mean by make the GPE equal to zero.

You can set the zero point anywhere when working out GPE, since you're almost invariable having to work out GPE (initial) - GPE (final), or the other way round. And it's the difference in height between the initial and final position that determines the change in GPE.

If you set the zero point for GPE to be the final position, then GPE(final) is zero.

If you still have problems, post working.
Thank you! I'll give it a go now
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