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A particle of mass $2$ kg is being held in equilibrium on a smooth slope by a horizontal force $p$ and a light elastic spring. The spring has modulus of elasticity $10$N and is attached to the particle and also to the slope $1.5$m up the slope from the particle and also to the slope is inclined at $25°$ and the force $p$ is of magnitude $5$N find the two possible natural lengths of the spring.

J.G.
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kaushik das
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    Don't you think that this is more of a physics question, than mathematics? – Matti P. Nov 30 '20 at 12:46
  • By what definition of modulus of elasticity would it have units of force? All the ones I know have units of pressure. – J.G. Dec 30 '20 at 11:51
  • Does it not also experience gravity & a reaction force? – J.G. Dec 30 '20 at 11:52
  • @J.G. this seems to be quite a common misunderstanding about the units of the modulus of elasticity! :) See my recent question on Physics SE: https://physics.stackexchange.com/questions/602573/variation-of-hookes-law-confirmation . I'd say that the OP here is also taking the UK qualifications (A-Levels; hence my username). See here for info: https://revisionmaths.com/advanced-level-maths-revision/mechanics/elastic-strings It appears that this meaning for the modulus of elasticity is not used outside of the A Levels syllabuses. – A-Level Student Dec 30 '20 at 22:08

1 Answers1

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It may be helpful to draw a free body diagram, annoted with all the relevant angles. There are $4$ forces involved:

  1. The normal reaction force from the slope
  2. Tension or thrust in the spring (depending on whether's it's stretched or compressed)
  3. The particle's weight
  4. The horizontal force $p$.

Does that help? Please tell me if you require any more help.

A-Level Student
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