Mechanics 3 Elastic Springs and Strings Problems

[garyljc]

Hello everyone ,
I'm new in this forum . I'm 16 and currently doing self study in Mechanics 3 . I've encounter a problem in the 2nd chapter of Mechanics 3 which is Elastic Springs and Strings . Here goes :

A ball of mass 0.5kg is attached to one end of a cord of unstretched length 0.6m whose other end is fixed. When a horizontal force magnitude Q N is applied to the ball holding the ball in equilibrium, the cord increase in length by 10% and is inclined at an angle of arcsin 3/5 to the downwards vertical. Calculate the value of Q and the modulus of the cord.

A few things that kept me wondering is that what do they mean by horizontal ? Does it means it acts along the slope or acts parellel to the ground ? Please help me , thank you = )

 

[Hootenanny]

Hello everyone ,
I'm new in this forum . I'm 16 and currently doing self study in Mechanics 3 . I've encounter a problem in the 2nd chapter of Mechanics 3 which is Elastic Springs and Strings . Here goes :

A ball of mass 0.5kg is attached to one end of a cord of unstretched length 0.6m whose other end is fixed. When a horizontal force magnitude Q N is applied to the ball holding the ball in equilibrium, the cord increase in length by 10% and is inclined at an angle of arcsin 3/5 to the downwards vertical. Calculate the value of Q and the modulus of the cord.

A few things that kept me wondering is that what do they mean by horizontal ? Does it means it acts along the slope or acts parellel to the ground ? Please help me , thank you = )

Hi there garyljc and welcome to PF,

A horizontal force will act parallel to the ground. To answer this question, you will need to find the components of the force exerted by the chord, take vertical (y) and horizontal (x) components. Now, as the ball is in equilibrium what can we say about the forces acting on the ball? Next you will need to identify the forces acting on the ball. You should then be able to formulate to expressions, one vertically and one horizontally, which you may solve simultaneously. I am assuming here that the chord is thin, since we have not been given a diameter. (A diagram may be helpful in answering this question)

 

[garyljc]

If the ball is in equilibrium , sum of the forces wil be equal to zero =) Got it . But I've found 2 equations ( Vertical and Horizontal ) , when I have 3 variables , which is Q , modulus of elasticity , R (normal reaction) . Is there anything I'm missing out ? What does the vertical equal to ? Thanks anyway

 

[vijay123]

sup garlyci...force exerted by spring is (spring constant)*lenght displaced.

 

[vijay123]

i can solve you the problem...butcan you please tell me what arcsine means beacasue in my country, we only have angles in terms of radians and degress...if you would convert it into degress...it would be a great help in my calculation.
thank you!

 

[garyljc]

arcsin 3/5 means sin @ = 3/5

 

[Hootenanny]

sup garlyci...force exerted by spring is (spring constant)*lenght displaced.

This is the wrong formulae to use. We are dealing with chords here, not springs. We are required to calculate young's modulus for the chord not the spring constant.

 

[Hootenanny]

If the ball is in equilibrium , sum of the forces wil be equal to zero =) Got it . But I've found 2 equations ( Vertical and Horizontal ) , when I have 3 variables , which is Q , modulus of elasticity , R (normal reaction) . Is there anything I'm missing out ? What does the vertical equal to ? Thanks anyway

You should have only two unknowns is each equation (Q and a component of the tension). In this situation there are only three forces acting, (1)Q, (2)The tension and (3)The weight of the ball. There should be no reaction force.

 

[garyljc]

But what will R be equal to ? There must be a normal reaction the particle

 

[Hootenanny]

But what will R be equal to ? There must be a normal reaction the particle

HINT: Look up the definition of tension

Tension is a reaction force applied by a stretched string (rope or a similar object) on the objects which stretch it. The direction of the force of tension is parallel to the string, towards the [centre of the] string.

 

[garyljc]

Ahhhh , I got it , thanks anyway . Kinda hard though for me doing self study =) Cheers Hoot =)

 

[Hootenanny]

Ahhhh , I got it , thanks anyway . Kinda hard though for me doing self study =) Cheers Hoot =)

No problem