Mechanics 3 Elastic Springs and Strings Problems

In summary, the ball is equilibrium when the sum of the forces acting on it is equal to zero. The vertical force is equal to the tension in the string, and the normal reaction force is equal to the weight of the ball.
  • #1
garyljc
103
0
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 = ):-p
 
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  • #2
garyljc said:
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 = ):-p
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)
 
  • #3
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
 
  • #4
sup garlyci...force exerted by spring is (spring constant)*lenght displaced.
 
  • #5
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!
 
  • #6
arcsin 3/5 means sin @ = 3/5
 
  • #7
vijay123 said:
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.
 
  • #8
garyljc said:
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.
 
  • #9
But what will R be equal to ? There must be a normal reaction the particle
 
  • #10
garyljc said:
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.
 
Last edited:
  • #11
Ahhhh , I got it , thanks anyway . Kinda hard though for me doing self study =) Cheers Hoot =)
 
  • #12
garyljc said:
Ahhhh , I got it , thanks anyway . Kinda hard though for me doing self study =) Cheers Hoot =)
No problem :smile:
 

Related to Mechanics 3 Elastic Springs and Strings Problems

What is the definition of elastic springs and strings?

Elastic springs and strings refer to objects that can stretch or compress when a force is applied to them, and then return to their original shape and size when the force is removed. These objects possess elastic potential energy, which is a form of potential energy that is stored when the object is stretched or compressed.

What is Hooke's Law and how is it related to elastic springs and strings?

Hooke's Law states that the force exerted by an elastic object is directly proportional to the amount of stretch or compression of the object. In other words, the greater the force applied, the greater the deformation of the object. This law is applicable to elastic springs and strings, as they follow a linear relationship between force and displacement.

How do you calculate the spring constant of an elastic spring?

The spring constant, also known as the stiffness constant, is a measure of how easily an elastic spring can be stretched or compressed. It is calculated by dividing the force applied to the spring by the displacement it undergoes. This value is usually denoted by the symbol k and has units of newtons per meter (N/m).

What is the difference between a simple harmonic motion and a damped harmonic motion?

Simple harmonic motion refers to the repetitive back-and-forth movement of an object around an equilibrium point, where the force acting on the object is directly proportional to its displacement from the equilibrium point. On the other hand, damped harmonic motion occurs when there is a resistive force acting on the object, causing its amplitude to decrease over time. This resistive force can be due to factors such as friction or air resistance.

How can I solve problems involving elastic springs and strings?

To solve problems involving elastic springs and strings, you can use various equations and principles such as Hooke's Law, conservation of energy, and the equations of motion. It is important to identify the relevant variables and equations, and to use units consistently throughout your calculations. You can also use diagrams and free-body diagrams to visualize the problem and better understand the physical concepts involved.

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