Resolving forces involving an elastic string

In summary: You should be able to solve for the angle, α.In summary, the problem involves a light elastic string with one end fixed to a ceiling and a particle of mass M attached to the other end. When the particle is in equilibrium, the length of the string is 0.4m. Part (a) asks for the modulus of elasticity of the string in terms of M and g. The solution involves combining Hooke's law and the equation for modulus of elasticity. For part (b), a horizontal force is applied to the particle causing the string to make an angle α with the downward vertical. The length of the string is now 0.45m and the problem asks to find α to the nearest degree. To solve
  • #1
thebosonbreaker
32
5

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.
 
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  • #2
thebosonbreaker said:
Could someone please help me by explaining how they would answer part (b)?
Consider the forces acting on the particle when the string is at an angle. (One of them will be the tension in the string.) Apply the conditions for equilibrium (for horizontal and vertical forces).
 

1. What is an elastic string?

An elastic string is a type of string or cord that can easily stretch and return to its original length. It is made of a material, such as rubber or elastic, that has the ability to deform and then regain its shape.

2. How do you resolve forces involving an elastic string?

To resolve forces involving an elastic string, you need to use the principles of vector addition and trigonometry. First, draw a diagram of the forces acting on the string. Then, use trigonometric functions to calculate the components of the forces in the horizontal and vertical directions. Finally, use vector addition to find the net force and direction of the resulting force.

3. What is the difference between tension and magnitude in resolving forces involving an elastic string?

Tension is the pulling force exerted by an elastic string, while magnitude refers to the size or strength of a force. In resolving forces involving an elastic string, the tension of the string is one of the forces that need to be calculated, while the magnitude refers to the overall strength of the resulting force.

4. How does the elasticity of the string affect the resolution of forces?

The elasticity of the string affects the resolution of forces by determining how much the string will stretch when a force is applied. If the string is very elastic, it will stretch more and the tension will be greater. This can change the direction and magnitude of the resulting force, and thus impact the resolution of forces involving the string.

5. Can you resolve forces involving multiple elastic strings?

Yes, forces involving multiple elastic strings can be resolved by treating each string separately and then combining the resulting forces using vector addition. The elasticity of each string will affect the overall resolution of forces, so it is important to consider this when analyzing the forces acting on the system.

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