Elastic String,Beam and Object

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In summary, the conversation discusses a problem involving a 10kg mass attached to an elastic string, with one end fixed to a beam 2.5m above the ground. The string has a spring constant of 600 Nm-1 and the mass is allowed to fall freely from the beam. The question asks for the distance above the ground where the mass will first come to rest, assuming g=10 m s-2. The solution involves finding the stretched length of the string, calculating the object's potential energy at the beam's height, and determining the equilibrium position and minimum distance from the floor. The conversation also includes a discussion of the object's motion and clarification of the question.
  • #1
ZxcvbnM2000
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Homework Statement



A mass of 10kg is attached to one end of an elastic string of unstretched length 1.5 m, the other end of the string being fixed to a beam located 2.5 m above ground level. The spring constant of the string is 600 Nm-1. If the mass is allowed to fall freely from the beam, at what distance above the ground will it first come to rest? (for this question, assume that g = 10 m s-2.)


Homework Equations



U=mgh
E=1/2 D*A2

The Attempt at a Solution



I am really confused here.

First of all , i found by how much the wire is stretched when the object is attached .so
ΣF=0 <=> mg=kx <=> x= (1/6) m .

When we lift the object to the height of the beam the object will have Potential energy =mgh = 10*10*1.5=150J ( from the equilibrium position )

So i said that 1/2 D*A2 = 150 so A=0.707 m

The distance of the position of equilibrium from the floor will be 2.5 - 1.5 -(1/6)=5/6 .

So the object will go as down as 5/6 + A Therefore the minimum distance from the floor will be (5/6) - A = 0.1263 m .

is my solution correct ? Thank you for your time :°)
 
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  • #2
ZxcvbnM2000 said:
… If the mass is allowed to fall freely from the beam, at what distance above the ground will it first come to rest?

First of all , i found by how much the wire is stretched when the object is attached .so
ΣF=0 <=> mg=kx <=> x= (1/6) m .

When we lift the object to the height of the beam the object will have Potential energy =mgh = 10*10*1.5=150J ( from the equilibrium position )

So i said that 1/2 D*A2 = 150 so A=0.707 m

The distance of the position of equilibrium from the floor will be 2.5 - 1.5 -(1/6)=5/6 .

So the object will go as down as 5/6 + A Therefore the minimum distance from the floor will be (5/6) - A = 0.1263 m .

ZxcvbnM2000, you're not asked for the equilibrium position, you're asked for the (initial) rest position.

The object will sail through the equilibrium position at high speed, and come to rest well below it! :wink:

Start again. :smile:
 
  • #3
Yeah that's what i am saying . It will come to rest every time it reaches +A or -A , right ?
 

1. What is elastic string, beam, and object?

Elastic string, beam, and object are all physical objects that exhibit elastic behavior, meaning they can stretch and return to their original shape when a force is applied and removed. Elastic string refers to a thin, flexible cord or rope, while a beam is a long, narrow structure that can bend under applied force. An object can refer to any solid material that can undergo elastic deformation.

2. How is elasticity measured?

Elasticity is typically measured using a property called Young's modulus, which is the ratio of stress (force per unit area) to strain (change in length divided by original length). This value is specific to each material and is used to determine the amount of force required to cause a certain amount of deformation.

3. What factors affect the elasticity of a material?

The elasticity of a material can be affected by several factors, including the type of material, its composition, and any external factors such as temperature and humidity. Generally, materials with strong intermolecular forces, such as metals, tend to be more elastic than materials with weaker forces, such as rubber.

4. How is elastic behavior used in real-life applications?

Elastic behavior is used in various real-life applications, such as in the design of springs, rubber bands, and bungee cords. It is also utilized in the construction of bridges and other structures to ensure they can withstand external forces without breaking or deforming permanently.

5. What happens when an elastic material is stretched beyond its elastic limit?

When an elastic material is stretched beyond its elastic limit, it will undergo plastic deformation, meaning it will not return to its original shape once the force is removed. This can cause permanent damage to the material and reduce its elasticity.

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