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A point A of the ceiling is directly above a point B of the floor 2.5 meters below. A and B are joined by a light spring of natural length 2 meters; the tension in the spring is then 20 Newtons. A Lump of Putty of weight 4 Newtons is now attached to the spring at the point 1 meter above the floor. At what height above the floor will the Putty rest in equilibrium?

My working and diagram;

http://www.flickr.com/photos/90383971@N05/10050116394/in/photostream/

My Ans:

First i found natural length of the spring.

Without the Putty:

through Hooke's Law, we know

T= λx ⁄ l

where T = tension, l= natural length, λ = modulus of elasticity, x = extension

λ = Tl ⁄ x

λ = 20 * 2 / 0.5

λ = 80 Newtons

So this is the modulus of elasticity of the spring. From here the problem becomes complicated for me. Because after the Putty is attached, the spring is streched from the top and i do not know how to bring into my calculation how the spring below the Putty affects the extension. I'm lost, Could you PLEASE help.

The

My working and diagram;

http://www.flickr.com/photos/90383971@N05/10050116394/in/photostream/

My Ans:

First i found natural length of the spring.

Without the Putty:

through Hooke's Law, we know

T= λx ⁄ l

where T = tension, l= natural length, λ = modulus of elasticity, x = extension

λ = Tl ⁄ x

λ = 20 * 2 / 0.5

λ = 80 Newtons

So this is the modulus of elasticity of the spring. From here the problem becomes complicated for me. Because after the Putty is attached, the spring is streched from the top and i do not know how to bring into my calculation how the spring below the Putty affects the extension. I'm lost, Could you PLEASE help.

The

**answer**in my book is given**0.976**meters (which is the height of the putty above the floor)
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