a body of mass 1 kg initially at rest gives a height of 2m on to a vertical spring having force constant 490N/m . Calculate the max distance through which will be the spring compressed?
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Answer:
11th
Physics
Work, Energy and Power
The Potential Energy of a Spring
A block of mass 2 kg is dro...
PHYSICS
A block of mass 2 kg is dropped from a height of 40 cm on a spring whose force-constant is 1960 Nm
−1
. The maximum distance through which the springs is compressed by:
MEDIUM
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ANSWER
Given data,
Mass of the body is ( m ) =2Kg
spring's constant (K)=1960N/m
height of the body =0.4m
Let the maximum distance spring will compressed =xm
initial potential energy of body =mg(h+x)
final potential energy = spring potential energy =
2
1
Kx
2
according to the law of conservation of energy,
initial potential energy = final potential energy
mg(h+x)=
2
1
Kx
2
2mgh+2mgx=Kx
2
Kx
2
−2mgx−2mgh=0
⇒1960x
2
−2×2×9.8×x−2×2×9.8×0.4=0
⇒1960x
2
−39.2x−15.68=0
after solving this quadratic equations , we get x=0.1m
hence, answer is x=0.1m