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Sir ji please help for question number nineteen and twenty.

Sir ji please help for question number nineteen and twenty. 

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Grade:12th pass

1 Answers

Arun
25750 Points
4 years ago
Suppose the object compresses the spring by length = x 
Frictional force = μmg 
KE lost by the spring is coverted into work done against the friction + PE stored in the spring 
=> (1/2) mv^2 = μmgx + (1/2) kx^2 
=> mv^2 = 2μmgx + kx^2 ... ( 1 ) 

On the return path, initial and final velocity of the object are both zero. So there is no change in energy of the object. 
=> PE stored in the spring is used up in overcoming frictional force on the return path 
=> (1/2) kx^2 = μmgx 
=> x = 2μmg/k 

Plugging this value of x in eqn. ( 1 ), 
mv^2 = (2μmg)^2 / k + (1/2) k( 2μmg/k)^2 
=> mv^2 = 4(μmg)^2 / k + 4(μmg)^2 / k 
=> k = 8 μ^2 g^2 m / v^2

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