Question

A 16 kg block moving on a firtictionless horizontal surface with a velocity of 4 m/s compresses an ideal spring and comes to rest .if the force constant of the spring be 100 N/m ,then the spring is compreesed by

Answer 1

1/2 kx2 = 1/2 mv2 

1/2 X 100 X x2 = 1/2 X 16 X (4)2

50 X x2 = 256/2

x2 = 128/50

x2 = 2.56

x = 1.6 

so, the spring is compressed 1.6 m .

Answer 2

• Let the initial velocity be u then the initial energy which is the kinetic energy is :
• KE = 1/2mu²
• Let the length by which the spring is compressed be x and the spring constant be k.
• The final potential energy is given by :
• P.E = 1/2kx²
• By law of conservation of energy :
• K.E = P.E
• Equating the two we have:
• 1/2 × 16 × 4² = 1/2 × 100 × x²
• 128 = 50x²
• x² = 2.56
• x = √2.56
• x = 1.6

The spring is compressed by 1.6 m