Referring to Figure Suppose the block has a mass of 1.4 kg and an initial speed of 0.62 m/s. (a) What force constant must the spring have if the maximum compression is to be 2.4 cm? (b) If the spring has the force constant found in part (a), find the maximum compression if the mass of the block is doubled and its initial speed is halved.
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We have to find the force constant a spring must have if its maximum compression is 2.4 cm .
The force constant of a spring can be found using the expression for the work done by the spring on the block.
force constant in N/m
maximum distance by which the spring
is compressed = 2.4 cm = 0.024 m
Now, by WorkEnergy theorem, the total work done on the block by the spring is equal to the change in the kinetic energy of the block.
mass of the block = 1.4 kg
initial speed of the block
= 0.62 m/s