Question

Consider a block connected to a light spring of spring constant `100Nm^(-1)`. Now the block is displaced by applying a constant force F which gives zero resultant force when spring is stretched through 10 cm.
Evaluate
(i) Work done by the spring force when the block attains equilibrium.
(ii) Net work done on the block when it attains maximum speed.

Answer 1

(i) Work done by the spring force, `W=(1)/(2) kx^(2)`
`k=100 Nm^(-1) " and " x=10 cm=0.1 m`
`:.W_(s)=(1)/(2)xx100(0.1)^(2)=-0.5 J`
Negative sign indicates that the work done by the spring force is negative.
(ii) When the block attains equilibrium, its speed is maximum.
`:.` Work done on the block by external force F
`W=F.x=(10)((10)/(100))=1 J`
Thus, net work done on the block
`W_(N)=W_(S)+W=-0.5+1 =0.5 J`