Question

.A block of mass 5.0 kg is suspended from the end of a vertical spring which is stretched by 10 cm under the load of the block. The block is given a sharp impulse from below so that it acquires an upward speed of 2.0 m/s. How high will it rise ? Take g = $10m/s^2$

Answer 1

$m=5kg,x=10cm=0.1m$

$v=2m/sec,h=?,g=10m.se{c}^2$

So, $k=\frac{mg}{x}$

$=\frac{50}{0.1}=500N/m$

Total energy just the blow

$E=\frac{1}{2}m{v}^2+\frac{1}{2}k{x}^2$ ...(i)

Total energy at a height h

$=\frac{1}{2}h(h-x{)}^2-mgh$

On solving, we can get,

$h=0.2m$

$=20cm$