Extension in Spring Homework: Find x

[cupid.callin]

Homework Statement

The Attempt at a Solution

first using the initial extension i found out that k = 200.

velocity of block = √(2gh) = √(2*10*.45) = 3

then using conservation of momentum ...

120 * 3 = 320 * V
V = 1.125

this kinetic energy converts into potential energy of spring

.5 * .32 * ^V = .5 * 200 * ^x
x = 4.5 cm

but answer is given as 6.1 cm

 

[Mr.A.Gibson]

You haven't taken into account the gravitational potential energy, GPE is lost by both masses as the spring extents from equilibrium.


$$\frac{1}{2} m v^2=\frac{1}{2}kx^2 -mgx$$

 

[cupid.callin]

Thanks for your help ... :)