Answer:
<h2>0.082m</h2>
Explanation:
Step one:
given data
mass of block m=0.4kg
initial length of spring=0.15m
spring constant= 1040N/m
height of mass= 0.7m
assume g=9.81m/s²
Step two:
When the mass is released it will have potential energy
PE=mgh-------1
when the mass comes to rest on the spring, the potential energy of the mass will be equal to the energy stored in the spring
the energy stored in the spring is given as
E=1/2kx²- -------------2
where e is the compression
mgh = mgh' + ½kx²
where h' = 0.15m - x = height of block at maximum spring compression
0 = mg(0.15m - x - 0.7m) + ½kx²
0 = 0.4* 9.81 * (-x - 0.55) + ½ * 1040 * x²
0=-3.924x-2.1582+ 520x²
rearrange
520x²-3.924x-2.1582=0
the roots are
x=0.068
x=-0.061----not possible
and x = 0.068 m
so
h' = 0.15m - 0.068m = 0.082m
