Answer:
7200 N/m
Explanation:
Metric unit conversion
100g = 0.1 kg
5 cm = 0.05 m
50 cm = 0.5 m
As the block is released from the spring and travelling to height h = 1.5m off the ground, the elastics energy is converted to work of friction force and the potential energy at 1.5 m off the ground
The work by friction force is the product of the force F = 15N itself and the distance s = 0.5 m
[tex]W_f = F_fs = 15*0.5 = 7.5 J[/tex]
Let g = 10 m/s2. The change in potential energy can be calculated as the following:
[tex]E_p = mgh = 0.1*10*1.5 = 1.5 J[/tex]
Therefore, as elastic energy is converted to potential energy and work of friction:
[tex]E_e = W_f + E_p[/tex]
[tex]kx^2/2 = 7.5 + 1.5 = 9 J[/tex]
[tex]k = 9*2/x^2 = 18/0.05^2 = 7200 N/m[/tex]