Answer:
a
[tex]x = 0.0507 \ m[/tex]
b
[tex]d = 0.1014 \ m[/tex]
Explanation:
From the question we are told that
The spring constant is [tex]k = 116 \ N/m[/tex]
The mass of the block is [tex]m = 0.60 \ kg[/tex]
Considering question a
Generally the weight of the block is mathematically represented as
[tex]W = m * g[/tex]
=> [tex]W = 0.60 * 9.8[/tex]
=> [tex]W = 5.88\ N[/tex]
Generally the force exerted on the spring is mathematically represented as
[tex]F = k * x[/tex]
At equilibrium
[tex]W = F[/tex]
=> [tex]k * x = 5.88[/tex]
=> [tex]116 * x = 5.88[/tex]
=> [tex]x = 0.0507 \ m[/tex]
Considering question b
Generally the energy stored in the spring is mathematically represented as
[tex]E = \frac{1}{2} * k * d^2[/tex]
Now the potential energy of the block before it is drooped is mathematically represented as
[tex]PE = m * g * d[/tex]
Generally from the law of energy conservation we have that
[tex]E = PE[/tex]
=> [tex]\frac{1}{2} * k * d^2 = m * g * d[/tex]
=> [tex]\frac{1}{2} * 116 * d = 0.60 * 9.8[/tex]
=> [tex]d = 0.1014 \ m[/tex]
