Answer:
1) k = 10 [N/m]
2) a-) x = 0.4 [m]
b) x = 0.075 [m]
Explanation:
To be able to solve this type of problems that include springs we must use Hooke's law, which relates the force to the deformed length of the spring and in the same way to the spring coefficient.
F = k*x
where:
F = force [N] (units of Newtons]
k = spring constant [N/m]
x = distance = 10 [cm] = 0.1 [m]
Now, the weight is equal to the product of the mass by the gravity
W = m*g = F
where:
m = mass = 100 [g] = 0.1 [kg]
g = gravity acceleration = 10 [m/s²]
F = 0.1*10 = 1 [N]
Now clearing k
k = F/x
k = 1/0.1
k = 10 [N/m]
2)
a ) if the force is 4 [N]
clearing x
x = F/k
x = 4/10
x = 0.4 [m]
m = 75 [g] = 0.075 [kg]
W = m*g = F
F = 0.075*10 = 0.75 [N]
x = .75/10
x = 0.075 [m]
