The length of the unstretched spring is 10 cm, if a weight of 200 g is suspended from this spring, its length will

The length of the unstretched spring is 10 cm, if a weight of 200 g is suspended from this spring, its length will be equal to 14 cm. 1) What is the length of the spring if a weight of 400 g is suspended from it? 2) What is the length of the spring if a weight of 300g is placed on top of it? 3) What weight should be placed on top of the springs to make its length equal to 5 cm? 4) What mass must be suspended from the spring to make its length equal to 20cm, 5) If you apply a horizontal force equal to 5N to the spring, what will its length be? 6) What horizontal force must be applied to the spring to make it 8cm long? Hint: from the data in the problem statement, you can find the coefficient of spring stiffness, and then use this value to solve all the points of the problem.

l0 = 10 cm = 0.1 m.
l = 14 cm = 0.14 m.
l3 = 5 cm = 0.05 m.
g = 9.8 N / kg.
m = 200 g = 0.2 kg.
l4 = 20 cm = 0.2 m.
m1 = 400 g = 0.4 kg.
m2 = 300 g = 0.3 kg.
F5 = 5 N.
l6 = 8 cm = 0.08 m.
l1 -?
l2 -?
m3 -?
m4 -?
l5 -?
F6 -?
The force of elasticity is balanced by the force of gravity: m * g = k * (l – l0).
Let’s find the stiffness of the spring: k = m * g / (l – l0).
k = 0.2 kg * 9.8 N / kg / (0.14 m – 0.1 m) = 49 N / m.
1) m1 * g = k * (l1 – l0).
l1 = m1 * g / k + l0.
l1 = 0.4 kg * 9.8 N / kg / 49 N / m + 0.1 m = 0.18 m.
2) m2 * g = k * (l0 – l2).
l2 = l0 – m1 * g / k.
l2 = 0.1 m – 0.3 kg * 9.8 N / kg / 49 N / m = 0.04 m.
3) m3 * g = k * (l0 – l3).
m3 = k * (l0 – l3) / g.
m3 = 49 N / m * (0.1 m – 0.05 m) / 9.8 N / kg = 0.25 kg.
4) m4 * g = k * (l4 – l0).
m4 = k * (l4 – l0) / g.
m4 = 49 N / m * (0.2 m – 0.1 m) / 9.8 N / kg = 0.5 kg.
5) F5 = k * (l5 – l0).
l5 = l0 + F5 / k.
l5 = 0.1 m + 5 N / 49 N / m = 0.2 m.
6) F6 = k * (l0 – l6).
F6 = 49 N / m * (0.1 m – 0.08 m) = 0.98 N.