To stretch the spring by 4 mm, it is necessary to do a work of 0.02 J. What work must be done to stretch the spring by 4 cm?

To stretch the spring by 4 mm, it is necessary to do a work of 0.02 J. What work must be done to stretch the spring by 4 cm? A body weighing 400 g freely falls from a height of 2 m. Find the kinetic energy of the body at the moment of impact on the ground. A body weighing 3 kg, freely falls from a height of 5 m. Find the potential and kinetic energy of the body at a distance of 2 m from the earth’s surface.

First question:
E1 = k * x1 ^ 2/2; E2 = k * x2 ^ 2/2
E1 / E2 = x1 ^ 2 / x2 ^ 2 from here:
E2 = E1 * x2 ^ 2 / x1 ^ 2 = 0.02 * 0.04 ^ 2 / 0.004 ^ 2 = 2 Joules.
Answer: to stretch the spring by 4 cm, you need to do a work of 2 Joules.

Second question:
Ek = Ep = m * g * H = 0.4 * 10 * 2 = 40 * 2 = 80 Joules.
Answer: the kinetic energy at the moment of impact on the ground is 80 Joules.

Third question:
Ep = Ep1 + Ek1
Ep = m * g * H = 3 * 10 * 5 = 150 Joules;
Ep1 = m * g * H1 = 3 * 10 * 2 = 60 Joules;
Ek1 = Ep – Ep1 = 150 – 60 = 90 Joules.
Answer: at a distance of 2 meters from the earth’s surface, the potential energy is 60 Joules, the kinetic energy is 90 Joules.