# 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 this spring by 4 cm?

A1 = 0.02 J.
x1 = 4 mm = 0.004 m.

x2 = 4 cm = 0.04 m.

A2 -?

Work is determined by the formula: A = F * S, where F is force, S is displacement.

According to Hooke’s law: F = k * x, k is the stiffness of the spring, x is the elongation of the spring.

Move S = x.

A1 = k * x1 ^ 2, k = A1 / k * x1 ^ 2.

A2 = k * x2 ^ 2 = A1 * x2 ^ 2 / x1 ^ 2.

A2 = 0.02 J * (0.04 m) ^ 2 / (0.004 m) ^ 2 = 2 J.

2.R1 = 2 * Rz.

F / F1 -?

Gravity is the force of gravity on the surface of the earth.

The force of universal gravitation is determined by the formula: F = G * m * Mz / Rz ^ 2.

F1 = G * m * Mz / (R1 + Rz) ^ 2 = G * m * Mz / (2 * Rz + Rz) ^ 2 = G * m * Mz / (3 * Rz) ^ 2 = G * m * Ms / 9 * Rs ^ 2.

F / F1 = G * m * Mz / Rz ^ 2: G * m * Mz / 9 * Rz ^ 2 = 9.

Answer: at altitude, the force of gravity will decrease by a factor of 9: F / F1 = 9.

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