The potential energy is given by the function U(x) = kx⁻¹, where k is a constant, and variable x is the position, the coordinate. (a) Derive the function of the coordinate x, which describes the force produced by this potential energy.
F(x) = - d U(x) / dx
F(x) = - d kx⁻¹ / dx = kx⁻²
F(x) = kx⁻²
(b) Let this potential energy is obtained by the body with the mass of 10kg. The constant is known: k = -3.98 × 10¹⁵ Jm.
Find the force on this body when it is located atx = 6.38 × 10⁶ m?
Find the force on this body when it is located atx = 6.38 × 10⁶ m?
F(x) = kx⁻² = -3.98 × 10¹⁵ Jm / ( 6.38 × 10⁶ m)²
The code for the Google calculator: (-3.98E15J*m) / ( 6.38E6m )^2
Google calculator's result: -97.7781272 newtons
Problem's answer: F = -97.8 N or 97.8 N towards x = 0
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