Question

springlike systems store energy (u_s) in joules, j according to which equation?

○ u_s = m a

○ u_s = 1/2 k x^2

○ u_s = g m1 m2 / r^2

○ u_s = m g h

○ u_s = - k x

○ u_s = 1/2 m v^2

Explanation:

To determine the equation for the energy stored in a spring - like system, we analyze each option:

• Option \(U_s = ma\): This is Newton's second law (\(F = ma\)), which relates force, mass, and acceleration, not spring energy.
• Option \(U_s=\frac{1}{2}kx^{2}\): The elastic potential energy (energy stored in a spring - like system) is given by this formula, where \(k\) is the spring constant and \(x\) is the displacement from the equilibrium position.
• Option \(U_s=\frac{Gm_1m_2}{r^{2}}\): This is Newton's law of universal gravitation (for gravitational force), not related to spring energy.
• Option \(U_s = mgh\): This is the formula for gravitational potential energy, which depends on mass, gravitational acceleration, and height, not spring energy.
• Option \(U_s=-kx\): This is Hooke's law (\(F=-kx\)), which relates the force exerted by a spring to its displacement, not the energy.
• Option \(U_s=\frac{1}{2}mv^{2}\): This is the formula for kinetic energy, which depends on mass and velocity, not spring energy.

Answer:

\(U_s=\frac{1}{2}kx^{2}\) (the second option in the list)