Final answer:
The mass that must be attached to a spring to have 7.5 J of kinetic energy at 5 m/s is 0.6 kg or 600 g.
Step-by-step explanation:
The question asks for the mass that must be attached to a spring with a specific spring constant (k) to have a certain amount of kinetic energy at a given velocity. This involves applying the principles of conservation of energy in the context of simple harmonic motion.
To solve this, we use the formula for kinetic energy, KE = 0.5 * m * v2 where KE is kinetic energy, m is mass, and v is velocity. With a kinetic energy of 7.5 J and a velocity of 5 m/s, we can rearrange the formula to solve for mass (m).
Substituting the given values: 7.5 J = 0.5 * m * (5 m/s)2, we arrive at m = 7.5 J / (0.5 * 25 m2/s2) = 0.6 kg or 600 g.