Final answer:
The energy stored in a spring with a spring constant of 490 N/m and a maximum stretch of 19 cm is 8.8395 joules, calculated using the formula for spring potential energy.
Step-by-step explanation:
The amount of energy stored in a spring is determined by the spring's potential energy, which can be calculated using the formula U = (1/2)kx², where 'U' is the potential energy, 'k' is the spring constant, and 'x' is the displacement of the spring from its equilibrium position. In this case, the spring constant (k) is 490 N/m and the maximum stretch (x) given is 19 cm, which should be converted to meters (0.19 m).
To find the energy that can be stored in this spring at its maximum stretch, we use:
U = (1/2) * 490 N/m * (0.19 m)²
This calculation results in:
U = (1/2) * 490 * 0.0361 J
U = 8.8395 J
Therefore, the energy stored in the spring at its maximum possible stretch of 19 cm is 8.8395 joules.