Final answer:
The total energy in the system is the sum of the elastic potential energy stored in the spring and the kinetic energy of the masses. This is calculated using the formulas for elastic potential energy and kinetic energy, leading to a total energy of 1.5 Joules.
Step-by-step explanation:
The student's question pertains to the physical scenario involving two identical masses and a compressed spring, which relates to the concept of elastic potential energy in Physics, specifically within the topic of mechanics and Hooke's Law. To find the total energy in the system described by the question, we need to consider both the elastic potential energy stored in the spring and the kinetic energy of the masses due to their motion.
Total Energy Calculation
The total energy E in the system is the sum of the elastic potential energy U plus the kinetic energy K. The elastic potential energy can be calculated using the formula U = 1/2 k x^2 where k is the spring constant and x is the compression or extension from the equilibrium position. The kinetic energy for each mass can be calculated using the formula K = 1/2 m v^2 where m is the mass and v is the velocity. Therefore, the total energy is:
E = U + 2K
E = 1/2 (25 N/m) (0.20 m)^2 + 2 * 1/2 (4.0 kg) (0.50 m/s)^2
E = 1/2 (25) (0.04) + 2 * 1/2 (4) (0.25)
E = 0.5 + 1.0
E = 1.5 J
The correct answer is (b) 1.5 J.