Answer:
Therefore, the velocity of the mass when the displacement is -1.5 cm is 0.121 m/s.
Step-by-step explanation:
To calculate the velocity of the mass attached to a spring with the given parameters, we can use the principle of conservation of energy. At the maximum displacement (2 cm), all the potential energy stored in the spring is converted into kinetic energy of the mass. Therefore, we can write:
1/2 * m * v^2 = 1/2 * k * x^2
where m is the mass of the object, v is the velocity of the object, k is the spring constant, and x is the displacement of the mass from the equilibrium position.
Substituting the given values, we get:
1/2 * 8 kg * v^2 = 1/2 * 200 N/m * (0.02 m)^2
Solving for v, we get:
v = sqrt((0.02 m)^2 * 200 N/m / 8 kg) = 0.2 m/s
Therefore, the velocity of the mass when the displacement is 2 cm is 0.2 m/s.
Similarly, at a displacement of -1.5 cm, we can use the same equation to calculate the velocity:
1/2 * 8 kg * v^2 = 1/2 * 200 N/m * (-0.015 m)^2
Solving for v, we get:
v = sqrt((-0.015 m)^2 * 200 N/m / 8 kg) = 0.121 m/s (rounded to three decimal places)