Question

A spring with a spring constant of 120 J/m2 is fixed to a wall, free to oscillate. On the other end, a ball with a mass of 1500 g is attached. The spring-mass is then stretched 50 cm, and released. What is the top speed of the attached ball? 0 A. 4.47 m/s B. 447 m/s C. 0.14 m/s D. 6.32 m/s

Answer 1

Answer:

A. 4.47 m/s

Explanation:

As the ball oscillates, it mechanical energy, aka the total kinetic and elastics energy stays the same. For the ball to be at maximum speed, its elastic energy i 0 and vice versa. When the ball is at rest, its kinetic energy is 0 and its elastic energy is at maximum at 50 cm, or 0.5 m

1500 g = 1.5 kg

$E_e = E_k$

$kx^2/2 = mv^2/2$

$120*0.5^2/2 = 1.5*v^2/2$

$15 = 0.75v^2$

$v^2 = 15 / 0.75 = 20$

$v = \sqrt{20} = 4.47 m/s$