A 0.46 kg mass is attached to a light spring with a force constant of 39.9 N/m and set into oscillation on a horizontal frictionless surface. If the spring is stretched 5.0 cm and released from rest, determine the following. (a) maximum speed of the oscillating mass

Respuesta :

Answer:

0.466 m/s

Explanation:

We are given that

Mass =m=0.46 kg

Spring constant,k=39.9 N/m

Length of stretched spring=A=5 cm=[tex]5\times 10^{-2} m[/tex]

1 m=100 cm

a.We have to find the maximum speed of the oscillating mass.

Maximum speed,v=[tex]A\sqrt{k}{m}}[/tex]

Using the formula

Maximum speed,v=[tex]5\times 10^{-2}\sqrt{\frac{39.9}{0.46}}[/tex]

Maximum speed,v=0.466 m/s

Answer:

Explanation:

mass of block, m = 0.46 kg

Spring constant, K = 39.9 N/m

extension in spring, Δs = 5 cm = 0.05 m

By the conservation of energy, the maximum potential energy stored in the spring is equal to the kinetic energy of the block.

1/2 K Δs² = 1/2 m v²

39.9 x 0.05 x 0.05 = 0.46 x v²

v = 0.47 ms