Question

What is the velocity of the mass as it loses contact with the spring?

A 1448.0 g mass is on a horizontal surface with mu=0.47? And is in contact with a massless spring with a force constant of 616.0 N/m which is compressed .When the spring is released, it does12.32J of work on the mass while returning to its equilibrium position. Calculate the distance the spring was compressed ,

Answer 1

x = compression of the spring

k = spring constant = 616 N/m

m = mass = 1448 g = 1.448 kg

$\mu$ = coefficient of friction = 0.47

spring energy = 12.32 J

spring energy is given as ::

E = (0.5) k x²

12.32 = (0.5) (616) x²

x = 0.2 m

frictional force is given as ::

f = u mg

the energy of the spring is converted to work done by friction and kinetic energy

E = f x + (0.5) m V²

12.32 = umg x + (0.5) m V²

12.32 = (0.47)(1.448)(9.8)(0.2) + (0.5) (1.448) V²

V = 3.8954 m/s