Aspring has a force constant of 40,000 n/m. it is resting horizontally on a 20 m tall roof top and fires a 2 kg mass to the ground below. the mass hits the ground a 21 m/sec. how far was the spring compressed? (no energy was lost)

in the previous problem, if the mass hits the ground at 19 m/sec, how much energy was lost due to air resistance?

1) 4.9 cm

The initial mechanical energy of the spring+mass system is sum of gravitational potential energy and elastic potential energy of the spring:

where:

m = 2 kg is the mass

g = 9.8 m/s^2

h = 20 m is the height of the roof top

k = 40,000 N/m is the spring constant

x is the compression of the spring

When the mass hits the ground, its mechanical energy is just kinetic energy:

where v = 21 m/s is the speed. Since energy is conserved, we can equalize the two expressions, and solving for x we find the compression of the spring:

2) 79 J

The initial mechanical energy of the spring-mass system is

While the final mechanical energy of the mass is

So, the energy lost due to air resistance is