Velocity of a cork from a toy gun

[hansel13]

Homework Statement

A cork gun contains a spring whose spring constant is 10 N/m. The spring constant is compressed 5 cm and then used to propel a 6 gram cork. The cork, however, sticks to the spring for 1 cm beyond its unstretched length before separation occurs. What is the muzzle velocity of this cork? (in m/s)

Homework Equations

K_f - K_i = -1/2kd²

The Attempt at a Solution

-1/2mv² = -1/2kd²
v = d*(k/m)^1/2
v = 5/100m*(10/(6/1000))^1/2
v = 2.04 m/s

Not sure I did that right though because the part where the cork sticks to the spring for 1 cm throws me off. Could someone help me out?

 

[mgb_phys]

It could mean that the spring is stretched 1cm by the bullet so some energy is retained in the spring.

 

[hansel13]

It could mean that the spring is stretched 1cm by the bullet so some energy is retained in the spring.

So the answer then would not be 2.04 then... How would I go about solving this problem?

 

[mgb_phys]

You worked out how much energy was given out by the spring, assuming that stretching the spring by 'x' uses the same energy as compressing it by 'x' how much energy went back into the spring? So how much was available as ke for the cork?

 

[hansel13]

Let me see if I'm reading this right.

The velocity from the spring is v = 2.04 m/s.

So we could say that 1/5 of the velocity from the spring would be .2*2.04 = .408

And 2.04-.408 = 1.63, so the velocity is 1.63

 

[mgb_phys]

initial spring energy = final spring energy + ke of cork
1/2 k 0.05^2 = 1/2 k 0.01^2 + 1/2 m v^2

 

[hansel13]

initial spring energy = final spring energy + ke of cork
1/2 k 0.05^2 = 1/2 k 0.01^2 + 1/2 m v^2

1/2 k 0.05^2 = 1/2 k 0.01^2 + 1/2 m v^2

V = (2/m*(1/2*10*.05² - 1/2 * 10 * 0.01² ))^1/2
V = 2

Thanks :)