A toy cork gun contains a spring whose spring constant is 10.0 N/m.The spring is compressed 5.00 cm and then used to propel a 6.00-g cork.The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs.The muzzle velocity of this cork is:
A)1.02 m/s
B)1.41 m/s
C)2.00 m/s
D)2.04 m/s
E)4.00 m/s

Question

A toy cork gun contains a spring whose spring constant is 10.0 N/m.The spring is compressed 5.00 cm and then used to propel a 6.00-g cork.The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs.The muzzle velocity of this cork is: 
A)1.02 m/s 
B)1.41 m/s 
C)2.00 m/s 
D)2.04 m/s 
E)4.00 m/s

Quizplus · Accepted Answer

We can use the conservation of mechanical energy to find the velocity of the cork:

Initial mechanical energy = Final mechanical energy

(1/2)kx^2 = (1/2)mv^2

Where k is the spring constant, x is the distance the spring is compressed, m is the mass of the cork, and v is the velocity of the cork.

Solving for v:

v = sqrt((kx^2)/m)

v = sqrt((10 N/m)(0.05 m)^2 / 0.006 kg)

v ≈ 2.00 m/s

Note that the additional 1.00 cm distance that the cork sticks to the spring beyond its unstretched length does not affect the final velocity of the cork.

A Toy Cork Gun Contains a Spring Whose Spring Constant