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:

Answer 1

2 m/s

Step-by-step explanation:

We will apply the law of conservation of energy to solve this.

The initial spring potential energy = final spring potential energy + kinetic energy of cork, this means that

1/2kx² = 1/2kx'² + 1/2mv², and this is

kx² = kx'² + mv²

From the question, we are given that

k = 10N/m

x = 5cm = 0.05 m

x' = 1cm = 0.01 m

m = 6g = 0.006 kg

Substituting these values to the formula, and we get,

10(0.05)² = 10(0.01)² + 0.006v²

10 * 0.0025 = 10 * 0.0001 + 0.006 v²

0.025 = 0.001 + 0.006v², multiplying all sides by 1000, we have

25 = 1 + 6v²

6v² = 25 - 1

6v² = 24

v² = 24 / 6

v² = 4

v = √4

v = 2 m/s

⇒25 - 1 = 6v²

⇒v² = 24/6 = 4

⇒v = 2 m/s