Speed of launcher?

Question

Dwight uses a spring (k = 40 N/m) on a horizontal surface to make a launcher for model cars. The spring is attached to a holder that has a mass of 0.5 kg. If he compresses the spring and releases it, the launcher will move back and forth in periodic motion.

a. He compresses the spring by 0.2 m and lets it go. What is the maximum speed of the launcher?

b. He compresses the spring by 0.2 m and lets it go again. What is the speed of the launcher at the point where the spring is compressed exactly 0.1 m?

Answer 1

(a)

 

From energy conservation,

 

1/2 k x^2 = 1/2 m v^2

 

v = sqrt(k x^2 / m) = sqrt [40 (0.2)^2 / 0.5] m/s = 1.79 m/s

 

 

(b)

 

Again, from energy conservation,

 

E = KE + PE = 1/2 k (delta x)^2 + 1/2 m v^2

 

E = same E as in part (a), which is 1/2 * 40 * (0.2)^2 J = 0.8 J

 

E = 1/2 k (delta x)^2 + 1/2 m v^2

 

v = sqrt{2/m * [E - 1/2 * k *(delta x)^2]} = sqrt{2/0.5 * [0.8 - 1/2 * 40 *(0.1)^2]} = 1.55 m/s