A toy gun uses a spring to project a 5.30-g soft rubber ball. The spring is orig

Question

A toy gun uses a spring to project a 5.30-g soft rubber ball. The spring is originally compressed by 5.00 cm and has a force constant of 8.0 N/m. When the gun is fired, the ball moves 15.0cm through the barrel of the cannon that is inclined at an angle of 30 degree, and the barrel exerts a constant friction force of 0.0320 N on the ball. (a) With what speed does the projectile leave the barrel of the cannon? (b) At what point from the start does the ball have maximum speed? (c) What is this maximum speed with in the barrel?

Explanation / Answer

use the law of conservtion of energy as

KE = EPE - Workmdue to friction

so

0.5 mv^2 = 0.5 kx^2 - u mdg

0.5 * 5.3*10^-3 -3 * V^2 = 0.5 * 8 * 0.05^2 - 0.032 * 5.3 *10^-3 * 9.81 * 0.15

V = 6.62 m/s
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b. Applying the balance force

Fs = F + mg sin theta

Kx = F + mg sin theta

x = 0.032 + 0.0053 * 9.81 * sin 30/100

x = 0.058cm

=----------------------------------------------
0.5 mv^2 = 0.5 kx^2 - u mdg

0.5 * 5.3*10^-3 -3 * Vmax^2 = 0.5 * 100 * 0.058^2 - 0.032 * 5.3 *10^-3 * 9.81 * 0.15

Vmx = 46 m/s

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