Use the exact values you enter in previous answer(s) to make later calculation(s

Question

Use the exact values you enter in previous answer(s) to make later calculation(s).

A toy gun shoots spherical plastic projectiles by means of a spring. A typical projectile has mass

m = 30 g.

The spring used has spring constant

k = 25 N/m,

and when put under load, it is displaced an amount

?x = 6.0 cm

as shown in the figure below. The barrel of the gun exerts a slight frictional force of magnitude

Ffriction = 0.064 N

on the pellet as it moves down the barrel from its starting point a total length

L = 15 cm.

(a) If the toy gun is fired in a horizontal position, at what position measured from the starting point does the pellet reach maximum velocity? Hint: Consider an equilibrium condition between the spring force and the friction force on the pellet before it leaves the spring.

(b) What is the maximum speed achieved by the pellet as it is fired from the gun?

(c) At what speed does the pellet leave the barrel?

Explanation / Answer

a)at the equilibrium. (when the pellet leaves the spring)

b) net work done on the pellet = Workdone by sring + workdone by friction

= 0.5*k*x^2 - Ff*x

= 0.5*25*0.06^2 - 0.064*0.06

= 0.04116 J

Apply W0rk-enrgy theorem

Wnet = 0.5*m*v^2

==> vmax = sqrt(2*Wnet/m)

= sqrt(2*0.04116/(30*10^-3))

= 1.66 m/s

c) total workdone on the pellet before leaving the barrel

= 0.5*k*x^2 - Ff*L

= 0.5*25*0.06^2 - 0.064*0.15

= 0.0354 J

Apply W0rk-enrgy theorem

Wnet = 0.5*m*v^2

==> vmax = sqrt(2*Wnet/m)

= sqrt(2*0.0354/(30*10^-3))

= 1.54 m/s

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.