The spring of a spring gun has force constant k=400N/m and negligible mass. The

Question

The spring of a spring gun has force constant k=400N/m and negligible mass. The spring is compressed 6.00cm, and a ball with mass 0.0300kg is placed in the horizontal barrel against the compressed spring. The spring is then released, and the ball is propelled out the barrel of the gun. The barrel is 6.00cm long, so the ball leaves the barrel at the same point that it loses contact with the spring. The gun is held so the barrel is horizontal. (a) Calculate the speed of the ball as it leaves the barrel if you can ignore friction. (b) Calculate the speed of the ball as it leaves the barrel if a constant resisting force of 6.00N acts on the ball as it moves along the barrel. (c) For the situation in part (b), at what position along the barrel does the ball have the greatest speed, and what is the speed? (In this case, the maximum speed does not occur at the end of the barrel)

Explanation / Answer

P(spring)=.5 k x^2 (see ref) Potential energy of a spring Ke(ball)=.5 m v^2 Kinetic energy of the ball P(spring)=Ke(ball) A) Velocity v=Sqrt(2Ke/m) v=Sqrt(2(.5 k x^2)/m) v=Sqrt(k x^2)/m) v=V(400 N/m (.06)^2 /0.0300 ) v=6.93 m/s B) Some equation F(spring) - ma - F(resistance)=0 [forces involved] a = ((Fs - Fr)/m d=.5at^2 t=sqrt(2d/a) v=at=a sqrt(2d/a) v=sqrt(2 d a) since a=((Fs - Fr)/m v=sqrt(2d ((Fs - Fr)/m) C) Vmax will take place at Ft=0 Ft = Fs - Fr=0 kx-Fr=0 x=Fr/k=6/400=0.015m (1.5cm) before leaving the barrel. D ) Same as A) but now the X=6-1.5 =4.5cm

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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