The spring of a spring gun has force constant k = 400 and negligible mass. The s

Question

The spring of a spring gun has force constant k = 400 and negligible mass. The spring is compressed 6.00 and a ball with mass 0.0300 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 6.00 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.
What position along the barrel does the ball have the greatest speed when there is a resisting force of 6N acting on the ball as it moves out of the barrel?

Explanation / Answer

The ball is accelerated down the barrel, call this direction positive. Thus the constant force of 6 N acts in a negative direction to reduce the spring force. The net force acting on the ball in the barrel is:
Fnet = spring force - resistance force = (kx - 6.00)

Although at the start of travel, the spring force = (400)(6.00) = +24 N and
Fnet = 24-6 = +18 N,
there is a point where the spring force = the resistance force and after that the resistance force beomes larger than the spring force, resulting in a negative acceleration (reduction of ball's speed).

Thus the point of maximum ball speed is when:
spring force = resistance force
kx = 6.00
400(x) = 6.00
x = 6.00/400 = 0.015 m ANS

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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