Question

An air gun with a 30-cm long barrel fires a 56-g ball straight upwards. While the ball is in the barrel, compressed air exerts a constant force of 3.2-N force upwards. Calculate the maximum height above the end of the air gun that the ball reaches. Ignore any air resistance. [The pressure from the air gun is not air resistance]

Notes

• Solve this problem using Work and Energy. NO KINEMATICS ALLOWED!!!

• The ball travels 1.45 m above the end of the gun

. • This problem will require forces. Draw free-body diagrams for the ball

Answer 1

Suppose 'h' is the maximum height attained by the ball after firing.

So, potential energy gained by the ball, PE = m*g*h

Magnitude of the force, F = 3.2 N

Distpalcement, d = 30 cm = 0.30 m

Hence, work done by the force, W = F*d = 3.2 * 0.30 J

Apply work - energy theorem -

Work done = Potential energy gained by the ball

=> 3.2 * 0.30 J = m*g*h

=> 3.2 * 0.30 J = 0.056*9.8*h

=> h = (3.2 * 0.30) / (0.056*9.8) = 1.75 m

Hence, maximum height of the ball from the end of the gum = 1.75 - Length of the barrel

= 1.75 - 0.30 = 1.45 m (Answer)

Drwa the free-body diagram just considering the weight 'mg' acting in the downward direction.

Force, F acts in upward direction upto a distance 'd'.

Hope, you understand the solution!