Question

Neil and Gus are having a competition to see who can launch a marble highest in the air using their own spring. Neil has a firm spring (kNeil = 50.8 N/m), but it can be compressed only a maximum of yNeil, max = 14.0 cm. Gus’s spring is less firm than Neil’s (kGus = 12.7 N/m), but its maximum compression is greater (yGus, max = 27.0 cm). Given that the mass of the marble is 4.5 g and ignoring the effects of air resistance, who can launch the marble the highest and what is the winning height? Assume the marble starts from the same height, in both cases when the springs are at maximum compression.

Answer 1

Answer:

Neil (221.2m) can throw the marble higher than Gus (205.4 m)

Explanation:

Let's use the law of conservation of energy, the selected points are, the - --    maximum compression of the spring

        Eo = Ke = ½ k x2

Maximum height

        Ef = U = mgh

As there is no rubbing

         E = Ef

         ½ k x² = ½ m g h

         h = k x² / m

Let's calculate for each person

Neil

         x1 = 14.0 cm (1m / 100cm) = 0.140 m

         m = 4.5 gr (1 kg / 1000 g) = 4.5 10⁻³ kg

         h1 = 50.8 0.140 2 /4.5 10⁻³

         h1 = 221.2 m

Gus

        x2 = 27.0 cm = 0.270 m

        h2 = 12.7 0.270 2 /4.5 10⁻³

        h2 = 205.4 m

We see that Neil (221.2m) can throw the marble higher than Gus (205.4 m)