1.) The amazing \"Howard the Human Projectile\" is fired straight forward from a

Question

1.) The amazing "Howard the Human Projectile" is fired straight forward from a 300 kg circus canon during a recent Ringling Bro. Barnum and Baily performance in Bel Alton. If Howard has a mass of 20 kg and the canon recoils with a velocity of 2.5 m/s, at what initial velocity does Howard leave the cannon?

a.) -50 m/s b.) -75.6 m/s c.) -20 m/s d.) -37.5 m/s e.) -25 m/s

2.) A wheel of radius 12 cm is mounted on a frictionless, horizontal axle that is perpendicular to the wheel and passes through the wheel's center of mass. A light cord wrapped around the wheel supports a 0.40 kg weight. When released from rest with the string taut, the weight accelerates downward at 3.0 m/s^2. What is the wheel's moment of inertia?

a.) 0.035 kg m^2 b.) 0.013 kg m^2 c.) 0.023 kg m^2 d.) 0.020 kg m^2 e.) 0.016 kg m^2

Explanation / Answer

1) Linear momentum is conserved.

=> 20v + [300 * (-2.5)] = 0

=> 20v = 750

=> v = 37.5 m/s

2) For the weight: mg - T = ma

=> T = m(g - a) = 0.40(9.81 - 3) = 2.72 N

For the wheel:

Tr = I(a/r)

=> I = Tr2/a = 2.72 * 0.122 / 3 = 0.013 kg-m2

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