The Red Cross has arranged to send a helicopter with supplies into a town in the

Question

The Red Cross has arranged to send a helicopter with supplies into a town in the Texas gulf that is isolated by flood waters. The crates holding the supplies will burst if they hit the ground with a downward speed of more than 12 m/s. Suppose a crate of food, which has a mass of 125 kg, is released from the helicopter with it is rising at a rate of 5.3 m/s at an altitude of 11 m above the ground. If air resistance can be neglected: What is the total mechanical energy of the Earth-Crate system relative to the Earth's surface? What is the potential energy of the crate when it reaches its highest point? How high is this point? What is the kinetic energy of the crate when it hits the ground? How skilled is the copter pilot at making the drops? In other words, is the crate likely to break apart?

Explanation / Answer

a)

total energy = E1 = m*g*h + 0.5*m*u^2 = (125*9.8*11)+(0.5*125*5.3^2) = 15230.625 J

b)

PE = E = 15230.625 J

c)

PE = m*g*H = E

H = E/mg = 15230.625/(125*9.8) = 12.43 m/s

d)

KE when it hits the ground = PE = 15230.625 J

e)

speed with which crate hits = v = sqrt(2*g*H) = 15.6 m/s

crate will break

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