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 floodwaters. 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 when the helicopter is rising at a rate of 5.3 m/s at an altitude of 11 m above the ground. Air resistance can be neglected. (You do not need to, nor may you, use kinematics on any part of this problem.)

(a) What is the total mechanical energy of the Earth-Crate system relative to the Earth’s surface?

(b) What is the potential energy of the crate when it reaches its highest point?

(c) How high is this point?

(d) What is the kinetic energy of the crate when it hits the ground?

(e) How skilled is the copter pilot at making the drops. In other words, is the crate likely to break apart?

Explanation / Answer

(a)
Initial Kinetic Energy of Crate = 1/2 * mv^2
Initial Potential Energy of Crate = m*g*h

Total Mechanical Energy =  Kinetic Energy of Crate + Potential Energy of Crate
Total Mechanical Energy = 1/2 * mv^2 + m*g*h
Total Mechanical Energy = 1/2 * 125 * 5.3^2 + 125 * 9.8 * 11 J
Total Mechanical Energy = 15230.6 J
(b)
Using Energy Conservation -
Potential Energy of Crate at Highest point = = 15230.6 J
(c)
m*g*h = 15230.6
h = 15230.6/(125*9.8)
h = 12.43 m

(d)
Using Energy Conservation -
kinetic energy of the crate when it hits the ground = 15230.6

(e)
1/2 * mv^2 = 15230.6
v = sqrt((2 * 15230.6)/125)
v = 15.6 m/s

Yes as the speed is greater than 12 m/s , Crate will likely break.

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