1. A 2,200-kg pile driver is used to drive a steel I-beam into the ground. The p
ID: 1432646 • Letter: 1
Question
1. A 2,200-kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 4.40 m before coming into contact with the top of the beam, and it drives the beam 14.2 cm farther into the ground as it comes to rest. Using energy considerations, calculate the average force the beam exerts on the pile driver while the pile driver is brought to rest.
magnitude in N
2. A 7.80-g bullet moving at 560 m/s penetrates a tree trunk to a depth of 5.80 cm.
(a) Use work and energy considerations to find the average frictional force that stops the bullet.
in N
(b) Assuming the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment it stops moving.
in s
Explanation / Answer
1)
work in equals work out:
F1 d1 = F2 d2
F2 = F1 d1 / d2 = (2200 kg * 9.8 m/s^2) (4.40 m) / (14.2 cm) = 6680.56 kN
2)
The energy of the bullet is ½*m*v²; the energy absorbed by the hand is Fav*d
Fav = ½*m*v²/d = ½*0.00780*560²/0.058 = 21086.89 kN
Momentum change = impulse
m*v = F*t
t = m*v/F = 0.00780*560/21086.89 = 2.07*10^-3 s
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