the answer is provided please show me in details how to arrive at it A 950 kg ri
ID: 1605891 • Letter: T
Question
the answer is provided please show me in details how to arrive at it
A 950 kg rigid pile is driven into the ground using a 250 kg hammer. The hammer is dropped from rest at a height of 2.0 meters above the top of the pile. Note that the soil in which the pile is embedded is loose sand, which means that the hammer does not rebound off the pile. Given the situation posed, determine the following: (a) What is the velocity of the hammer right before it hits the pile? (Answer: 6.264 m/s) (b) What is the velocity of the hammer just after the collision with the pile? What is the velocity of the pile after the collision? (Answer: 1.305 m/s) (c) What is the impulse which the pile imparts to the hammer? (Answer: 1240 Ns)Explanation / Answer
let
m1 = 250 kg
m2 = 950 kg
a) velocity of the hammer right before it hits the pile,
v1i = sqrt(2*g*h)
= sqrt(2*9.8*2)
= 6.26 m/s
b)
velocity of hammer just after the collision, v1f = (m1 - m2)*v1i/(m1+m2)
= (250 - 950)*6.26/(250 + 950)
= -3.65 m/s (upward)
velocity of pile just after the collision, v2f = 2*m1*v1i/(m1+m2)
= 2*250*6.26/(250 + 950)
= 2.608 m/s
c) Impulse on the hammer = m1*delta_V1
= 250*(6.26 - (-3.65))
= 2478 N.s
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