- #1
darkminos
- 8
- 0
Hi,
I did some calculations but somehow I feel it's not 100% correct. Could someone have a look please.
Many Thanks
"Task"
A pile driver of mass mh has struck a pile of mass mp and driven the pile D meters into the ground, if the velocity of the strike is V, determine the force due to the resistance in the ground by the following methods:
1. D’Alembers Principle
2. Conservation of energy
V = 3.62m/s
mh = 100kg
mp = 200kg
D = 0.08m
g = 9.81 m/s^2
SOLUTION:
v^2 = u^2 + 2as
where
v = initial velocity
u = final velocity
a = acceleration
s = displacement
transposed the formula to get the acceleration.
Deceleration
a = v^2 - u^2 / 2s
a = 3.62^2 - 0 / 2 * 0.08
a = -81.9 m/s^2
F = ma
F = (200 + 100) * 81.9
F = 24570N
Ground Resistance
R = 300 * 9.81 + 24570
R = 27513N
For the second part I'm trying to work out the Potential and Kinetic energy but then i have no idea what to do next...
K.E = 1/2 mv^2
K.E = 1/2 * 200 * 3.62^2
K.E = 1310.44J
Height of fall
1/2mv^2 = mgh
Transposed to make h the subject
h= 1/2*mv^2 / mg
h = (300 * 3.62^2) / 2+ (200 * 9.81)
h = ~1m
P.E = mgh
P.E = 200 * 9.81 * 1
P.E = 1962J
I did some calculations but somehow I feel it's not 100% correct. Could someone have a look please.
Many Thanks
"Task"
A pile driver of mass mh has struck a pile of mass mp and driven the pile D meters into the ground, if the velocity of the strike is V, determine the force due to the resistance in the ground by the following methods:
1. D’Alembers Principle
2. Conservation of energy
V = 3.62m/s
mh = 100kg
mp = 200kg
D = 0.08m
g = 9.81 m/s^2
SOLUTION:
v^2 = u^2 + 2as
where
v = initial velocity
u = final velocity
a = acceleration
s = displacement
transposed the formula to get the acceleration.
Deceleration
a = v^2 - u^2 / 2s
a = 3.62^2 - 0 / 2 * 0.08
a = -81.9 m/s^2
F = ma
F = (200 + 100) * 81.9
F = 24570N
Ground Resistance
R = 300 * 9.81 + 24570
R = 27513N
For the second part I'm trying to work out the Potential and Kinetic energy but then i have no idea what to do next...
K.E = 1/2 mv^2
K.E = 1/2 * 200 * 3.62^2
K.E = 1310.44J
Height of fall
1/2mv^2 = mgh
Transposed to make h the subject
h= 1/2*mv^2 / mg
h = (300 * 3.62^2) / 2+ (200 * 9.81)
h = ~1m
P.E = mgh
P.E = 200 * 9.81 * 1
P.E = 1962J