D'alembert's principle

Alex Christie · May 5, 2016

1. The problem statement, all variables and given/known data
i have a question on D'alemberts principle in which it asks me to find the velocity of a hammer immediately before impact with a pile

the information i have been given is as follows:
mass of hammer;300kg
height of hammer;3.5m
gravity to be taken as;9.81
mass of pile ;500kg

I have solved the question using the conservation of energy technique in which
KE = GPE
0.5mv^2 = mgh
0.5x300xv^2 = 300x9.81x3.5
v=square root of 9.81x3.5/0.5
v=8.287m/s

2. Relevant equations
KE=1/2mv^2
GPE=mgh
F=Ma=-Fi
3. The attempt at a solution
all attempts at a solution have proved to be futile as i cannot wrap my head around it, i have read about inertia forces and that an applied force must overcome this inertia force in order to accelerate however im stumped when it comes to this question Any help would be massively appreciated

PhanthomJay · May 5, 2016

I think there may be a second part to this problem that might be asking to use the inertia force during the impact period. But in terms of just find hammer speed before impact, either use conservation of energy or the kinematic free fall equations.

rude man · May 11, 2016

Alex Christie said: ↑

1. The problem statement, all variables and given/known data
i have a question on D'alemberts principle in which it asks me to find the velocity of a hammer immediately before impact with a pile

the information i have been given is as follows:
mass of hammer;300kg
height of hammer;3.5m
gravity to be taken as;9.81
mass of pile ;500kg

I have solved the question using the conservation of energy technique in which
KE = GPE
0.5mv^2 = mgh
0.5x300xv^2 = 300x9.81x3.5
v=square root of 9.81x3.5/0.5
v=8.287m/s

Well, this would be a trivial application of d'Alembert's principle, but it would go as follows:
F = ma can be rewritten as F - ma = 0.
So we consider the term -ma as a force F2 = -ma; then F + F2 = 0 and we now think of the problem as a static one (the hammer does not move since ΣF = 0.) This is entirely acceptable, weird though it may sound, since the equation remains unchanged.

So we have mg - ma = 0 or a = g. Then of course knowing a you can compute v from the appropriate kinematic free fall equations as post #2 says.

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D'alembert's principle

Alex Christie

PhanthomJay

rude man

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