Calculating Average Force Exerted on Pile Driver by I-Beam

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AI Thread Summary
To calculate the average force exerted on the pile driver by the I-beam, the mass of the pile driver (2580 kg) and gravitational acceleration (9.8 m/s²) are used to find the initial force of impact, resulting in 25,284 N. The problem requires considering the deceleration as the pile driver comes to rest after driving the beam 5.58 cm into the ground. To find the average force, the initial velocity of the pile driver, calculated from its fall of 2.52 m, must be determined first. The negative acceleration during the deceleration phase is crucial for accurately calculating the average force. Understanding these dynamics is essential for solving the problem correctly.
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Homework Statement


A 2580 kg pile driver is used to drive a steel I-Beam into the ground. The pile driver falls 2.52 m before contacting the beam, and it drives the beam 5.58 cm into the ground before coming to rest.
Find the magnitude of the average force for the beam exerts on the pile driver while the pile driver is brought to rest.


Homework Equations


F=ma



The Attempt at a Solution


ok so looking at this problem the first thing that came to my head is that i need to find the proper force and divide in by the 5.58 cm converted to meters to get the magnitude of force.
So i plugged in F=ma F=(2580)9.8
giving me 25284
but I am not seeing where the 2.52 meters should come into play.
 
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f=ma is correct but acceleration also means slowing down as well as speeding up.
You are looking for the force needed to slow the pile driver from whatever speed it was doing qwhen it hits to zero in a distance of 5.58cm.
 
okay so i need to take the negative acceleration into play that makes sense.
so do i first need to first the velocity of the pile driver while it is falling 2.52 meters?
 
Yes and yes
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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