Hammer Drive
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Article Source: http://www.earticlesonline.com/Article/Industrial-Electronics-Repair-USA--Servo-Motor-Repair--Servo-Drive-Repair-USA/978370
Work Energy Theorem?
A 500 kg hammer drives a spike into the wall. The hammer has a velocity of 20 m/s just as it impacts the spike. If the resisting force on the spike is 2x10^6 N, how far is the spike driven on each stroke? Please show work.
This is a conservation of energy problem.
Total energy just prior to impact is TE(V) = 1/2 mV^2; where m = 500 kg and V = 20 mps.
Total energy after the spike is driven in is TE(delX) = 1/2 F delX where F = 2e6 kg-m/sec^2 and delX is the distance driven you are looking for.
Thus TE(V) = 1/2 mV^2 = 1/2 FdelX = TE(delX); so that delX = mV^2/F = 500*20^2/2e6 = .1 meter
Note the 1/2 F is the average force over the distance delX; we assume the resistance is a friction force so the work is average force (F/2) times the distance driven. On the other hand, if the force were a constant force from the moment of impact, there would be no 1/2 factor.
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