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values of potential and kinetic energy (of a pile driver)?
A Pile Driver of mass 50kg is raised to a height of 4m above the Pile of mass 6 kg, and then is allowed to fall freely onto the Pile on the ground. The pile and the Pile driver travel into the ground a depth of 24 cm after impact, without rebounding.
b. Determine the values of potential and kinetic energy (of the pile driver)
i. Before it starts to fall,
ii. When it has fallen by 1m
iii. When it strikes the pile?
c. Initial velocity of the pile and the driver after impact.
d. Also calculate the retarding force causing the Pile and the pile driver to come to rest.
can anyone find the potential and kinetic energy of a pile driver?
1 Answer
- oldschoolLv 74 years agoFavorite Answer
You find the initial PE = m*g*hmax of the pile driver at max height. Ignoring losses, the PE + KE at lower heights sum to the initial PE. Thus at height = 0, PE = mg*0 = 0 and KE is at its maximum and = the initial PE = m*g*hmax at max height.
i. Before it starts to fall
m*g*hmax = 50*9.8*4 = 1960J
ii. When it has fallen by 1m
PE = m*g*h = 50*9.8*3 = 1470 -----> KE = 1960-1470 = 490J
iii. When it strikes the pile?
PE = m*g*0 = 0, KE = 1960-PE = 1960-0 = 1960J
c. Initial velocity of the pile and the driver after impact.
Energy may not be conserved but momentum is
mgh = ½mV² ------2*1960/50 = V² = 78.4 ------> V = 8.85m/s
50*√(78.4) = (50+6)*V -----> V = 7.9m/s <----- c.
F*d = ½*(50+6)7.9² = 1750 -----> F = 1750/0.24 = 7292N <----- d.
