Posted by Ali on Saturday, October 22, 2011 at 12:30am.
(a)
recall that potential energy is stored energy, and is given by the formula:
PE = mgh (units in Joules)
where
m = mass (in kg)
g = acceleration due to gravity = 9.8 m/s^2
h = height (in m)
if the reference position is at the floor (that is, h = 0), the PE is equal to
PE = 4*9.8*0
PE = 0
(b)
recall that kinetic energy is energy in motion and is given by the formula:
KE = (1/2)*m*v^2
where
v = velocity (in m/s)
since it's not moving (v = 0),
KE = 0
(c)
at 2 m high,
PE = 4*9.8*2
PE = 78.4 J
(d)
at 4 m high,
PE = 4*9.8*4
PE = 158.8 J
(e)
at 45 m high,
PE = 4*9.8*45
PE = 1764 J
(f)
recall that the motion of the block is uniformly accelerated motion, and we can therefore use the formula:
(v,f)^2 - (v,o)^2 = 2gh
where
v,f = final velocity (in m/s)
v,o = initial velocity (in m/s)
since it is dropped from rest, v,o = 0:
v,f^2 = 2gh
v,f = sqrt(2gh)
v,f = sqrt(2*9.8*45)
v,f = 29.7 m/s
(g)
KE = (1/2)mv^2
KE = (1/2)*4*29.7^2
KE = 1764.18 J
this actually shows the law conservation of energy, which is ΔPE = -ΔKE
hope this helps~ :)
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