Suppose you push a hockey puck of mass m across frictionless ice for a time, change of t, starting from rest, giving the puck speed v after traveling distance . If you repeat the experiment with a puck of mass 2m, a)How long will you have to push for the puck to reach the same speed v? b)How long will you have to push for the puck to travel the same distance d?
v = at, since the puck starts from rest
If you apply the same force on the heavier mass, then the acceleration will only be half that of the the lighter mass:
F/m = a
F/(2m) = a/2
v = AT
v = (a/2)(T)
Clearly, you must push the heavier for a time 2t.
d = ½at²
d = ½(a/2)(T)²
½at² = ¼aT²
2t² = T²
T = (sqrt2)t
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