What is the answer to this physics question?
Suppose you push a hockey puck of mass ( m ) across frictionless ice for a time ( \Delta t ), starting from rest, which gives the puck a speed ( v ) after traveling a distance ( d ). If you repeat the experiment with a puck of mass ( 2m ), how long will you need to push for the puck to reach the same speed ( v )? Additionally, how long will you need to push for the puck to travel the same distance ( d )? I initially thought the answer was ( 2\Delta t ), but that doesn't seem to be correct. I have tried various values for the acceleration ( a ), time ( t ), and ( \Delta t ), but I keep getting the result that the answer does not depend on these variables. Thank you for your help!
1 Answers
What you left out, it the force you use to push the two pucks. Are they the same, or different?
Assuming they are the same magnitude force, then, from F=ma, the second one will have half the acceleration.
a) Half the acceleration, means to reach the same speed, from
a = v/t or
t = v/a
with half the acceleration that becomes
t = v/(a/2) = 2v/a
Comparing the two, the second time is twice of the first to reach the same speed (a)
b) Half the acceleration, means to reach the same distance, from
d = ½at² or
t = √(2d/a)
with half the acceleration that becomes
t = √(2d/(a/2)) = √(4d/a) = 2√(d/a)
dividing the two times, that is Δt = [ √(4d/a) ] / [ √(2d/a) ] = √2
the second time is √2 of the first, or 1.4 times longer to reach the same distance (b)
.
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