So I haven't done this before but I honestly don't know where to start.
A bead slides without friction around a loop-the-loop. The bead is released from a height
14.1 m from the bottom of the loop-the-loop
which has a radius 5 m.
g = 9.8 m/s^2
What is its speed at the top of the loop-the-loop?
Please help, normally i would know how to do this but i don't know how to do it when mass is not given. Any response will help, thanks.
A bead slides without friction around a loop-the-loop. The bead is released from a height
14.1 m from the bottom of the loop-the-loop
which has a radius 5 m.
g = 9.8 m/s^2
What is its speed at the top of the loop-the-loop?
Please help, normally i would know how to do this but i don't know how to do it when mass is not given. Any response will help, thanks.
-
by conservation of energy:
KEi + PEi = KEf + PEf
KEi = 0
0 + mgh_1 = (1/2)mv^2 + mgh_2
Divide both sides by m
gh_1 = (1/2)v^2 + gh_2
isolating v...
2g(h_1 - h_2) = v^2
sqrt(2g(h_1 - h_2)) = v
h_1 = 14.1m
h_2 = diameter = 5m*2 = 10m
g = 9.8 m/s^2
plug in.
i think this is right xD
KEi + PEi = KEf + PEf
KEi = 0
0 + mgh_1 = (1/2)mv^2 + mgh_2
Divide both sides by m
gh_1 = (1/2)v^2 + gh_2
isolating v...
2g(h_1 - h_2) = v^2
sqrt(2g(h_1 - h_2)) = v
h_1 = 14.1m
h_2 = diameter = 5m*2 = 10m
g = 9.8 m/s^2
plug in.
i think this is right xD
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Always use conservation of energy in problems when you can't use kinematics,
first part,
as there is no non conservative forces acting,
we shall use conservation of energy
U1 + K1 =U2 + K2
where U=mgh
and K=1/2mv²
taking h=0 at bottom, and v1=0
mgh1=1/2mv²+mgh2
so, v=√[2g(h1-h2)]
=8.964 m/s
for your problem, second part,
from FBD,
mg+N=mv²/R
where V is speed at that moment,
answer=37.6 N
first part,
as there is no non conservative forces acting,
we shall use conservation of energy
U1 + K1 =U2 + K2
where U=mgh
and K=1/2mv²
taking h=0 at bottom, and v1=0
mgh1=1/2mv²+mgh2
so, v=√[2g(h1-h2)]
=8.964 m/s
for your problem, second part,
from FBD,
mg+N=mv²/R
where V is speed at that moment,
answer=37.6 N