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Physics problem help please?
A wrecking ball weighs 1000kg. if it is tethered to a 6 meter steel cable rated at 100,000 newtons. what is the maximum velocity that the ball can be swung?
Max tension occurs at the bottom of the swing, there will only be gravity and tension at that point.
Fnet = ma
Ft - Fg = ma
But we have centripetal acceleration:
Ft - Fg = (mv^2)/r
Ft = (mv^2)/r + Fg
But Ft must not exceed 100000 N.
100000 N > (mv^2)/r + Fg
100000 N > (mv^2)/r + mg
100000 N > [m][v^2/r + g]
Isolate and solve for v:
[100000 N] / [m] > v^2/r + g
[100000 N] / [m] - g > v^2/r
sqrt{[r][[100000 N] / [m] - g]} > v
sqrt{[6m][[100000 N] / [1000 kg] - 9.81 m/s^2]} > v
23.26 m/s > v
So the maximum velocity is 23.26 m/s.
Done!
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