Sided Pendulum
Physics Pendulum Question?
A pendulum is made by tying a 490 g ball to a 43.0 cm-long string. The pendulum is pulled 25.0 degrees to one side, then released. What is the ball's speed at the lowest point of its trajectory? To what angle does the pendulum swing on the other side?
This is a conservation of mechanical energy problem. The only non-conservative force in the problem is the string tension. But it always perpendicular to the direction of motion and does no work. Therefore;
PE(f) + KE(f) = PE(i) + KE(i)
Where initial (i) and final (f) are any two points you want to look at;
mgy(f) + (1/2)mv^(f) = mgy(i) + (1/2)mv^2(i)
You get the height "y" measured up from the lowest point of the swing from;
y = L - LCos(theta)
So for your problem, L= .43 m , theta = 25 deg , and m cancels everywhere.
(a) Given v(i) = 0 and theta = 25, find v(f) at theta = 0 (or y(f)=0)
0 + (1/2)v^2(f) = g[.43-.43Cos(25)] + 0
solve thise for v(f)
(b) This You Can do by inspection. If energy is conserved the pendulum rises to the same height (and angle) as initially.
Or since the velocity is zero at the turn around point and its zero at the start point then KE=0 at both points. then;
mgy(f) + 0 = mgy(i) + 0
y(f) = y(i)
and this will lead to; (theta)(f) = (theta)(i)
TRX Straddle Sit to half flair.MOV
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