Speed Resistance
What is the balls speed at the point P? Neglect air resistance and other frictional forces.?
The two highest points of the ball’s trajectory are Q and Q’; at these points the string is +/- 24 from the vertical. Point P is the lowest point of the ball’s trajectory where the string hangs down with a 2 m length. Acceleration of gravity it 9.8 m/s^2. What is the balls speed at the point P?
For the following, I will assume that the +/- 24 is in degrees.
We need to know the difference in height between P and Q. We’ll measure height from the top of the string.
At point P, h = -2
At point Q, h = -2 cos 24
Then Δh = -2 cos 24 – (-2) = .17 m
This gives us the difference of potential energy between P and Q:
PE = mgΔd = m(9.8 m/s^2)(.17 m) = 1.7m
and this must be the Kinetic energy at P
(1/2)mv^2 = 1.7m
v^2 = 3.4
v = 1.8 m/s
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