Suggestions:
- Draw an FBD of the particle P. From this FBD you can argue that angular momentum of the particle about point O is conserved.
- Use the definition of H_O to find the angular momentum about O: H_O = m*r_P/O x v_P. Note that at position A, the velocity of P is in the y-direction (and with the given speed of 8 ft/sec). Note that at position B, the velocity of P is in the negative x-direction (unknown speed).
- Use conservation of angular momentum to find the speed of P at position B.
- Use Newton's 2nd Law (normal component) to find the tension T. Note that you need to find the radius of curvature from the given equation of the path.
5 comments:
I am not able to get answer that is in the book but I have worked through it a few times and am still not seeing my problem is the velocity at B 10 ft/sec?
Garrett, I got 10 ft/s as well. My radius of curvature at that point is 4 feet and my mass is (1.5/g) slugs, and the only force normal to the path is that cord...but I'm not getting the answer either.
Please note that IF the path were circular, then the radius of curvature would be the distance from O to B (4 feet). However, the path is elliptical, not circular...
How do you find the radius of curvature of the path when you are given y=y(x)??
p = [abs val((1 + (f'(t))^2))^(3/2)] / [abs val(f''(t))] Solve the given equation for y find y' and y'' and plug in the values for y(0) since x is 0 at point b. p comes out to be 6.25 feet. this value works
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