Pendulum Parts
Pendulum Parts
Pendulum, please explain this concept and help me solve! 10 points for best answer!?
A 0.430 kg pendulum bob passes through the lowest part of its path at a speed of 3.80 m/s.
(a) What is the tension in the pendulum cable at this point if the pendulum is 80.0 cm long?
(b) When the pendulum reaches its highest point, what angle does the cable make with the vertical?
(c) What is the tension in the pendulum cable when the pendulum reaches its highest point?
(a) What is the tension in the pendulum cable at this point if the pendulum is 80.0 cm long?
Tension T = W + F = mg + mv^2/r = m(g + v^2/r) = ? Newtons where m = .43 kg, v = 3.8 mps, and r = .8 m. F is the centrifugal force and W is the weight. Both forces are acting in the same direction (down) when the pendulum bob is bottomed out. You can do the math.
(b) When the pendulum reaches its highest point, what angle does the cable make with the vertical?
KE = 1/2 mv^2 = mgh = mgL(1 - cos(theta)) = PE; solve for theta where theta = 0 is the angle when bottomed out as in (a) above. Note h = L - L cos(theta) is the height of the bob above the bottom point, KE is the kinetic energy at the bottom, and PE is the potential energy at the top of the swing. L = .8 m the length of the cable and g = 9.81 m/sec^2 near Earth's surface. You can do the math.
(c) What is the tension in the pendulum cable when the pendulum reaches its highest point?
There is no centrifugal force acting on the cable as v = 0 at the highest point where all the energy is PE, potential energy. So the only force acting along the cable, if any, would be from the weight w = W cos(theta) = tension. But, as you can see, that depends on theta. For example, if theta = 90 deg (straight out to one side), then w = W cos(90) = 0; so there would be no tension on the cable whatsoever. Use theta from (b) and plug your finding into the w equation to get the tension at theta.
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