A 0.440-kg pendulum bob passes through the lowest part of its path at a speed of 3.38 m/s.(a) What is the magnitude of the tension in the pendulum cable at this point if the pendulum is 77.0 cm long? Your response differs from the correct answer by more than 10%. Double check your calculations. N(b) When the pendulum reaches its highest point, what angle does the cable make with the vertical? (Enter your answer to at least one decimal place.) Your response differs from the correct answer by more than 10%. Double check your calculations.°(c) What is the magnitude of the tension in the pendulum cable when the pendulum reaches its highest point? Your response differs from the correct answer by more than 100%. N
Question
A 0.440-kg pendulum bob passes through the lowest part of its path at a speed of 3.38 m/s.(a) What is the magnitude of the tension in the pendulum cable at this point if the pendulum is 77.0 cm long? Your response differs from the correct answer by more than 10%. Double check your calculations. N(b) When the pendulum reaches its highest point, what angle does the cable make with the vertical? (Enter your answer to at least one decimal place.) Your response differs from the correct answer by more than 10%. Double check your calculations.°(c) What is the magnitude of the tension in the pendulum cable when the pendulum reaches its highest point? Your response differs from the correct answer by more than 100%. N
Solution
(a) To find the tension in the pendulum cable at the lowest point of its path, we first need to calculate the gravitational force acting on the pendulum bob. This can be found using the formula F = mg, where m is the mass of the bob and g is the acceleration due to gravity.
F = 0.440 kg * 9.8 m/s^2 = 4.312 N
At the lowest point of its path, the pendulum bob is also experiencing a centripetal force, which is provided by the tension in the cable. The centripetal force can be calculated using the formula F = mv^2/r, where m is the mass of the bob, v is its speed, and r is the length of the pendulum.
F = 0.440 kg * (3.38 m/s)^2 / 0.77 m = 6.384 N
The total tension in the cable is the sum of these two forces.
T = 4.312 N + 6.384 N = 10.696 N
(b) At the highest point of its path, the pendulum bob has converted all of its kinetic energy into potential energy. This means that its speed is 0 m/s, and the only forces acting on it are gravity and the tension in the cable. Since these forces are balanced, the cable is in a straight vertical line with the bob, so the angle it makes with the vertical is 0 degrees.
(c) Since the only forces acting on the bob at its highest point are gravity and the tension in the cable, and these forces are balanced, the tension in the cable is equal to the gravitational force on the bob.
T = 4.312 N
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