The figure shows a conical pendulum, in which the bob (the small object at the l

Question

The figure shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass m, the string has length L and negligible mass, and the bob follows a circular path of circumference C. What are (a) the tension in the string and (b) the period of the motion? State your answers in terms of the given variables, using g and when appropriate.

Answer only with the variables given please!!

Explanation / Answer

First of all in these questions is to find mg.

mg = 0.04 kg x 9.8 m/s^2 = 0.392 N

Next you need to find the angle.

Use arccos (thats cos-1 on your calculator)

arccos((0.96/(2pi))/0.67) = 76.82 degrees from horizontal.

Next you need to find the force required to pull the bob out to 76.82 degrees.

mg/tan(angle) = horizontal force

0.392/tan(76.82) = 0.091812 N

0.091812 N = Centripetal force.

0.091812/mass = centripetal acc

0.091812/0.04 = 2.2953 m/s^2

centripetal acc = v^2/r

v^2 = acc x r = 2.2953 x (0.96/(2pi)) = 0.3507, sq-root = v = 0.5922 m/s

What is the tension in the string?

Using above information:

76.82 degrees from horizontal.

mg = 0.392 N

0.392/sin(76.82) = 0.4026 N (answer)



(b) What is the period of the motion?

0.96m/0.5922 m/s = 1.621 secs (answer)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.