Question

A massless rigid rod whose length L = 21.0 cm has a ball of mass m = 0.079 kg attached to one end (see Figure). The other end is pivoted in such a way that the ball will move in a vertical circle. The system is launched from the horizontal position A with an initial downward speed v₀. The ball just reaches point D and then stops. Calculate v₀.

What is the tension in the rod at B?

· Rod Pivot point Vo

Answer 1

here,

L = 21 cm

L = 0.21 m

m = 0.079 kg

the initial speed is v0

0.5 * m* v0^2 = m * g * L

v0^2 = 2 * 9.8 * 0.21

v0 = 2.03 m/s

at point B

let the speed at B be v

0.5 * m * v^2 - 0.5 * m * v0^2 = m *g*L

v^2 - 2.03^2 =2 * 9.8 * 0.21

v = 2.87 m/s

let the tension in the rod be T

T = m*g + mv^2/r

T = 0.079 *9.8 + 0.079* 2.87^2 /0.21

T = 3.87 N

the tension in the rod is 3.87 N