8 Pendulum A pendulum of length l=2 m and mass m =0.2 kg is swinging from the ce

Question

8 Pendulum A pendulum of length l=2 m and mass m =0.2 kg is swinging from the ceiling. The amplitude of the oscillation is thetamax=10 degrees. 1. Compute the total force acting on the bob at the lowest point P of the trajectory. Give magnitude and direction. 2. Compute the tangential acceleration of the object at the lowest point P of the trajectory. [Hint: use the second law.] Can we say that instantaneously this is a uniform circular motion? 3. If the bob was just hanging from the ceiling without swinging, would the tension in the rope be less than, greater than, or equal to the tension you found in question 2? Why?

Explanation / Answer

1)
let h is the height raised from lowest point, h = L*(1 - cos(10))

= 2*(1 - cos(10))

= 0.0304 m

so, speed of the at the lowest point,

v = sqrt(2*g*h)

= sqrt(2*9.8*0.0304)

= 0.77 m/s

Total force acting, F_total = m*a

= m*v^2/L

= 0.2*0.77^2/2

= 0.06 N (pward)

2) here, a_tan = 0

beacuse the bob has only radial accelration.

yes. we can say the bob is instantaneously in uniform circular mootion)

3) Less.

Beacuse

when the bob is in rest postion, Tension, T = m*g

but when the bob swings, tencion, T = m*g + m*v^2/L

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