11 7 P054 My 0 A 0.500-kg pendulum bob passes through the lowest part of its pat

Question

11 7 P054 My 0 A 0.500-kg pendulum bob passes through the lowest part of its path at a speed of 3.12 m/s. (a) What is the magnitude of the tension in the pendulum cable at this point if the pendulum is 72.0 cm long? (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.) (c) What is the magnitude of the tension in the pendulum cable when the pendulum reaches its highest point? Need Help? Read M Submit Answer Save Progress Practice Another Version 15 points SorCP117 P075 My Notes Ask Your T

Explanation / Answer

here,

mass of pendulam , m = 0.5 kg

speed , u = 3.12 m/s

a)

length , l = 0.72 cm

the magnitude of tension in the cable at the lowest point , Tl = m * g + m * v^2 /l

Tl = 0.5 * ( 9.81 + 3.12^2 /0.72) N

Tl = 11.7 N

b)

let the maximum height above the initial position be r

using conservation of energy

m * g * r = 0.5 * m * v^2

9.81 * r = 0.5 * 3.12^2

solving for r

r = 0.5 m

theta = arccos((l - r)/l)

theta = arccos((0.72 - 0.5)/0.72) = 72 degree

c)

let the tension in the string be T

T * cos(theta) = m * g

T * cos(72) = 0.5 * 9.81

solving for T

T = 15.8 N

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