A simple pendulum has a 250-g mass tied to it. 17 seconds are required to comple

Question

A simple pendulum has a 250-g mass tied to it. 17 seconds are required to complete 10 oscillations, If g = 9.80 m/s^2, what is the length of the pendulum? It is pulled aside and released from a height so that its speed as it passes its lowest point is measured to be 1.7 m/s. Calculate the tension in the string at the pendulum's lowest point. If the pendulum were transported to the moon (g = 1.65 m/s^2), find its frequency of oscillation on the moon. A student doing the centripetal force experiment wanted to understand how the various parameters depended on one another. For a particular experiment, the total accelerated mass m is constant m_o when the radius r is r_o, the breakaway speed v is v_o, and the maximum magnetic force F is F_o. If F is increased to 1.20 F_o and r is decreased to 0.900 r_0, calculate the new v in terms of v_0.

Explanation / Answer

10 oscillation in 17 sec =

T = 17/10 = 1.7 s

T = 2pi * sqrt(L/g)

T^2 = 4pi^2 * L/g

L = g*T^2 / 4pi^2

L = 0.717 m

part b )

at lower point

Ftension = mg

T = 0.250 kg * 9.80

T = 2.45 N

part c )

T = 2pi*sqrt(L/g)

T = 2pi*sqrt(0.717/1.65)

T = 4.142 s

f = 1/T = 0.241 Hz

part 5 )

Fo = mvo^2/ro .....(1)

new conditions are

1.2Fo = m*v'^2/0.9ro ....(2)

(1) divide (2)

v = 1.04 vo

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