A. 10.47) Two physical pendulums (not simple pendulums) are made from meter stic

Question

A. 10.47) Two physical pendulums (not simple pendulums) are made from meter sticks that are suspended from the ceiling at one end. The sticks are uniform and are identical in all respects, except that one is made of wood (mass=0.27 kg) and the other of metal (mass=0.76 kg) They are set into oscillation and execute simple harmonic motion. Determine the period of (a) the wood pendulum and (b) the metal pendulum

B.)10.51)A tow truck is pulling a car out of a ditch by means of a steel cable (Y = 2.0 x 1011 N/m2) that is 9.16 m long and has a radius of 0.420 cm. When the car just begins to move, the tension in the cable is 859 N. How much has the cable stretched?

Explanation / Answer

10.47)

time period   physical pendulum

T = 2 I/ mgh

or T = 2 2L/3g

   from the above equations time period does not depend on mass

time period T = 1.63s

so both pendulum have same time period.

10.51)

Lo = 9.16 m
R = 0.420 cm. = 0.00420 m

Then the area of the cross section is (A) =pr2
= (3.14)(0.00420 m)2 = 5.54*10-5 m2
F = 859 N
The young's modulus of the Y steel = 2.0 x 10¹¹N/m²
We know that magnitude of F is given by
F = Y (?L/Lo)A
Then the stretched length in the cable is give by
?L = FL0/YA
= ( 859 N)(9.16m)/( 2.0 x 1011 N/m²)(5.54*10-5)
= 7.1*10-4 m

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