The free fall acceleration on mars is 37 ms2 a what length...

The free-fall acceleration on Mars is 3.7 m/s2. (a) What length pendulum has a period of 1.4-s on Earth? cm (b) What length pendulum would have a 1.4-s period on Mars? cm An object is suspended from a spring with force constant 10 N/m. (c) Find the mass suspended from this spring that would result in a 1.4 s period on Earth. kg (d) Find the mass suspended from this spring that would result in a 1.4 s period on Mars. kg

Transcript

00:01 In this problem for the first part we have to find out the length of pendulum which has period of 1 .4 second on earth so the period of a pendulum is given by t equal to 2 pi square root l upon g here l is length of the pendulum and g is the acceleration due to gravity on the surface of earth from this we get t upon 2 pi equal to square root l upon g so squaring both sides we get l upon g equal to t upon 2 pi square and from this we get length l equal to t upon 2 pi square times g now t is 1 .4 seconds and on earth surface the value of g is 9 .8 meter per second square so this gives the length of pendulum equal to 0 .48 6 5 meters for part b we have to find the length of pendulum with period of 1 .4 seconds on mars we forgot one thing in part a we have to convert the length in centimeters so to convert in centimeter we multiply meter with 100 because 1 meter is equal to 100 centimeter so we get 48 .65 centimeters as length of pendulum.

01:48 For the second part again we use the equation for length which we found in part a length l equal to t upon 2 pi square times g here period is same but value of g in on surface of mars is 3 .7 meter per second square so from this figure get length of pendulum on mars equal to 0 .184 meters to convert this into centimeter we multiply it by 100 and we get 18 .4 centimeters now for the third part we have to find the mass suspended from a spring which has force constant of 10 newton per meter and period 1 .4 second on earth so for spring mass system the period is given by t equal to 2 pi square root m upon k so in the period the acceleration due to gravity does not appear so the period for spring mass system does not depend on acceleration due to gravity.

03:16 Now again we have t upon 2 pi equal to square root m upon k.

03:25 So from this mass m is equal to t upon 2 pi square times k.

03:31 Now period is 1 .4 seconds and k is the spring constant which is 10 newton per meter.

03:40 So from this we get mass equal to 0 .496 kilogram...

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