a) Consider a conical pendulum with a bob of mass m = 94.0 kg on a string of len

Question

a) Consider a conical pendulum with a bob of mass m = 94.0 kg on a string of length L = 10.0 m that makes an angle of = 4.00° with the vertical. (Consider +i to be towards the center of the circular path and +j to be upward.)

b)A 340-N child is in a swing that is attached to a pair of ropes 1.90 m long. Find the gravitational potential energy of the child–Earth system relative to the child's lowest position at the following times.

(i) when the ropes are horizontal
J

(ii) when the ropes make a 29.0° angle with the vertical
J

(iii) when the child is at the bottom of the circular arc
J

Explanation / Answer

part(a)force F due to gravity=m*g=94 kg*10 m/sec2=940 N

This force=horizontal component=FY=940j

to find the vertical component tan4=FX/FY

   0.0699*940=65.73120N=FX

THEREFORE vertical component=Fx=65.73 I

F net=65.73 i+940 j

(ii)Force is due to horizontal =940=m*a

940/94=10 m/sec2=radial acceleration

part(b)(ii) mgl(1-cos angle)=340*1.90(1-0.8746)=81.0084N

(i)340 *1.90(1-cos 90)=646 N

(iii)at the bottom angle is cos zero=1 and the (1-cos 0)=0

therefore at bottom it is zero

(

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