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Three monkeys A,B,C with masses of 10,15,8 kg respec are climbing up and down the rope suspended from D.At the instant represented,A is descending the rope with an acceleration of 2m/s^2 and C is pulling himself up with an acceleration of 1.5m/s^2. Monkeys B is climbing up with a constant speed of 0.8m/s .Treat the rope and monkeys as a complete system and calculate the tension T in the rope at D.

Asked by m.nilu 23rd July 2018, 12:47 PM
Answered by Expert
Answer:
The force diagram for all three monkeys are shown in figure.
 
for monkey-C, we have 
 
begin mathsize 12px style T subscript 1 minus m subscript C space g space equals space m subscript C space a space space semicolon space space T subscript 1 space equals space m subscript C cross times left parenthesis g plus a right parenthesis space equals space 8 cross times open parentheses 9.8 plus 1.5 close parentheses space equals space 90.4 space N space.......... left parenthesis 1 right parenthesis
end style
for Monkey-B, we have  begin mathsize 12px style T subscript 2 space equals space T subscript 1 space plus space m subscript B g space equals space 90.4 plus 15 cross times 9.8 space equals space 237.4 space N end style
for monkey-A, we have
 
 begin mathsize 12px style T subscript 3 space minus space T subscript 2 space minus space m subscript A g space equals space m subscript A cross times left parenthesis negative 2 right parenthesis space semicolon space T subscript 3 space equals space T subscript 2 space plus space m subscript A left parenthesis g minus 2 right parenthesis space equals space 237.4 plus 10 cross times 7.8 space equals space 315.4 space N
end style
Hence tension at D = 315.4 N
Answered by Expert 23rd July 2018, 4:02 PM
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