Find 'T'
4.
Three monkeys A, B and C with masses of 10, 15 & 8 Kg respectively are climbing up & down the rope
suspended from D. At the instant represented, A is descending the rope with an acceleration of 2 m/s2
& C is pulling itself up with an acceleration of 1.5 m/s2. Monkey B is climbing up with a constant speed
of 0.8 m/s. Calculate the tension T in the rope at D. (g = 10 m/s-2)
IND
Answers
Answer:322N
Explanation:
Monkey B is climbing up with a constant speed, therefore a=0
T -33 g = mAaA + mBaB + mCaC
= 10 (-2) + 15 (0) + 8 (3/2)
=>T = 33 g - 8 = 322
Answer:
The tension T in the rope is 322N.
Explanation:
Since monkey C hung on the rope in the last place so, we start from monkey C
For monkey C,
The mass of the monkey C is 8kg.
The acceleration at which the monkey C climbs up is 1.5m/s²
The tension due to the body moving upward is, T = mg + ma
The tension exerted on the rope due to the monkey C is,
T(C) = (8×10) + (8×1.5)
T(C) = 80 + 12
T(C) = 92N
For monkey B,
The mass of monkey B is 15kg.
The monkey B is climbing the rope with a constant speed of 0.8m/s
We know that the tension due to the body moving at a uniform speed is
T = mg
T(B) = 15×10
T(B) = 150N
For monkey A,
The mass of the monkey A is 10kg.
The acceleration at which the monkey A climbing down is 2m/s²
The tension due to the body moving downwards is, T = mg − ma
T(A) = (10×10)−(10×2)
T(A) = 100 - 20
T(A) = 80N
The tension on the rope at point D is the sum of three tensions acting on the rope.
T(ABC) = T(A) + T(B) + T(C)
T(ABC) = 80 + 150 + 92
T(ABC) = 322N
Therefore, the tension in the rope at point D is 322N.
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