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Two crates A and B shown are supported by an inextensible cable on frictionless and massless pulleys. The mass of the heavier crate A is 37 kg. when free to move, the acceleration of A with respect to B, aA/B = 6m/s/s. Determine the mass of crate B in kg.The pulley shown in P9 is supported by a single chain at C. Determine the tension in this chain in N when the two crates described in P9 are free to move.

Question

Two crates A and B shown are supported by an inextensible cable on frictionless and massless pulleys. The mass of the heavier crate A is 37 kg. when free to move, the acceleration of A with respect to B, aA/B = 6m/s/s. Determine the mass of crate B in kg.

The pulley shown in P9 is supported by a single chain at C. Determine the tension in this chain in N when the two crates described in P9 are free to move.

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check_circleAnswer
Step 1

Both the crates are free to move with a same cable, the acceleration of the both crates are same magnitude with opposite direction. Consider the acceleration of the both crates be a.

 

From the relative acceleration, the acceleration of the crates can be calculated as,

адв — а, - (-а,)
АВ
адв — а, + а,
AIB
ав—а+а
AB
адв
а
АВ
2
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Image Transcriptionclose

адв — а, - (-а,) АВ адв — а, + а, AIB ав—а+а AB адв а АВ 2

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Step 2

Apply the Newton’s second law on the crate A.

УF -т,а,
W -T%3Dт,а
адв
т,g-T%3Dт,
2
Т - т,g-т, 44 в
2
т--)
адв
g
Т 3D т
2
help_outline

Image Transcriptionclose

УF -т,а, W -T%3Dт,а адв т,g-T%3Dт, 2 Т - т,g-т, 44 в 2 т--) адв g Т 3D т 2

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Step 3

Apply the Newton’s second la...

УF, -m,а,
Т-W; — т,а
Т-wз
(-f-3) -ва-
адв
AB
АВ
-т,g —т,
2
2
адв
адв +g|3т 8-
2
A
т
2
адв
g
т,
2
тв
+g
2
help_outline

Image Transcriptionclose

УF, -m,а, Т-W; — т,а Т-wз (-f-3) -ва- адв AB АВ -т,g —т, 2 2 адв адв +g|3т 8- 2 A т 2 адв g т, 2 тв +g 2

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Science

Physics

Kinematics

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