Suppose two boxes on a frictionless table are connected by a heavy cord of mass

Question

Suppose two boxes on a frictionless table are connected by a heavy cord of mass 1.0 kg.(Figure 1) Assume FP=54.0N, and ignore sagging of the cord.

A) Calculate the acceleration of the box (a), using the free-body diagrams shown in the figure.

B)Calculate the tension at the left end of the cord, using the free-body diagrams shown in the figure.

C) Calculate the acceleration of the box (c), using the free-body diagrams shown in the figure.

DCalculate the tension at the right end of the cord, using the free-body diagrams shown in the figure.

Suppose two boxes on a frictionless table are connected by a heavy cord of mass 1.0 kg.(Figure 1) Assume FP=54.0N, and ignore sagging of the cord.

Explanation / Answer

Fp = 54.0 N

acceleration of A = Fp - Fat / mA

a=( 54 - Fat ) / 10

Fat = 54 - 10 a

For box b, a = Fbt / 12

Fbt = 12a

For rope, a = (Fat - F bt) / 1

a = (54 - 10a - 12a)

a = 54 / 22 = 2.45 m/s2

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(b) Ftb = 12a = 29.45 N

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(c) a = 2.45 m/s^2

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(d) Fat = 54-10a = 29.5 N

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