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=55.0N, and ignore sagging of the cord.

Part A

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

  m/s2

Part B

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

  N

Part C

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

Part D

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

  m/s2

Explanation / Answer

Fp = 55 N
acceleration of A = Fp-Fat / mA
a =( 55- F at )/10
Fat = 55-10a
For box b, a = Fbt/12
Fbt = 12a
For rope, a = (F at - F bt)/1
substitute Fat and Fbt values
a = 55/23 = 2.39 m/s^2

(a) Acceleration of (a) is 2.39 m/s^2

(b) Ftb = 12a = 28.69 N

(c) a = 2.39 m/s^2

(d) Fat = 55-10*2.39 = 31.1 N

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