A tugboat pulls three different unladen cargo barges—P, Q

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A tugboat pulls three different unladen cargo barges—P, Q, and R—one at a time through the same stretch of calm water. The tow cable transmits a constant horizontal force of

1.2\times10^{3}\,\text{N}

to each barge. The masses of the barges are

1.0\times10^{4}\,\text{kg}

(barge P),

1.5\times10^{4}\,\text{kg}

(barge Q), and

2.4\times10^{4}\,\text{kg}

(barge R). Assume resistive forces from the water are negligible during the brief interval considered. (a) For each barge, calculate the magnitude of its acceleration while being towed by the tugboat. (b) Each barge starts from rest. Determine the time required for each barge to reach a speed of 3.0 m/s under the tow force. (c) Using your numerical results, state the mathematical relationship between the barge’s mass and its acceleration when the applied force is the same. Support your statement with specific evidence from parts (a) and (b).

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