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Chapter 7: Q.46 (page 180)

A long, 1.0kgrope hangs from a support that breaks, causing the rope to fall, if the pull exceeds 40N. A student team has built a 2.0kgrobot “mouse” that runs up and down the rope. What maximum acceleration can the robot have—both magnitude and direction—without the rope falling?

Short Answer

Expert verified

The maximum acceleration can the robot have is about19.62m/s

Step by step solution

01

Given information and assumptions

mass of the rope 1.0kg

mass of the robot m=2.0kg

Tension of the ropeT=40N

Let us consider the Free Body Diagram (FBD) for the robot to move up and down in the rope.

Weight of the robot be w⇀=mg

Tension of the rope beT⇀

02

Explanation

To calculate acceleration of robot to move downward

From FBD, following Newton's third law, the Fnet⇀=0

role="math" localid="1649705336120" T⇀=-w⇀mropea=-mga=-mgmropea=-2×9.811=-19.62m2/s

By symmetry, the acceleration of robot to move upward is19.62m2/s

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