Answered: 4) If the end of the cable at A is…

4) If the end of the cable at A is pulled down with a speed of 2 m/s, determine the speed at which block B rises. De UA 2 m/s

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter6: Beams And Cables

Section: Chapter Questions

Problem 6.78P: The chain OA is 25 ft long and weighs 5 lb/ft. Find the maximum force in the chain and the distance...

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Please help with the attached problem

DEPENDENT MOTION
4) If the end of the cable at A is pulled down with a speed of 2 m/s, determine
the speed at which block B rises.
UA
2 m/s

Expert Solution

Step 1

Equation for the length of the string is

$3 s_{B} + s_{A} = l$

Here $s_{B} and s_{A}$ are the displacement of the B and A that change with time and l is the constant

Differentiate with respect to the time

$\begin{array}{rcl} 3 v_{B} + v_{A} & = & 0 \\ 3 v_{B} + 2 m / s & = & 0 \\ v_{B} & = & \frac{- 2}{3} \\ = & - 0.667 m / s \end{array}$

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