the end of the cable at a is pulled down with a speed of 2 m / s.

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06-12-2022
Engineering

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the end of the cable at a is pulled down with a speed of 2 m / s.

Sagot :

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kumarravichandra kumarravichandra · Answer 1 · 2022-12-13T04:16:27-05:00

Write the relation for length of the ropes in terms of position of the blocks. Differentiate the length of the cables to find the relation between velocities.

Kinematics deals with the geometry of motion. If the relation for a geometric variable like position is known, velocity can be determined by taking the time derivative of position.

V = ds/dt

Here, position of the particle is s

and time is t

The fixed surface is considered as datum and the position of blocks is taken with respect to datum.

Use the relation of length of the cable to find the relation between positions of the blocks.

Find the expression for length of the cable connecting pulleys at point C and point D.

l = sA + 2sC

Differentiate with respect to time.

dl/dt = d/dt (sA + sC)

0 = VA + 2VC

VC = -VA/2

Find the expression for length of the cable connecting pulleys at point C and point D.

l2 = (SB - SC) + SB

= 2SB - SC

Differentiate with respect to time.

dl/dt = d/dt (2sB - sC)

0 = 2VB - VC

0 = 2VB - (-VA/2)

VB = -VA/4

= - 2/4

= - 0.5 m/s

Write the relation for length of the ropes in terms of position of the blocks. Differentiate the length of the cables to find the relation between velocities. Substitute 0 for dl/dt

because the rope is inextensible.

Therefore, the speed of block B is 0.5 m/s

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