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Chang L Chang L
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A year ago
In the figure, two boxes, each of mass 24 kg, are at rest and connected as shown. The coefficient of kinetic friction between the inclined surface and the box is 0.31. Find the speed of the boxes just after they have moved 1.6 m.

Textbook 

Essential University Physics


Edition: 3rd
Author:
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007006007006
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A year ago Edited: A year ago, bio_man
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More solutions for this book are available here
Balancing the forces,

T - (mg sin(theta)) - (u mg cos(theta)) - ma = 0

T = (24 x 9.8 sin(30)) + (0.31 x 24 x 9.8 cos(30)) - (24 x a) .... (1)

For hanging box,

Tension, T = m(g - a)

T = 24(9.8 - a) ...... (2)

Substituting in equation (1)

24 (9.8 - a) = (24 x 9.8 sin(30)) + (0.31 x 24 x 9.8 cos(30)) - (24 x a)

Acceleration, a = 1.136 m/s^2

Using 3rd equation of motion,

v^2 = u^2 + 2as

Velocity, v = sqrt(2 x 1.136 x 1.6) = 1.91 m/s

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