A 12.0-{\ m kg} box resting on a horizontal, frictionless surface is attached to

Question

A 12.0-{ m kg} box resting on a horizontal, frictionless surface is attached to a 5.00-{ m kg} weight by a thin, light wire that passes without slippage over a frictionless pulley (the figure (Figure 1) ). The pulley has the shape of a uniform solid disk of mass 2.50{ m kg} and diameter 0.600{ m m} .

a)After the system is released, find the horizontal tension in the wire.

b)After the system is released, find the vertical tension in the wire.

c)After the system is released, find the acceleration of the box.

d)After the system is released, find magnitude of the horizontal and vertical components of the force that the axle exerts on the pulley.

Explanation / Answer

Th = 12a

5*9.8 - Tv = 5a

(Tv - Th)*0.300 = (2.5*0.3^2/2)*a/(0.300)

solving these we get

a = 2.685 m/s^2 ( part (c))

Th = 32.22 N ( part(a))

Tv = 35.58 N (part (b))

d)

magnitude of the horizontal and vertical components =

32.22 N and 35.58 N respectively

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