Show work on how to find the moment of inertia of the pulley. As shown in the fi

Question

Show work on how to find the moment of inertia of the pulley.

As shown in the figure below, two blocks are connected by a string of negligible mass passing over a pulley of radius 0.250 m and moment of inertia I. The block on the frictionless incline is moving with a constant acceleration of magnitude a = 2.00 m/s2 (Let m1 = 15.0 kg. m2 = 20.0 kg. and theta = 37.0 degree .) From this information, we wish to find the moment of inertia of the pulley. Draw a free body diagram of the blocks and decide what concept you are going to apply to the masses and then the pulley. Without doing any calculations which of the T1, T2 and m2 is biggest? Rank them from lowest to highest. Explain your ranking briefly Find the moment of inertia of the pulley Now assume that there is friction between the incline and m1 - micro k=0.1. If m2 has fallen a distance of 1.5 m find the speed of m1. Use the I for the pulley you found above.

Explanation / Answer

M1 and M2 are both moving with acceleration,

a = 2.00 m/s²

T1 = M1*a

= 15 * 2.00 m/s

= 30.0 N

T2 = M2 * a

= 20kg * 2.00 m/s

= 40.0 N

angular acceleration is related to the linear acceleration

r* = a

= a/r

the sum of the moments about the axle of the pulley is equal to its inertia (I'll use J) times angular acceleration

(T2 - T1) * r = J * = J *a / r

J = (T2 - T1)*r²/a

= (40 - 30) * (0.250)² / 2.00

J = 0.3125 kg m²

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