Two blocks with masses M1 and M2 are connected by a massless string that passes over a massless pulley as shown. M1 has a mass of 2.25 kg and is on an incline of 47.5° with coefficient of kinetic friction μ1 = 0.205. M2 has a mass of 5.95 kg and is on an incline of 35.5° with coefficient of kinetic friction μ2 =...

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## Answers

Split the weight of each black into a component along the ramp vs. a component normal to the ramp.

Use the latter and μ to find the force of friction.

The massless pulley makes the blocks-and-rope system act like it's one-dimensional. Write an expression for the total force on this system.

(Note: tension, being internal to the system, cancels itself out).

Find the acceleration of the system.

Let’s determine the component of the block’s weight is parallel to the incline.

For M1, force parallel = 2.25 * 9.8 * sin 47.5 = 22.05 * sin 47.5

This is approximately 16.25 N.

For M2, force parallel = 5.95 * 9.8 * sin 35.5 = 58.31 * sin 35.5

This is approximately 33.66 N.

Since this is greater than 29.9 N, M2 will be sliding down its incline. This means M1 will be sliding up its incline. The net force on both blocks is equal to the parallel component of the weight of block 2 minus the sum of the other three forces.

For M1, Ff = 0.205 * 22.05 * cos 47.5 = 4.52025 * cos 47.5

For M2, Ff = 0.105 * 58.31 * cos 35.5 = 6.12255 * cos 35.5

Net force = 58.31 * sin 35.5 – (22.05 * sin 47.5 + 4.52025 * cos 47.5 + 6.12255 * cos 35.5)

This is approximately 9.5655 N

Total mass = 2.25 + 5.95 = 8.2 kg

a = [58.31 * sin 35.5 – (22.05 * sin 47.5 + 4.52025 * cos 47.5 + 6.12255 * cos 35.5)] ÷ 8.2

This is approximately 1.17 m/s2.