# Two Blocks and a Pulley

1. A block with mass m1 is placed on an inclined plane with slope angle α and is connected to a second hinging block with mass m2> m1 by a massless cord passing over a small frictionless pulley. The coefficient of kinectic freiction between mass ma and the incline is negligible. Find:

(a) the acceleration vector of mass m1

(b) the acceleration vector of mass m2

(c) the magnitude of the normal force on mass m1

(d) the magnitude of the tension in the cord

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## Homework Equations

Newton's Equations

## The Attempt at a Solution

(a.) Drawing a FBD diagram for mass 1 gives that the sum of the forces for the x-component Fx = T - wsinα.

Fy = n - wcosα.

Since there is no acceleration in the y-direction, the only acceleration we need to worry about is that for the x-component.

ƩFx = m1a

m1a = T - wsinα

a = (T - wsinα)/m1

a = (T - m1gsinα)/m1?

Doc Al
Mentor
So far, so good. But you're not done. You need to express the answer in terms of the given quantities only, not in terms of T. (Hint: Set up an equivalent equation for m2.)

An equation for m2:

ƩFy = m2ay

∴m2ay = T - m2g

Solving for a in this case gives (T - mag)/m2.

If we could find an equivalent for T in terms of m2, we could plug it into the equation for part A. Can this be done by manipulating the same equation to obtain an equation in terms of m2, ay and g?

Doc Al
Mentor
An equation for m2:

ƩFy = m2ay

∴m2ay = T - m2g

Solving for a in this case gives (T - mag)/m2.
OK, but use the same letter for the magnitude of the acceleration. And be careful with signs.

You'll have two equations (one for each mass) and two unknowns (the acceleration and the tension), which you can solve together.