- #1

- 1

- 0

**Challenging Ramp and Pulley Problem**

## Homework Statement

Two blocks of masses 2m and m are connected by a weightless string over a frictionless, massless pulley, as shown in the figure. The coefficient of kinetic friction between the block and the incline is [itex]\mu[/itex]. The system is in a uniform gravitational field directed downward of strength [itex]g[/itex]. Find the incline angle [itex]\theta[/itex] such that the blocks move at a constant speed. Distinguish between the cases of upward and downward motion. Rationalize your solutions using a simple physical picture.

## Homework Equations

[tex]\mathbf{F} = m\mathbf{a} [/tex]

## The Attempt at a Solution

So we start by looking at the forces acting on each block. In this case, we will be looking at downward motion. For the [itex]2m[/itex] mass:

[tex] 2mg\sin\theta - \mu mg\cos\theta - T = 0 [/tex]

And for the second block:

[tex] T - mg = 0 \implies T = mg [/tex]

Using the second equation and plugging into the first equation, we find:

[tex] 2\sin\theta - 2\mu\cos\theta = 1 [/tex]

I can't figure out how to solve for [itex]\theta[/itex]. Wolfram's answer is pretty ugly.

#### Attachments

Last edited: