# Dual inclined plane problem

1. Nov 17, 2004

### bassmann

Here's one from my HW:

Two blocks are connected by a massless string on a triangle with a pulley at the top corner. The angle of the left corner is 35 degrees. the angle on the right is 60 degrees. the left block equals 7kg and the right is 9 kg. mu k = 0.25

Determine acceleration of block A and B

Will the tension exceed 70 N?

What is the magnitude and direction of frictional force on A? on B?

2. Nov 18, 2004

### Andrew Mason

The frictional force on each block is determined by the component of gravitational force perpendicular to the inclined surface and the coefficient of friction.

So resolve into gravitation force components perpendicular to and along the inclined surfaces. The forces on the blocks are gravity, friction and tension. Tension depends on the acceleration of the other block, which is a function of the friction and gravity forces on it. Let $\alpha = 35\degree, \beta = 60\degree$ angles.

So:
$$F_{1gr}-F_{1fr}-T=m_1a_1$$
$$m_1gsin\alpha - Km_1gcos\alpha - T = m_1_a_1$$

Similarly:
$$m_2gsin\beta - Km_2gcos\beta - T = m_2_a_2$$

The recognition that T is the same for both blocks, enables you to express the equation in terms of both accelerations. Since |a1|=|a2| you can figure out the acceleration. Then substitute acceleration back into one of the equations to get T.

AM