# A bus, a pendulum and acceleration

1. Feb 27, 2009

### jemerlia

1. The problem statement, all variables and given/known data

A bus is descending a uniform 20 degree slope. It brakes with constant deceleration. A pendulum moves 10 degrees away from the vertical to the downward side. Find the acceleration of the bus.

.............|
............/|
........ ../.|
........./10|
......../....|......./
......O.....|..../
.............|/
.........../.|
......../....|
...../.......|
../....20...|vertical
/_______ |___________horizontal_____

2. Relevant equations

F=ma

3. The attempt at a solution

I can deduce the x-component of the acceleration:

ax = g tan 10 = 1.73ms^-2

The expected answer is 2.0ms^-2. I can't see how to relate the twenty degree slope to the x component of the acceleration to calculate the total acceleration.

2. Feb 27, 2009

### Staff: Mentor

Careful: The acceleration is not horizontal.

Do this: Analyze force components parallel and perpendicular to the incline surface.

3. Feb 28, 2009

### jemerlia

Thanks - point taken - I reworked the expressions for Fy and Fx in terms of string tension:

sumFy = FTcos 10 - mg cos 20

sumFx=FT sin10 - mg sin 20

m x ax = mg cos 20. tan 10 -mg sin 20

ax =g(cos20.tan10 -sin 20)

N.B. ax is x acceleration with xy co-ordinates of the slope!

Sadly the result is still 1.72ms^-2

Perhaps there is an error with FT cos10 and FT sin 10 in the two sum of forces expressions... and perhaps elsewhere...