What is the acceleration if an accelerometer hangs 13掳 behind the vertical, opposite the direction of motion?

An accelerometer-a device to measure acceleration-can be as simple as a small pendulum. Suppose you are flying a small plane in a straight horizontal line and your accelerometer hangs 13掳 behind the vertical, opposite the direction of motion. What is your acceleration?What is the acceleration if an accelerometer hangs 13掳 behind the vertical, opposite the direction of motion?危Vertical = 0



T cos 13掳 = mg................(1)



危Horizontal = m a



T sin 13掳 = m a................(2)



eqs (2) divided by eqs (1)



tan 13掳 = a/g



a = g tan 13掳 where g is gravitational accelerationWhat is the acceleration if an accelerometer hangs 13掳 behind the vertical, opposite the direction of motion?F = Force backward on pendulum

W = weight of pendulum

a = acceleration of plane

m = mass of pendulum

g = 9.81 m/s^2 - gravitational field strength on the earth.



First, find the horizontal component of the force on the pendulum (opposing tension)



tan 13 = F/W

F = W tan13



F = ma (From Newton's Laws) therefore

a = F / m



Substituting in F:

a = (Wtan13) / m but... W = mg, so

a = (mgtan13)/m = gtan13



a = 9.81 * tan13 = 9.81 * 0.231

a = 2.27 m/s^2