Pendulum accelerometer problem

[skiracer88_00]

Homework Statement

A pendulum has a length L = 1.04 m, with mass m=0.43 kg at the end. It hangs straight down in a jet plane about to take off as shown by the dotted line in the figure. The jet then accelerates uniformly, and while the plane is accelerating, the equilibrium position of the pendulum shifts to the position shown by the solid line, with D = 0.380 m. Calculate the magnitude of the plane's acceleration.

Homework Equations

F=ma

The Attempt at a Solution

I really don't know where to start with this problem.. I drew a free body diagram for the pendulum weight and didnt know what to do next


Thanks for anyone who can help :)

 

[Doc Al]

First identify all the forces acting on the mass. (If you've drawn your free body diagram, you've got that step done.) Now apply Newton's 2nd law to both vertical and horizontal components.

 

[m2003]

I would approach this problem by first understanding the concept of an accelerometer and how it measures acceleration. An accelerometer measures acceleration by detecting the change in position of a mass relative to a fixed point or reference frame. In this case, the reference frame is the jet plane.

Next, I would break down the problem into smaller parts and use the given information to solve for the magnitude of the plane's acceleration.

First, I would calculate the gravitational force acting on the pendulum weight using the equation F=mg, where m is the mass of the pendulum weight (0.43 kg) and g is the acceleration due to gravity (9.8 m/s^2). This would give me a value for the gravitational force acting on the weight.

Next, I would use the concept of equilibrium to determine the force acting on the pendulum weight in the direction of the plane's acceleration. Since the pendulum is no longer hanging straight down and has shifted to a new equilibrium position, there must be a net force acting on the weight in the direction of the plane's acceleration. This force can be calculated using the equation F=ma, where a is the plane's acceleration and m is the mass of the pendulum weight.

Finally, I would equate the gravitational force and the force in the direction of acceleration to solve for the magnitude of the plane's acceleration. This would give me the solution to the problem.

Overall, this problem requires an understanding of basic physics principles such as force, equilibrium, and acceleration. It also requires the use of mathematical equations to solve for the unknown variable. By breaking down the problem into smaller parts and using the given information, it is possible to arrive at a solution for the magnitude of the plane's acceleration.