Analyzing the Acceleration Problem: Which Frame Should You Choose?

[nate9519]

A truck is moving with constant acceleration "a" up a hill that makes an angle phi with the horizontal. A small sphere of mass "m" is suspended from the ceiling of the truck by a light cord. If the pendulum makes a constant angle theta with the perpendicular to the ceiling, what is a?

What equations should I use for this problem?

 

[Matterwave]

Have you tried to do this problem yourself first? I think the first step would be to draw a picture. If the truck were not accelerating, what angle would the pendulum make? What does the acceleration of the truck up the hill do to this pendulum?

 

[nate9519]

if it were flat the angle would be 0 because it would be pointing straight down at constant velocity. The acceleration pushes the pendulum back. I just don't know how write acceleration in terms of the variables they gave me

 

[berkeman]

A truck is moving with constant acceleration "a" up a hill that makes an angle phi with the horizontal. A small sphere of mass "m" is suspended from the ceiling of the truck by a light cord. If the pendulum makes a constant angle theta with the perpendicular to the ceiling, what is a?

What equations should I use for this problem?

if it were flat the angle would be 0 because it would be pointing straight down at constant velocity. The acceleration pushes the pendulum back. I just don't know how write acceleration in terms of the variables they gave me

As with most problems like this, start by drawing a Free Body Diagram (FBD) that shows the string and the sphere. Show the forces on the sphere from the string and from gravity...

 

[Matterwave]

To add on to berkeman, there are 2 frames in which you can analyze this problem, the frame of the ground (inertial) or the frame of the truck (non-inertial). If you choose the frame of the ground, the good news is is that it is an inertial frame and there are no fictitious forces, the bad news is that the pendulum is not stationary in this frame, but is moving up the hill along with the truck, so you have to figure out what that means as far as an angle between the pendulum and the ceiling of the truck goes. If you choose the frame of the truck, then you are in a non-inertial frame, and you have to introduce one additional fictitious force into your problem, but the good news is, now in this frame, the pendulum is stationary.

I suggest you work in the frame of the truck because including a fictitious force is easier than to worry about a moving pendulum in my opinion.