Problem: Watch attached to a string in an airplane

[N_L_]

I'm having trouble with the correct setup for the following problem:

A physics student, who likes physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport. She notices that the string makes an angle of 25 degrees with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 seconds. Estimate the takeoff speed of the aircraft.


Given: Theta = 25 degrees ; time = 18 s
Unknown: Ft, acceleration (ax and ay)

I drew an FBD and split up gravity into its x and y components.

I have the equations as:

mg sin 25 = m ax

Ft - mg cos 25 = m ay

What's wrong with this approach?

 

[phucnv87]

Here's my solution to your problem
$$a=g\tan\theta$$
where $$\theta=25^o$$
And the takeoff speed of the aircraft is
$$v=at=gt\tan\theta$$

 

[nrqed]

I'm having trouble with the correct setup for the following problem:

A physics student, who likes physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport. She notices that the string makes an angle of 25 degrees with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 seconds. Estimate the takeoff speed of the aircraft.


Given: Theta = 25 degrees ; time = 18 s
Unknown: Ft, acceleration (ax and ay)

I drew an FBD and split up gravity into its x and y components.

I have the equations as:

mg sin 25 = m ax

Ft - mg cos 25 = m ay

What's wrong with this approach?

First, what forces do you have in your FBD? There are only two forces: the tension in the string and gravity.

Second, a_y = 0.

Imposing a_y = 0 will allow you to find the tension. Then using the tension you found and plugging it into the x equation will allow you to find the acceleration along x.

The answers of the other posters are right.

Patrick

 

[fuzzy]

hehe I had to do this exact problem!
see here:
https://www.physicsforums.com/showthread.php?t=109527
and here:
https://www.physicsforums.com/showthread.php?t=43811

 

[lightgrav]

As nrged implied, ALWAYS set up a coordinate parallel to the direction of motion or parallel the acceleration. (implied by not even considering that anyone might set up a coordinate system parallel the string).
Otherwise, what's wrong with this approach is that you have 3 unknowns
(ax, ay, T ) so you need an equation to relate ax with ay.
By geometry, ax + ay must add up to a horizontal total acceleration,
and you're back to the "straight-forward" equation.