Solve Tension in a String: Acceleration & Angle Given

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AI Thread Summary
The discussion revolves around a physics problem involving a car accelerating from rest and an air freshener changing by 27.8 degrees. The user initially calculated acceleration using the formula (g)sin(angle) but struggled to find the correct tension in the string, which is expected to be between 1 and 1.2N. Participants suggest using a free body diagram to analyze the forces acting on the air freshener, considering the x and y components of acceleration. The user later proposed using a right triangle to relate these components, which was deemed a valid approach but required justification. Overall, the exchange emphasizes the importance of correctly applying physics principles to solve for tension and acceleration.
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Homework Statement


The problem I am working on seems simple but I can't seem to get the answer. Basically what I know is that a car accelerates from rest and a air freshener changes by 27.8 degrees. It first asked the acceleration which I thought was (g)sin(angle) so that came out to be about 4.45. It then asked for the tension in the string.

Homework Equations


F = ma
T-g =ma


The Attempt at a Solution


I've tried a few things using those equations and in different variations but can't seem to get the answer. It says the answer is between 1 and 1.2N. It seems simple so what am I missing? By the way this is my first post so I hope I did this right.
 
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welcome to pf!

hi weatherboy! welcome to pf! :smile:
weatherboy said:
… It first asked the acceleration which I thought was (g)sin(angle) so that came out to be about 4.45. It then asked for the tension in the string.

how did you get (g)sin(angle)? was it just an intelligent guess?

you should be able to read both the acceleration and the tension off the free body diagram
 


tiny-tim said:
hi weatherboy! welcome to pf! :smile:


how did you get (g)sin(angle)? was it just an intelligent guess?

you should be able to read both the acceleration and the tension off the free body diagram

The angle was given. I haven't submitted it yet but after I had typed my above info I had an idea. I figured the acceleration on the air freshener could probably be considered the x-component of the acceleration and that gravity might be the y component. Even though I had used gravity before to find the acceleration in the x-direction. So if I use a right triangle with this as my x and y components I at least get an answer in the acceptable range. Does this seem correct?
 
weatherboy said:
I figured the acceleration on the air freshener could probably be considered the x-component of the acceleration and that gravity might be the y component. … So if I use a right triangle with this as my x and y components I at least get an answer in the acceptable range. Does this seem correct?

are you just guessing?

yes, that does work, but you'd have to justify it …

what principle are you relying on? what frame are you in?

(the usual way to do it would be F = ma)
Even though I had used gravity before to find the acceleration in the x-direction.

you still haven't said how you did that :confused:
 

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