Solve Tension in a String: Acceleration & Angle Given

[weatherboy]

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.

 

[tiny-tim]

welcome to pf!

hi weatherboy! welcome to pf!

… 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

 

[weatherboy]

hi weatherboy! welcome to pf!


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?

 

[tiny-tim]

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

 

[rwisz]

Hello,

Thank you for sharing your problem with us. It seems like you are on the right track with using the equations F=ma and T-g=ma to solve for the acceleration and tension in the string. However, there may be some errors in your calculations or assumptions that are causing you to not get the expected answer.

Firstly, when solving for the acceleration, it is important to make sure that you are using the correct angle. In this case, it seems like the angle given is the angle at which the air freshener changes, not the angle at which the car accelerates. So, make sure to use the correct angle in your calculations.

Secondly, when solving for the tension in the string, you need to take into account all the forces acting on the string. In this case, there is the force of gravity (mg) and the force of the car's acceleration (ma). So, the correct equation to use would be T=mg+ma.

Finally, make sure to double-check your calculations and units to ensure that you are getting the correct answer. If you are still having trouble, it may be helpful to draw a free body diagram and label all the forces acting on the system.

I hope this helps and good luck with your homework! Remember, it's always important to double-check your work and ask for help if needed. Keep up the good work!