A small mass m hangs from a thing string and can swing....

[HappyFlower]

Homework Statement

a small mass m hangs from a thing string can swing like a pendulum. You attach it above the window of your car as shown in the figure. When the car is at rest the string hangs vertically. What angle does the string make? a) when the car accelerates 1.20m/s^2 b)when the car moves at a constant velocity v=90 km/h?

Homework Equations

The Attempt at a Solution

I don't understand why the components are the way they are in the force diagram.

 

[Gene Naden]

The T is for the tension in the string that the thing hangs from. It points in the direction of the string. If it were vertical then there would only be a vertical component. Since it is at an angle, it has a vertical component and a horizontal component. The vector that is the string tension is the sum of the two components. Look at the two arrows labeled T sin(theta) and T cos (theta). Together, they add up to the T vector. I hope that helps.

 

[HappyFlower]

The T is for the tension in the string that the thing hangs from. It points in the direction of the string. If it were vertical then there would only be a vertical component. Since it is at an angle, it has a vertical component and a horizontal component. The vector that is the string tension is the sum of the two components. Look at the two arrows labeled T sin(theta) and T cos (theta). Together, they add up to the T vector. I hope that helps.

It does just that usually the tcostheta and the tsintheta are switched .

 

[Gene Naden]

So, Happy Flower, I took another look at the diagram and it appears that the T cos and T sin are correct. If the string were hanging vertically you would have cosine of zero, which is equal to one.

 

[haruspex]

It does just that usually the tcostheta and the tsintheta are switched .

Do you mean that usually you find a sin(θ) in the vertical component and cos(θ) in the horizontal component? If so, that would be because usually θ is the angle to the horizontal.

 

[Gene Naden]

Yeah in this case theta is the angle to the vertical. In the diagram they have theta between the string and the vertical.