A sphere suspended from a cord -- Find the tension

[lola9]

Homework Statement

A sphere suspended from a cord
Find the tension

Relevant Equations

F=ma

I don't understand where F comes from because in the problem there is only the tension of the cord. And I have another question the forces along y-axis always be equal to zero? And why T cos q - m g = 0 equal zero? if it is along the X-axis

 

[phinds]

I don't understand where F comes from because in the problem there is only the tension of the cord.

The statement of the problem clearly shows F as the force of the wind pushing the sphere sideways.

Also, it seems to me that the origin of the problem should more appropriately be wher the end of the T is and the arrow on the T should be in the other direction. That would follow the problem statement more than does the current drawing.

 

[TSny]

And why T cos q - m g = 0 equal zero? if it is along the X-axis

Note that the angle $\theta$ in the diagram is measured from the y-axis (not the x-axis). So, the y-component of $T$ is $T \cos \theta$ (not $T \sin \theta$).

 

[lola9]

Note that the angle $\theta$ in the diagram is measured from the y-axis (not the x-axis). So, the y-component of $T$ is $T \cos \theta$ (not $T \sin \theta$).

From equation 1 ? this T sin q - F = 0 (eq.1) ?

 

[TSny]

From equation 1 ? this T sin q - F = 0 (eq.1) ?

This is the equation for equilibrium in the x-direction. Is there something in particular about this equation that you don't understand?

 

[lola9]

This is the equation for equilibrium in the x-direction. Is there something in particular about this equation that you don't understand?

why do you say that it is in equilibrium ? The wind is blowing right ?

 

[TSny]

why do you say that it is in equilibrium ? The wind is blowing right ?

Yes, the wind is blowing steadily toward the left which keeps the ball hanging at the angle shown. The ball remains in this position, so the ball is at rest. Therefore the ball is in static equilibrium. The three forces that act on the ball must add to zero. This means that the sum of the x-components of the three forces must add to zero and the sum of the y-components of the three forces must add to zero.

 

[lola9]

This is the equation for equilibrium in the x-direction. Is there something in particular about this equation that you don't understand?

so if the system is in equilibrium the forces along x and y will always be equal to zero ? How did you know that it is in equilibrium ?

 

[phinds]

How did you know that it is in equilibrium ?

Well, if you like you could assume that the wind is not steady and the ball is swinging all around, but then how would you possibly solve the problem? My point is that such simple mechanical problems always assume that things like wind are unchanging for the purposes of the problem so of course you take it as being in equilibrium.

 

[TSny]

so if the system is in equilibrium the forces along x and y will always be equal to zero ?

In equilibrium, the individual forces along the x direction are not zero, but the sum of the forces along the x direction is zero. That is, the sum of the x-components of the forces is zero. Same for the y direction.

 

[TSny]

How did you know that it is in equilibrium ?

Note that the problem statement says that the cord makes a constant angle. So, the angle is not changing.

 

[lola9]

Note that the problem statement says that the cord makes a constant angle. So, the angle is not changing.

so that is why the forces equals 0

 

[TSny]

so that is why the forces equals 0

That is why the sum of the forces equals zero. If an object remains at rest (in an inertial frame of reference) then the vector sum of the forces acting on the object must be zero.

 

[lola9]

That is why the sum of the forces equals zero. If an object remains at rest (in an inertial frame of reference) then the vector sum of the forces acting on the object must be zero.

ok thanks