Force Component of u nt 30cos30: Solution Explained

[goldfish9776]

Homework Statement

Why the force component of u nt 30cos30? The ans given is 30sin45/ sin105...

Homework Equations

The Attempt at a Solution

 

[PhanthomJay]

Homework Statement

Why the force component of u nt 30cos30? The ans given is 30sin45/ sin105...

Homework Equations

The Attempt at a Solution

It would be 30cos30 if the problem was asking you to determine the horizontal and vertical components of the force. But it is apparently asking you to determine the components of the force directed along the u and v axes. You should draw a sketch and do some geometry and a trig relationship.

 

[goldfish9776]

It would be 30cos30 if the problem was asking you to determine the horizontal and vertical components of the force. But it is apparently asking you to determine the components of the force directed along the u and v axes. You should draw a sketch and do some geometry and a trig relationship.

Why shouldn't the u axis = x axis? It's drawn like that in the figure...

 

[PhanthomJay]

Why shouldn't the u axis = x axis? It's drawn like that in the figure...

Yes the u axis is the horizontal x-axis but the v axis is not the vertical y
axis. You need to draw a sketch showing one component along the v axis and the other parallel to the u axis that graphically add to the resultant F vector to get a triangle that is not a right triangle , then use geometry and a trig relationship. .

.

.

 

[goldfish9776]

Yes the u axis is the horizontal x-axis but the v axis is not the vertical y
axis. You need to draw a sketch showing one component along the v axis and the other parallel to the u axis that graphically add to the resultant F vector to get a triangle that is not a right triangle , then use geometry and a trig relationship. .

.

.

Ok, but the ans given here for force along u is 30sin45/sin105, btw I managed to form the triangle nw.. Why the force along u axis isn't 30cos30?

 

[PhanthomJay]

Ok, but the ans given here for force along u is 30sin45/sin105, btw I managed to form the triangle nw.. Why the force along u axis isn't 30cos30?

If you drew the triangle correctly, you have the v component arrow vector along the v axis with its tail at the pipe, and the u component arrow vector horizontal starting at the arrow of the v vector and ending at the arrow of the 30 lb vector. You should note that the angles of the triangle thus formed are 45, 105, and 30 degrees. Now use the law of sines to solve for the v and u components.
https://www.mathsisfun.com/algebra/trig-sine-law.html
Once again, the u comp is not 30 cos 30 ...that is true only if you were breaking up the components along perpendicular x and y axes. But you are asked to break up the components along non perpendicular u and v axes.

 

[goldfish9776]

If you drew the triangle correctly, you have the v component arrow vector along the v axis with its tail at the pipe, and the u component arrow vector horizontal starting at the arrow of the v vector and ending at the arrow of the 30 lb vector. You should note that the angles of the triangle thus formed are 45, 105, and 30 degrees. Now use the law of sines to solve for the v and u components.
https://www.mathsisfun.com/algebra/trig-sine-law.html
Once again, the u comp is not 30 cos 30 ...that is true only if you were breaking up the components along perpendicular x and y axes. But you are asked to break up the components along non perpendicular u and v axes.

how do u knw that u axis can't be equal to x-axis ?

 

[PhanthomJay]

The u axis is the x-axis , so you can call it that if you wish. You cannot talk about a component of a vector along an axis without specifying another axis. The vector has 2 components. You can say it has components of 30 cos 30 along the x-axis and 30 sin 30 along the y axis, OR, you can say it has components of 30 sin 45/sin 105 along the x-axis and 30 sin 30/sin 105 along the v axis. It takes two to tango.

 

[goldfish9776]

The u axis is the x-axis , so you can call it that if you wish. You cannot talk about a component of a vector along an axis without specifying another axis. The vector has 2 components. You can say it has components of 30 cos 30 along the x-axis and 30 sin 30 along the y axis, OR, you can say it has components of 30 sin 45/sin 105 along the x-axis and 30 sin 30/sin 105 along the v axis. It takes two to tango.

If I say it has components of 30 cos 30 along the x-axis and 30 sin 30 along the y axis, then my ans is wrong ( different from the ans given )

 

[PhanthomJay]

If I say it has components of 30 cos 30 along the x-axis and 30 sin 30 along the y axis, then my ans is wrong ( different from the ans given )

Right, you would be wrong with that answer, based on the problem statement, because it asks you for non perpendicular u and v components, not perpendicular x and y components. Typically a vector is broken up into its perpendicular components, but the problem wants to test your knowledge of vectors by asking for the non perpendicular u and v components.

 

[goldfish9776]

Right, you would be wrong with that answer, based on the problem statement, because it asks you for non perpendicular u and v components, not perpendicular x and y components. Typically a vector is broken up into its perpendicular components, but the problem wants to test your knowledge of vectors by asking for the non perpendicular u and v components.

well, do u mean i can only use u = 30cos30 if u is perpendicular to the v( 30 sin30) ?
in this case , since only u can be resolved to become u =30cos30 , the v can't be resolved to become 30sin30 ... So , we are not allowed to use u=30cos30? But sine rule is used in this case?

 

[goldfish9776]

well, do u mean i can only use u = 30cos30 if u is perpendicular to the v( 30 sin30) ?
in this case , since only u can be resolved to become u =30cos30 , the v can't be resolved to become 30sin30 ... So , we are not allowed to use u=30cos30? But sine rule is used in this case?

 

[PhanthomJay]

well, do u mean i can only use u = 30cos30 if u is perpendicular to the v( 30 sin30) ?
in this case , since only u can be resolved to become u =30cos30 , the v can't be resolved to become 30sin30 ... So , we are not allowed to use u=30cos30? But sine rule is used in this case?

Yeah that's about right... You know typically a problem requires you to resolve a vector into its perpendicular components, but not this time. Although it's quite common to add two non perpendicular vectors to get a resultant vector, it's not too often the other way around that one is asked to resolve a vector into non perpendicular components, so I understand your issues.