Finding the intersection of a plane

[clickcaptain]

Here is the problem:

Replace the two forces afting on the pole by a wrench. Write a moment M associated with a wrench as a vector and specify the coordinates of the point P in the y-z plane through which the line of action of wrench passes.

I already figured the moment to be
("T" and "a" are both scalar)

M = Ta(4i - 3j)

How would I go about finding the intersection of the plane? My train of thought is leading me towards the idea that I need to set x=0 but I'm not sure...

thanks for the help in advance!

 

[tiny-tim]

Replace the two forces afting on the pole by a wrench. Write a moment M associated with a wrench as a vector and specify the coordinates of the point P in the y-z plane through which the line of action of wrench passes.

I already figured the moment to be
("T" and "a" are both scalar)

M = Ta(4i - 3j)

How would I go about finding the intersection of the plane? My train of thought is leading me towards the idea that I need to set x=0 but I'm not sure...

Hi clickcaptain!

I can't quite visualise this …

doesn't the moment go along the pole, to where the pole meets the y-z plane?

If I'm wrong, perhaps you'd better give us more details.

 

[baba89]

I would approach this problem by first understanding the concept of a wrench. A wrench is a type of force that is applied along a line of action and produces a moment around a point. This moment is a vector quantity that is defined by both magnitude and direction. In this case, the moment M is defined by the force T and the distance a from the point of rotation.

To find the intersection of the plane, we need to first define the plane in terms of equations. Since we are looking for the intersection in the y-z plane, we can set x=0 as you suggested. This means that the plane is parallel to the y-z plane and passes through the y-z axis.

Next, we need to find the point P in the y-z plane through which the line of action of the wrench passes. This can be done by using the given moment M and the force T. We know that the moment is defined as M = r x F, where r is the position vector from the point of rotation to the point P and F is the force vector. In this case, r = a and F = T. So we can write the equation as M = a x T.

Since we are only interested in the y-z plane, we can ignore the x component of the vectors. This means that we can write the equation as M = ayTz - azTy, where ay and az are the y and z components of the moment M and Tz and Ty are the y and z components of the force T.

Now we can solve for the point P by setting M = 0 and solving for ay and az. This will give us the coordinates of the point P in the y-z plane through which the line of action of the wrench passes.

In summary, to find the intersection of the plane, we need to define the plane in terms of equations and then use the given moment M to solve for the coordinates of the point P in the y-z plane. This will give us the intersection point of the plane with the line of action of the wrench.