SRL Archive - Mathematics

Ann and Beryl are both pushing a piano. Ann pushes in the direction 4i + 3j and Beryl in the direction 12i + 5j, where i and j are the standard unit vectors. Together they produce a force of (68i + 33j) N so that p(4i + 3j) + q(12i + 5j) = 68i + 33j, where p and q are constants. Calculate the force with which Beryl pushes.

Thanks in advance

4pi + 3pj + 12qi + 5qj = 68i + 33j

equate vector components:
4p + 12q = 68 (1)
3p + 5q = 33 (2)'

Solve simultaneously for p,q

So then Beryl's force = (12qi + 5qj) Newton

From: ZephyrsFury
4pi + 3pj + 12qi + 5qj = 68i + 33j

equate vector components:
4p + 12q = 68 (1)
3p + 5q = 33 (2)'

Solve simultaneously for p,q

So then Beryl's force = (12qi + 5qj) Newton

Never thought of that!! Thanks man :)

Usually if force is the final answer, you might want to just give the magnitude
|F| = sqrt(x^2 + y^2)

From: marpis
Usually if force is the final answer, you might want to just give the magnitude
|F| = sqrt(x^2 + y^2)

Force is a vector; unless specifically stated otherwise, you should provide a direction too.

From: ZephyrsFury
Force is a vector; unless specifically stated otherwise, you should provide a direction too.

If Ann and Beryl pull the piano, I think 500N is better answer than 244Nx4/3i + 333Nx5j :rolleyes:
I know those won't give the same answer.

An exception is if the plane is 2-dimensional, so there are only + and - directions.

From: marpis
If Ann and Beryl pull the piano, I think 500N is better answer than 244Nx4/3i + 333Nx5j :rolleyes:
I know those won't give the same answer.

An exception is if the plane is 2-dimensional, so there are only + and - directions.

Vector form is the more correct answer, especially since you're given the direction of the force in the question. If it were 1D then yeah a sign is usually sufficient as long as you define which direction is positive.

Besides in this case, its easier just to write the answer in vector component form. Why bother doing anything extra? :p