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Mechanics

Two forces, F1 and F2, are given by the vectors F1 = (3i-4j) newtons and F2 = (i+pj) newtons respectively.
The resultant force acts in a direction parallel to the vector (2i-3j).
Find p.
Help me?
Original post by Jeruel Camat
Two forces, F1 and F2, are given by the vectors F1 = (3i-4j) newtons and F2 = (i+pj) newtons respectively.
The resultant force acts in a direction parallel to the vector (2i-3j).
Find p.
Help me?


The resultant must be some +ve scalar multiple of 2i−3j2\mathbf{i} - 3\mathbf{j}. So you can say that

F1+F2=k⋅(2i−3j),k>0F_1 + F_2 = k \cdot (2\mathbf{i} - 3\mathbf{j}), \qquad k > 0

and consider the i,j\mathbf{i}, \mathbf{j} components separately. First you determine what kk must be, then you use it to obtain pp.
How do you work out k?
Original post by Jeruel Camat
How do you work out k?


Compare the i\mathbf{i} components in this case between the two sides of the equation. They must be equal. What do you get?
Original post by Jeruel Camat
Two forces, F1 and F2, are given by the vectors F1 = (3i-4j) newtons and F2 = (i+pj) newtons respectively.
The resultant force acts in a direction parallel to the vector (2i-3j).
Find p.
Help me?


Alternatively, the vector F1+F2F_1+F_2 must have the same gradient as 2i−3j2\mathbf{i} - 3\mathbf{j}.

Hence you can work out the gradients of both vectors and make them equal. In some cases this approach can have an ambiguitity as far as the direction of the vector is concerned, which is why you should check your final answer.
Original post by RDKGames
Alternatively, the vector F1+F2F_1+F_2 must have the same gradient as 2i−3j2\mathbf{i} - 3\mathbf{j}.

Hence you can work out the gradients of both vectors and make them equal. In some cases this approach can have an ambiguitity as far as the direction of the vector is concerned, which is why you should check your final answer.

Thanks for the help :smile:

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