A particle moving in the xy plane under goes displacement s=(2i+3j)m while the constant force is given by F=(5i+2j)N.calculate the work done by the force F.
Take the dot product of the displacement and force vectors.
Looks like 16 joules.
Review vector dot (scalar) products
http://www.netcomuk.co.uk/~jenolive/vect6.html
To calculate the work done by a force, you can use the formula:
Work = Force ∙ Displacement ∙ cos(θ)
In this case, the force F is given as F = (5i + 2j) N, and the displacement s is given as s = (2i + 3j) m.
To calculate the work done, we need to find the dot product of the force and displacement vectors. The dot product of two vectors A = (A1i + A2j) and B = (B1i + B2j) is given by:
A ∙ B = (A1 * B1) + (A2 * B2)
Using this formula, we can find the dot product of F and s:
F ∙ s = ((5 * 2) + (2 * 3)) N∙m
F ∙ s = (10 + 6) N∙m
F ∙ s = 16 N∙m
Therefore, the work done by the force F is 16 N∙m.