Pre calculus HW

Question

Find the work done by the force F in moving an object from P to Q. F = 3i - 5j; P(0, 0), Q(3, 6)

Answer 1

The problem is not feasible. The Force would have to be applied toward Q from P.

As it is the dot product FdotΔs=W=9-30=-21

the angle between the F vector and displacement vector is cos^-1[-21/((√34)(√45))]=122 degrees

which is greater than 90 degrees. This since FdotΔs=|F|*|Δs|cos(angle) is another valid computation of dot product.

Displacement vector needs to be within +/- 90 degrees from Force vector for Force to move object to

the displacement end point.

Answer 2

The work done by a force F in moving an object from point A to point B is given by the dot product of the force and the displacement vector between A and B:

W = F · Δr

where F is the force, Δr is the displacement vector from A to B.

In this case, the force is given by:

F = 3i - 5j

The displacement vector from P(0,0) to Q(3,6) is given by:

Δr = Q - P = (3i + 6j) - (0i + 0j) = 3i + 6j

Taking the dot product, we get:

W = F · Δr = (3i - 5j) · (3i + 6j) = 9i^2 - 15ij + 18ij + 30j^2

Since i^2 = j^2 = 1 and ij = 0, we can simplify this expression to:

W = 9 - 12 + 30 = 27

Therefore, the work done by the force F in moving an object from P to Q is 27 units of work.