Find the work done by the force $\mathbf { F } = 100 \mathbf { i } - 25 \mathbf { j }$ in moving an object from $P ( - 2,4 )$
To $Q ( 150,5 )$
A) $12,775$
B) $10,445$
C) $9,755$
D) $7,325$
E) none

Question

Quizplus · Accepted Answer

The work done by a force during a displacement is given by the dot product of the force vector and the displacement vector. First, find the displacement vector $\mathbf{d} = \mathbf{Q} - \mathbf{P} = (150 + 2)\mathbf{i} + (5 - 4)\mathbf{j} = 152\mathbf{i} + 1\mathbf{j}$. Then, calculate the dot product with the force vector: $\mathbf{F} \cdot \mathbf{d} = (100\mathbf{i} - 25\mathbf{j}) \cdot (152\mathbf{i} + 1\mathbf{j}) = 100 \times 152 - 25 \times 1 = 15200 - 25 = 15175$.

Find the Work Done by the Force F=100i−25j\mathbf { F } = 100 \mathbf { i } - 25 \mathbf { j }F=100i−25j

Find the Work Done by the Force $\mathbf { F } = 100 \mathbf { i } - 25 \mathbf { j }$