Question

A 4-lb. force acting in the direction of (4, -2) moves an object over 7 ft. from point (0, 4) to (5, -1). Find the work done to move the object to the nearest foot-pound.
A. 35 ft. - lbs
B. 27 ft.- lbs
C. 18 ft. - lbs
D. 7 ft. - lbs

Answer 1

Answer:

The work done to move the object is 27 ft-lbs

B is correct.

Step-by-step explanation:

A 4-lb. force acting in the direction of (4, -2).

First we find the unit vector of direction of force.

$\hat{a}=\dfrac{4i}{\sqrt{20}}-\dfrac{2j}{\sqrt{20}}$

4-lb force acting in direction of vector a

$\vec{F}=\dfrac{4}{\sqrt{20}}(4i-2j)$

Object move 7 ft from point (0,4) to (5,-1)

Displacement vector whose length 7 ft

$\vec{r}=\dfrac{7}{\sqrt{50}}(5i-5j)$

Now, we will find workdone by force

$W=\vec{F}\cdot \vec{r}$

$W=\dfrac{4}{\sqrt{20}}(4i-2j)\cdot \dfrac{7}{\sqrt{50}}(5i-5j)$

$W=\dfrac{28}{\sqrt{1000}}(20+10)$

$W=26.56\approx 27\text{ ft-lbs}$

Hence, The work done to move the object is 27 ft-lbs

Answer 2

The answer is 18ft-lbs