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

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

B is correct.

Explanation:

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

First we find the unit vector of direction of force.

`\hat{a}=(4i)/(√(20))-(2j)/(√(20))`

4-lb force acting in direction of vector a

`\vec{F}=(4)/(√(20))(4i-2j)`

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

Displacement vector whose length 7 ft

`\vec{r}=(7)/(√(50))(5i-5j)`

Now, we will find workdone by force

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

`W=(4)/(√(20))(4i-2j)\cdot (7)/(√(50))(5i-5j)`

`W=(28)/(√(1000))(20+10)`

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

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