Question

a force of 6 pounds acts in the direction of 40(degrees) to the horizontal. the force moves an object along a straight line from the point (5,9) to the point (8,20), with the distance measured in feet. find the work done by the force.

Answer 1

Therefore, the work done by the force is approximately 49.222 foot-pounds.

Step-by-step explanation:

To find the work done by the force, we can use the formula:

Work = Force * Distance * cos(theta)

Given:

Force = 6 pounds

Distance = sqrt((8 - 5)^2 + (20 - 9)^2) [distance between the points (5,9) and (8,20)]

Theta = 40 degrees

Calculating the distance:

Distance = sqrt((8 - 5)^2 + (20 - 9)^2)

Distance = sqrt(3^2 + 11^2)

Distance = sqrt(9 + 121)

Distance = sqrt(130)

Now, we can calculate the work done:

Work = 6 * sqrt(130) * cos(40)

Using a calculator:

Work ≈ 6 * 11.4018 * 0.7660

Work ≈ 49.222 foot-pounds

Therefore, the work done by the force is approximately 49.222 foot-pounds.