Question

A force of 4 pound acts in the direction of 48degree to the horizontal. The force moves an object along a straight line from the point (1,7) to the point (8,10), with distance measured in feet. What is the work done?

Answer 1

Work Done = 27.66 Joules

Explanation:

The work done is:

`W=F*d*Cos \theta`

Where

F is the fore

d is the distance moved

`\theta` is the angle

The force is "4"

The distance is the distance from (1,7) to (8,10)

The distance is the square root of change in y coordinates, squared and sum of change in x coordinates, squared. Hence, distance is:

`√((10-7)^2+(8-1)^2)\\=√(3^2+7^2)\\√(58)`

The angle is gotten by the formula:

`Cos\phi = (Force in x direction)/(Distance)\\Cos\phi = (8-1)/(√(58))\\Cos\phi=(7)/(√(58))\\\phi = Cos^(-1)(7)/(√(58))\\\phi = 23.21`

So, now:

`\theta = 48 - 23.21 = 24.79`

Work Done =
`F*d * Cos\theta = 4 * √(58) * Cos(24.79)`

Work Done = 27.66 Joules