Question

Find the work done by a force of 2 pounds acting in the direction of 35° to the horizontal in moving an object 8 feet from (0, 0) to (8, 0).

Answer 1

Answer to Question #88641 – Math – Trigonometry

Question

Find the work done by a force of 2 pounds acting in the direction of $35{}^{\circ}$ to the horizontal in moving an object 8 feet from $(0, 0)$ to $(8, 0)$.

Solution

Force F = 2 pounds

Force F is acting in the direction of OB in the above triangle OAB

Angle BOA = 35 degrees

Displacement is OA = 8 feet

Work done by a Force acting at an angle 35 degrees to the horizontal in moving an object from O to A is $W = F \times \cos \theta \times$ displacement

$$\begin{array}{l} = 2 \times \cos (35 \text{ degrees}) \times 8 \\ = 16 \times \cos (35 \text{ degrees}) \\ = 16 \times (0.819152) \text{ (Since, } \cos (35 \text{ degrees}) = 0.819152) \\ = 13.10643 \\ \end{array}$$

Therefore, the work done by the force F, in moving the object from $(0,0)$ to $(8,0)$, is $W = 13.10643$ ergs

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