Question

A force
F⃗
at an angle of
θ
above the horizontal displaces an object through a distance S in its along the horintal. Which of the following is the CORRECT expression for the work done on the object by the force?
a. F⃗ ⋅s⃗ cosθ
b. F⃗ ×s⃗
c. Fssinθ
d. Fscosθ

Answer 1

Answer on Question #41466, Physics, Mechanics

A force $F^{*}$ at an angle of $\theta$ above the horizontal displaces an object through a distance $S$ in its along the horizontal. Which of the following is the CORRECT expression for the work done on the object by the force?

a. $F^{*}\cdot s^{*}\cos \theta$

b. $F^{*}\times s^{*}$

c. Fssinθ

d. Fscosθ

Solution:

In order to accomplish work on an object there must be a force exerted on the object and it must move in the direction of the force.

Work is

$$W = \vec {F} \cdot \vec {s} = F s \cos \theta$$

$\vec{F} =$ Force vector applied to the object/system.

$F_{s} =$ Component of Force along the direction of movement.

$\vec{s} =$ Displacement vector.

$s =$ Distance the system is displaced.

$\theta =$ Angle between the displacement and the force.

$\vec{F} \cdot \vec{s} =$ Scalar or Dot product of the force vector and the distance vector.

Answer. d. Fscosθ.

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