Answer:
Approximately [tex]14300\; {\rm J}[/tex].
Explanation:
The work that a force exerted on an object is the product of the following:
- Magnitude of the force, and
- Displacement of the object in the direction of the force.
In this question, the magnitude of the force is given: [tex]F = 525\; {\rm N}[/tex]. The displacement of the object needs to be found.
Refer to the diagram attached (not to scale). The slope can be considered as part of a right triangle, where:
- One of the angles of this right triangle is [tex]\theta = 16^{\circ}[/tex].
- The height that the object gained, [tex]7.5\; {\rm m}[/tex], is the side opposite to the [tex]\theta = 16^{\circ}[/tex] angle.
- The hypotenuse of the right triangle is the displacement of the object in the direction of the external force.
To find the displace of the object in the direction of the external force, make use of the following relationship in a right triangle:
[tex]\begin{aligned}(\text{hypotenuse}) &= \frac{(\text{opposite})}{\sin(\theta)} \\ &= \frac{7.5\; {\rm m}}{\sin(16^{\circ})} \\ &\approx 27.210\; {\rm m}\end{aligned}[/tex].
In other words, the displacement of the object in the direction of the external force would be approximately [tex]27.210\; {\rm m}[/tex]. The work that this [tex]525\; {\rm N}[/tex] force exerted on the object would be:
[tex]\begin{aligned}(\text{work}) &= (\text{force})\, (\text{displacement}) \\ &\approx (525\; {\rm N}) \, (27.210\; {\rm m}) \\ &\approx 14300\; {\rm J}\end{aligned}[/tex].
