A constant force of 45 N directed at angle θ to the horizontal pulls a crate of weight 100 N from one end of a room to another a distance of 4 m. Given that the vertical component of the pulling force is 12 N, calculate the work done by the force in moving the crate.

Explanation:

information we know:

Total force:

Weight:

distance:

vertical component of the force:

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In this case we need the formulas to calculate the components of the force (because to calculate the work we need the horizontal component of the force).

horizontal component:

vertical component:

but from the given information we know that

so, equation these two and

and we know the force , thus:

now we clear for

the angle to the horizontal is 15.466°, with this information we can calculate the horizontal component of the force:

whith this horizontal component we calculate the work to move the crate a distance of 4 m:

the work done is W=173.48J

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