A constant force F = 2.4i^+ 3.3j^ N acts on an object as it moves along a straig

Question

A constant force F = 2.4i^+ 3.3j^ N acts on an object as it moves along a straight-line path. If the object's displacement is d =1.7i^ + 5.0j^m, calculate the work done by F using these alternate ways of writing the dot product:

Part A Calculate the work done by F using these alternate ways of writing the dot product: W=Fdcos. Express your answer using two significant figures.

Part B Calculate the work done by F using these alternate ways of writing the dot product: W=Fxdx+Fydy. Express your answer using two significant figures.

Explanation / Answer

is the angle between the vector F and the vector d.
In a 2D coordinate system you can find it from difference of the angels the vector from with one coordinate axis.
The angle a vector v formed with the positive x-axis is given by
tan(_v) = v_y/v_x
<=>
_v = arc tan(v_y/v_x)

Hence
W = |F| · |d| · cos ()
= ((F_x]² + (F_y)²) · ((d_x]² + (d_y)²)m · cos( _F - _d)
= ((2.4N)² + (3.3N)²) · ((1.7m)² + (5m)²) · cos(tan(3.3/2.4) - tan(5/1.7))
= 21.5J

(b)
W = F_x·d_x + F_y·d_y
= 2.4N · 1.7m + 3.3N · 5m
= 20.5J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.