Question #178937

Two forces of magnitude 80𝑁 and 45𝑁 act on an object, with an angle between the forces of 100°. What is the resultant force?


1
Expert's answer
2021-05-03T05:05:08-0400

Let force F1=80NF_1=80N

Let the force F2=45NF_2=45N

The resultant of the two forces can be obtained using:


R2=F12+F222F1F2cosθR^2 = F_1^2+F_2^2-2F_1F_2\cos\theta\\


The angle formed between the two forces lies in the second quadrant. Thus the value of cosθ\cos\theta will be negative.

Thus:


R2=802+4522×80×45×cos(180°100°)R2=6400+20257200×cos80°R2=84257200×0.1737R2=84251,250.64R2=7,174.36R=7,174.36R=84.7NR^2 = 80^2 + 45^2 - 2\times80\times45\times\cos(180\degree-100\degree)\\ R^2 = 6400 + 2025 -7200 \times \cos80\degree\\ R^2 = 8425 - 7200 \times 0.1737\\ R^2 = 8425 -1,250.64\\ R^2 = 7,174.36\\ R = \sqrt{7,174.36}\\ R = 84.7N


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS