Two workers are trying to move a heavy crate. One pushes on the crate with a for

Question

Two workers are trying to move a heavy crate. One pushes on the crate with a force , which has a magnitude of 210 newtons (N) and is directed due west. The other pushes with a force , which has a magnitude of 353 N and is directed due north. What are (a) the magnitude and (b) direction of the resultant force + applied to the crate? Suppose that the second worker applies a force - instead of . What then are (c) the magnitude and (d) direction of the resultant force - applied to the crate? In both cases express the direction as a positive angle relative to due west.

Explanation / Answer

let,

force F1=210 N due west

force F2=353 N due north

a)

here, angle between F1 and F2 is 90 degrees

magnitude ofresultant force F=sqrt(F1^2+F2^2+2*F1*F2*cos(90))

F=sqrt(210^2+353^2+0)

F=410.74 N ---is answer

b)

direction ,

tan(theta)=F2/F1

tan(theta)=353/210

=====> theta=59.25 degrees ---is answer

c)

if,

force F1=210 N

force F2=-353 N

here also,

angle between F1 and F2 is 90 degrees

magnitude of resultant force F=sqrt(F1^2+F2^2+2*F1*F2*cos(90))

F=sqrt(210^2+(-353)^2+0)

F=410.74 N ----is answer

d)

direction ,

tan(theta')=F2/F1

tan(theta')=-353/210

=====> theta'=-59.25 degrees

here

theta=360-59.25

theta=300.75 degrees ----is answer

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