Question #e4d20
1 Answer
I would begin by drawing a force diagram.
We are given that:
-
#|->vecF_1=30"N"# -
#|->vecF_2=50"N"#
The net force is given by:
#color(blue)(abs(vecF_"net")=sqrt((F_x)^2+(F_y)^2))#
We will first need to find the parallel (x, horizontal) and perpendicular (y, vertical) components of the given forces.
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For the northward force, there is no parallel component, as the force vector is entirely vertical, i.e. aligned with the y(north)-axis.
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For the northwest force, the force vector lies at an angle, and so this force has both parallel and perpendicular components. We can calculate these using basic trigonometry.
-
Because the force is said to act northwest and we are not given a specific angle, we assume it acts at exactly the midpoint between North and West, i.e. at
#45^o# above the negative x-axis.
#sin(theta)="opposite"/"hypotenuse"#
#sin(theta)=F_(2y)/F_2#
Solving for
#=>color(blue)(F_(2y)=F_2sin(theta))#
Similarly, using the cosine, we find that
Therefore, we have:
#F_"y net"=sumF_y=F_1+F_(2y)#
#F_"x net"=sumF_x=-F_(2x)#
So, we know that:
-
#F_y=30+50sin(45^o)# -
#F_x=-50cos(45^o)#
And so, the net force is:
#F_"net"=sqrt((-50cos(45^o))^2+(30+50sin(45^o))^2)#
#=>color(blue)(F_"net"~~74"N")#
Which is closest to answer choice c. The slight difference in values is due to rounding (I used exact values).
Hope that helps!