Question #e4d20

1 Answer
Sep 2, 2017

I would begin by drawing a force diagram.

enter image source here

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.

  • For the northward force, there is no parallel component, as the force vector is entirely vertical, i.e. aligned with the y(north)-axis.

  • 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 #F_(2y)#:

#=>color(blue)(F_(2y)=F_2sin(theta))#

Similarly, using the cosine, we find that #color(blue)(F_(2x)=F_2cos(theta))#. Note that because the parallel component is to the left of the origin, we will say that this is negative.

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!