1. Two ropes are attached to a wagon, one horizontal to the west with a tension force of 30 N, and the other east and at an angle of 30° northward and a tension force of 40 N. Find the components of the net force on the cart. Show all your work.
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Would the net force be 10 N to the east? Help I don't get this D:
Assuming the two ropes are tied onto the same point of the wagon (avoids torque), the net force is just the sum of the two mentioned. The westward force may be chosen as Fw = (-30,0), then the northeastward force is Fne = (40*cos(30°),40*sin(30°)). Adding the two is just adding each part, so the resulting force is Fnet = (-30+40*cos(30°),40*sin(30°)). Those are the components, so I guess that's done. Going more than that, the magnitude uses the Pythagorean formula, so √[(-30+40*cos(30°))²+(40*sin(30°))²] which is about 20.53N if I got that calculation right. And the angle is the arctangent of their ratio, so about 76.94° northward of east.
Jonathan · 4 years ago