An old tire of mass 20 kg lies on a frozen lake (see top view in diagram). Three
ID: 2273829 • Letter: A
Question
An old tire of mass 20 kg lies on a
frozen lake (see top view in diagram). Three
forces are applied to the tire, F1 = 200 N acts
?1=30 degrees north of east, F2 acts ?2 =20 degrees south
of west, and F3 acts to the south.
An old tire of mass 20 kg lies on a frozen lake (see top view in diagram). Three forces are applied to the tire, F1 = 200 N acts ?1=30 degrees north of east, F2 acts ?2 =20 degrees south of west, and F3 acts to the south. If the system remains stationary what are the magnitudes of F2 and F3? If the system has an acceleration of 3.4 m/s2 in the positive x direction, what are the magnitudes of F2 and F3? Assume that friction is negligible.Explanation / Answer
A) First, we calculate the x and y components of F1:
F1x = 200 x cos(30) = 173.205 N (east)
F1y = 200 x sin(30) = 100 N (north)
F2x will equal F1x, since F3 has no horizontal component. We solve for F2:
F2x = 173.205 (west)
173.205 = F2 x cos(20)
F2 = 184.321 N
Now we can solve for F2y:
F2y = 184.321 x sin(20)
F2y = 63.041 N (south)
Net force is zero, so:
F = F1y - F2y - F3y
0 = 100 - 63.04 - F3y
F3y = -36.959 N
Final answers:
F2 = 184.321 N (20 deg. south of west)
F3 = 36.959 N (south)
Cheers.