Two forces both in the x-y plane act on a 1.5 kg mass that accelerates at 7.4 m/

Question

Two forces both in the x-y plane act on a 1.5 kg mass that accelerates at 7.4 m/s^2 in a direction 30 degrees counterclockwise from the x-axis. One force has magnitude 7.0 N and points in the x direction Find the other force (direction and magnitude) Two forces both in the x-y plane act on a 1.5 kg mass that accelerates at 7.4 m/s^2 in a direction 30 degrees counterclockwise from the x-axis. One force has magnitude 7.0 N and points in the x direction Find the other force (direction and magnitude) Two forces both in the x-y plane act on a 1.5 kg mass that accelerates at 7.4 m/s^2 in a direction 30 degrees counterclockwise from the x-axis. One force has magnitude 7.0 N and points in the x direction Find the other force (direction and magnitude)

Explanation / Answer

a = (7.4 m/s2) (cos30 i + sin30 j) = (6.41 i + 3.7 j) m/s2

m = 1.5 kg

F1 = (7.0 N) (i + 0j) = (7.0 i) N

Let F2 = (xi + yj)

Total force = mass * acceleration

F1 + F2 = ma

(7.0 i) + (xi + yj) = (1.5) (6.41 i + 3.7 j)

(7+x) i + yj = 9.615 i + 5.55 j

comparing i and j components both sides

(7+x) = 9.615     and y = 5.55

x = 2.615     and y = 5.55

So, the second force is F2 = 2.615 i + 5.55 j

Magnitude of F2 = (2.6152 + 5.552)1/2 = 6.14 m

Direction of F2 is = tan-1(5.55/2.615) = 64.77 counterclockwise from the x-axis

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