Two forces, having magnitudes 3 and 5 act at angles 35 degrees and 72 degrees on

Question

Two forces, having magnitudes 3 and 5 act at angles 35 degrees and 72 degrees on mass m (in units of kg), initially located at (20,32) and with an initial velocity 41 making an angle 15 degrees wrt +x axis. Numerically determine the final velocity of the mass, as well as the final x and y positions, after a time t =6 seconds. Check your answers using graphical addition of vectors - for this, it is recommended that you have the tails of your vectors at the initial point (we used the origin for this in class, although any point will work).

Explanation / Answer

F1 = 3 Cos35 i + 3 sin35 j = 2.46 i + 1.72 j

F2 = 5 Cos72 + 5 Sin72 j = 1.55 i + 4.76 j

Vi = initial velocity = 41 Cos15 i + 41 Sin15 j = 39.6 i + 10.6 j

t = velocity = 6 sec

Fnet = net force = F1 + F2 = (2.46 i + 1.72 j) + (1.55 i + 4.76 j ) = 4.01 i + 6.48 j

a = acceleration = Fnet /m = (4.01 i + 6.48 j )/m

final velocity is given as

Vf = Vi + at

Vf = (39.6 i + 10.6 j ) + ( (4.01 i + 6.48 j )/m) (6)

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