Please Show all detailed work and formula that you use to solve it. Thanks a lot

Question

Please Show all detailed work and formula that you use to solve it. Thanks a lot.

The figure shows an overhead view of a 0.023 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force F1 rightarrow has a magnitude of 7 N and is at theta1 = 31 degree . Force F2 rightarrow has a magnitude of 6 N and is at theta2 = 25 degree . If the lemon half is stationary, what are projections of the third force on (a)x-axis, (b)y-axis? If the lemon half has constant velocity m/s, what are projections of the third force on (c)x-axis, (d)y-axis? If the lemon half has varying velocity m/s2, where t is time, what are projections of the third force on (e)x-axis, f(y)-axis?

Explanation / Answer

1). when the lemon half is stationary, the sum of all the forces = 0 because acceleration is zero. F1 = -7*cos31 (i) + 7*sin31 (j) = -6 i + 3.61 j F2 = 6*sin25 (i) - 6*cos25 (j) = 2.54 i - 5.44 j F1 + F2 = -3.46 i -1.83 j so, F3 = 3.46 i + 1.83 j 2).when the lemon half is moving with constant velocity, acceleration =0 , so, net force = 0 F3 = 3.46 i + 1.83 j 3). v = 13*t (i) -12*t (j) a = dv/dt = 13 i - 12 j F(net) = m*a => F1+F2+F3 = (0.023*13) i - (0.023*12) j => (-3.46 i -1.83 j) + F3 = 0.3 i - 0.276 j => F3 = 3.76 i + 1.554 j

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