the forces in (Figure 1) act on a 1.5 kg object.
a) What is the value of ax the xcomponent of the object’s acceleration?
Express your answer with the appropriate units.
b) What is the value of ay, the ycomponent of the object’s acceleration?
Express your answer with the appropriate units.
2 Answers

The xy axis is rotated 20˚ counter clockwise from horizontal. The 3.0 N force has an x and y components. Both of them are negative.
x = 3.0 * sin 20 ≈ 1.03 N
y = 3.0 * cos 20 ≈ 2.82 N
Total x = 1 + 3.0 sin 20 + 5 = 4 – 3 sin 20
This is approximately 3 N.
ax = (4 – 3 * sin 20) ÷1.5
This is approximately 2 m/s^2.
Total y = 2.82 + 3 * cos 20
This is approximately 0.0009 N.
ay = (2.82 + 3 * cos 20) ÷ 1.5
This is approximately 0.000 6 m/s^2 we know the x and y components, let’s determine the force and acceleration.
Force = √[(4 – 3 sin 20)^2 + (2.82 + 3 cos 20)^2]
This is approximately 3 N
a = √[(4 – 3 sin 20)^2 + (2.82 + 3 cos 20)^2] ÷1.5
This is approximately 2 m/s^2.

F(xcomponent) = (5.0  1.0  3.0 sin20) N
Acc (xcomponent) = (5.0  1.0  3.0 sin20 ) N / (1.5 g) = 1.98 m/s² towards positive xdirection
F(ycomponent) = (2.82  3.0 cos20) N
Acc (xcomponent) = (2.82  3.0 cos20) N / 1.5 kg = 6.15 x 10⁻⁴ m/s² towards positive ydirection