the forces in (Figure 1) act on a 1.5 kg object.
a) What is the value of ax the x-component of the object’s acceleration?
Express your answer with the appropriate units.
b) What is the value of ay, the y-component of the object’s acceleration?
Express your answer with the appropriate units.
2 Answers
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The x-y 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.
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F(x-component) = (5.0 - 1.0 - 3.0 sin20) N
Acc (x-component) = (5.0 - 1.0 - 3.0 sin20 ) N / (1.5 g) = 1.98 m/s² towards positive x-direction
F(y-component) = (2.82 - 3.0 cos20) N
Acc (x-component) = (2.82 - 3.0 cos20) N / 1.5 kg = 6.15 x 10⁻⁴ m/s² towards positive y-direction