# What is the value of ax the x-component of the object’s acceleration?

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?

b) What is the value of ay, the y-component of the object’s acceleration?

• 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.

• 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