Question

There are two forces on the 2 kg box in the overhead view of the following figure, but only one is shown. For F1=20N, a= 12 m/s2 and θ= 30◦, find the second force (a) in unit-vector notation and as (b) a magnitude and (c) an angle relative to the positive direction of the x axis.

Answer 1

Answer:

second force = 32.784

Magnitude =$\sqrt{32.784$

θ = -90°

Explanation:

a)

Fnet = ma

F1 + F2 = ma

20N + F2 = 2(12 × cos30° + 12 ×sin30°)

F2 = 2 × 12 ( sin 30° + cos 30°)

    = 24 × ( 1 + √3 )÷ 2

  =12 (1 +√3 )

  = 32.784

b) $\sqrt{12(1 +\sqrt{3}}$

= $\sqrt{12 ( 1+ 1.732)}$

= $\sqrt{12 (2.732)}$

= $\sqrt{32.784}$  

c)

θ = 30° + 180°

θ = 210°

210° - 300°

θ = -90°