Answer to Question #149424 in Mechanical Engineering for Smith

Question

Some forces act on an object with a mass of 20 kg, as shown in the figure below.
Determine the object’s acceleration.

Answer 1

$Fb = 2 j N$

$Fa = Fa cos\theta - Fb sin\theta = 3 x cos30 i - 3 x sin30 j = 2.59 i - 1.5 j$

$Fnet = Fa + Fb = 2 j + 2.59 i - 1.5 j = 2.59 i + 0.5 j$

$Fnet = sqrt [ 2.59 x 2.59 + 0.5 x 0.5 ] = 2.64 N$

$Fnet = ma = 2.64 N$

$a = 2.64/m = 2.64/2 = 1.32 m/s^2$

$Hence, a = 1.32 m/s^2$