Answer to Question #149424 in Mechanical Engineering for Smith

Question #149424
Some forces act on an object with a mass of 20 kg, as shown in the figure below.
Determine the object’s acceleration.
1
Expert's answer
2020-12-08T02:41:52-0500

Fb=2jNFb = 2 j N

Fa=FacosθFbsinθ=3xcos30i3xsin30j=2.59i1.5jFa = Fa cos\theta - Fb sin\theta = 3 x cos30 i - 3 x sin30 j = 2.59 i - 1.5 j

Fnet=Fa+Fb=2j+2.59i1.5j=2.59i+0.5jFnet = Fa + Fb = 2 j + 2.59 i - 1.5 j = 2.59 i + 0.5 j

Fnet=sqrt[2.59x2.59+0.5x0.5]=2.64NFnet = sqrt [ 2.59 x 2.59 + 0.5 x 0.5 ] = 2.64 N

Fnet=ma=2.64NFnet = ma = 2.64 N

a=2.64/m=2.64/2=1.32m/s2a = 2.64/m = 2.64/2 = 1.32 m/s^2

Hence,a=1.32m/s2Hence, a = 1.32 m/s^2


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