Check the attached file for the answer.
Solve for x and y algebraically:x + y = 8 and 3x + 2y = 21
2 answers:
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Answer:
the block that starts moving first is block A , fr = 1.625 N , fr = 1.5 N
Explanation:
For this exercise we use Newton's second law, for which we take a reference system with the x axis parallel to the plane and the y axis perpendicular to the plane
X axis
fr- Wₓ = 0
fr = Wₓ
Axis y
N- = 0
N = W_{y}
Let's use trigonometry to find the components of the weight
sin θ = Wₓ / W
Cos θ = W_{y} / W
Wₓ = W sin θ
W_{y} = W cos θ
Wₓ = 11 sin θ
W_{y} = 11 cos θ
The equation for friction force is
fr = μ N
We substitute
μ (W cos θ) = W sin θ
μ = tan θ
We can see that the system began to move the angle.
θ = tan⁻¹ μ
So the angles are
Block A θ = tan⁻¹ 0.15
θ = 8.5º
Block B θ = tan⁻¹ 0.26
θ = 14.6º
So the block that starts moving first is block A
The friction force is
Block A
fr = Wx = W sin θ
fr = 11 sin 8.5
fr = 1.625 N
Block B
fr = 6 sin 14.6
fr = 1.5 N