A vector A⃗ has a magnitude of 40.0 m and points in a direction 20.0∘ below the positive x axis. A second vector, B⃗, has a magn
1 answer:
The magnitude of the vector C is 96.32m
<h3>How to solve for the magnitude of vector c</h3>
Ax = AcosθA
= 40 cOS 20
= 37.59
Ay = AsinθA
-40sin20
= -13.68
Bx = B cos θ B
= 75Cos50
= 48.21
By = BsinθB
= 75sin50
= 57.45
Cx = AX + Bx
= 37.59 + 48.21
= 85.8
Cy = Ay + By
= -13.65 + 57.45
= 43.77
The magnitude is solved by
|c| =
= √85.8² + 43.77²
= 96.32m
The magnitude of the vector c is 96.32m
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The downward acceleration of the solid cylinder at the given tension in the string is determined as 2Tr/MR.
<h3>Downward acceleration of the cylinder</h3>
The downward acceleration of the solid cylinder is determined from the principle of conservation of angular momentum as shown below;
Iα = Tr
where;
- I is moment of inertia of the solid cylinder
- α is angular acceleration of the cylinder
- T is tension in the string
- r is length of the string
α = Tr/I
where;
- a is the downward acceleration of the solid cylinder
- R is radius of the cylinder
Thus, the downward acceleration of the solid cylinder at the given tension in the string is determined as 2Tr/MR.
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