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3 years ago

two vectors have a magnitude of 2.5km and 6.5 km . Predict the maximum and minimum magnitudes of their resultant vector

1 answer:

8 0

The maximum magnitude of their resultant vector is when the two vectors are parallel and in the same direction, so they lie on the same axis. In this case, the magnitude of their resultant vector is simply the sum of the two magnitudes:

$R=2.5 km+6.5 km=9.0 km$

The minimum magnitude of their resultant vector is when the two vectors are parallel but in opposite direction. In this case, the magnitude of their resultant vectors is just the difference between the two magnitudes:

$R=6.5 km-2.5 km=4.0 km$

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The equation representing Young's Modulus is:

$Y=\frac{F/A}{\Delta l/l}=\frac{Fl}{A\Delta l}$

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Y = Young's Modulus

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g = acceleration due to gravity = $9.81m/s^2$

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r = radius of the wire = $\frac{d}{2}=\frac{1.6mm}{2}=0.8mm=8\times 10^{-4}m$ (Conversion factor: 1 m = 1000 mm)

$\Delta l$ = change in length = 1.99 mm = $1.99\times 10^{-3}m$

Putting values in above equation, we get:

$Y=\frac{10\times 9.81\times 2.6}{(3.14\times (8\times 10^{-4})^2)\times 1.99\times 10^{-3}}\\\\Y=6.378\times 10^{10}N/m^2$

Hence, the Young's modulus for the wire is $6.378\times 10^{10}N/m^2$

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