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3 years ago

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In an arcade game a 0.117 kg disk is shot across a frictionless horizontal surface by compressing it against a spring and releas

ing it. If the spring has a spring constant of 194 N/m and is compressed from its equilibrium position by 7 cm, find th

1 answer:

Illusion [34]3 years ago

3 0

Find the speed with which the disk slides across the surface

Answer:

$\boxed{2.85 m/s}$

Explanation:

The Potential energy of spring is transformed to kinetic energy hence

$0.5kx^{2}=0.5mv^{2}\\kx^{2}=mv^{2}\\v=\sqrt{\frac {kx^{2}}{m}}$

Here k is the spring constant, x is the extension of spring, v is the velocity of disk and m is the mass of the disk.

Substituting 0.117 Kg for m, 194 N/m for k and 0.07 m for x then

$v=\sqrt{\frac {194\times 0.07^{2}}{0.117}}=2.850401081 m/s\approx \boxed{2.85 m/s}$

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Answer:

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Explanation:

Refer to the not-to-scale diagram attached. The circle is the cross-section of the sphere that goes through the center C. Draw a line that connects the top of the building (point B) and the camera on the robot (point D.) Consider: at how many points might the line intersects the outer rim of this circle? There are three possible cases:

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$\displaystyle r = \frac{c}{2\pi} = \rm \frac{4\times 10^{7}\; m}{2\pi}$ .

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$\rm DC = \rm \left(1.75 \displaystyle + \frac{4\times 10^{7}\; m}{2\pi}\right)\; m$ ;
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In the two right triangles $\triangle\mathrm{DAC}$ and $\triangle \rm BAC$ , the value of $\angle \mathrm{B\hat{C}A}$ and $\angle \mathrm{A\hat{C}D}$ can be found using the inverse cosine function:

$\displaystyle \angle \mathrm{B\hat{C}A} = \cos^{-1}{\rm \frac{AC}{BC}}$

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