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Strike441 [17]
3 years ago
5

A horizontal 803-N merry-go-round is a solid disk of radius 1.41 m and is started from rest by a constant horizontal force of 49

.7 N applied tangentially to the edge of the disk. Find the kinetic energy of the disk after 2.90 s.
Physics
1 answer:
Slav-nsk [51]3 years ago
5 0

Answer:

The kinetic energy of the disk is 254.4 J.

Explanation:

The kinetic energy of the disk is given by:

K = \frac{1}{2}I \omega^{2}

The moment of inertia of the solid disk is:

I = \frac{1}{2}mr^{2}

The mass is:

m = \frac{P}{g}

I = \frac{Pr^{2}}{2g} = \frac{803 N*(1.41 m)^{2}}{2*9.81 m/s^{2}} = 81.4 kgm^{2}

Now, we need to find the angular acceleration as follows:

\tau = I \alpha

Also, the torque is related to the tangential force:

\tau = F\times r

F\times r = I \alpha

\alpha = \frac{F \times r}{I} = \frac{49.7 N*1.41 m}{81.4 kg*m^{2}} = 0.86 rad/s^{2}

Now, we can find the angular speed:

\omega_{f} = \omega_{i} + \alpha t  

\omega_{i} = 0 since it is started from rest  

\omega_{f} = 0.86 rad\s^{2}*2.90 s = 2.50 rad/s

Finally, the kinetic energy of the disk is:

K = \frac{1}{2}I \omega^{2} = \frac{1}{2}81.4 kgm^{2}*(2.50 rad/s)^{2} = 254.4 J

Therefore, the kinetic energy of the disk is 254.4 J.

I hope it helps you!                                                                                                  

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