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phy131studiof15:lectures:m2f15info [2015/11/03 15:47] mdawber [Question 2 Solutions (23.7/35)] |
phy131studiof15:lectures:m2f15info [2015/11/03 15:52] mdawber [Question 2 Solutions (23.7/35)] |
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Now as this is the same distance the rope travels while the force $F$ is applied to it, the work done by $F$ is | Now as this is the same distance the rope travels while the force $F$ is applied to it, the work done by $F$ is | ||

- | $W=Fd=7.5\times\0.5=3.75\,\mathrm{J}$ | + | $W=Fd=7.5\times0.5=3.75\,\mathrm{J}$ |

Alternatively you could compute the change in kinetic energy of both the pulley and the object and the change in the potential energy of the object. The sum of these is equal to the work done by $F$. | Alternatively you could compute the change in kinetic energy of both the pulley and the object and the change in the potential energy of the object. The sum of these is equal to the work done by $F$. | ||

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$W=\frac{1}{2}\times\frac{1}{2}\times0.3\times0.15^2\times(\frac{2}{0.15})^2+\frac{1}{2}\times0.5\times2^2+0.5\times9.8\times0.5=3.75\,\mathrm{J}$ | $W=\frac{1}{2}\times\frac{1}{2}\times0.3\times0.15^2\times(\frac{2}{0.15})^2+\frac{1}{2}\times0.5\times2^2+0.5\times9.8\times0.5=3.75\,\mathrm{J}$ | ||

- | (e) (5 points) Once the object has reached a constant speed of $2\,\mathrm{ms^{-1}}$ what force should I apply to the rope maintain that constant speed. | + | E. (5 points) Once the object has reached a constant speed of $2\,\mathrm{ms^{-1}}$ what force should I apply to the rope maintain that constant speed. |

- | (f) (5 points) What is the angular velocity (in rpm) of the pulley while I am raising the object with a constant speed of $2\,\mathrm{ms^{-1}}$? | + | If the pulley is not accelerated the tension in the rope attached to the object must be the same as that in the rope on the other side. As the object is not accelerating |

- | (g) (5 points) What is the angular momentum of the pulley while I am raising the object with a constant speed of $2\,\mathrm{ms^{-1}}$? Give both the magnitude and the direction (ie. left, right, up, down, in to the page, out of the page). | + | $T=mg$ |

+ | | ||

+ | so | ||

+ | | ||

+ | $F=mg=0.5\times9.8=4.9\,\mathrm{N}$ | ||

+ | | ||

+ | F. (5 points) What is the angular velocity (in rpm) of the pulley while I am raising the object with a constant speed of $2\,\mathrm{ms^{-1}}$? | ||

+ | | ||

+ | $\omega=\frac{v}{r}=\frac{2}{0.15}=13.33\,\mathrm{s^{-1}}$ | ||

+ | | ||

+ | To convert to rpm | ||

+ | | ||

+ | $\frac{13.33\times60}{2\pi}=127.3\,\mathrm{rpm}$ | ||

+ | | ||

+ | G. (5 points) What is the angular momentum of the pulley while I am raising the object with a constant speed of $2\,\mathrm{ms^{-1}}$? Give both the magnitude and the direction (ie. left, right, up, down, in to the page, out of the page). | ||

+ | | ||

+ | $L=I\omega=\frac{1}{2}mr^{2}\omega=\frac{1}{2}\times0.3\times(0.15)^{2}\times13.33=.045\,\mathrm{kgm^{2}s^{-1}}$ | ||

+ | | ||

+ | Out of page from right hand grip rule. | ||