Archive for December, 2010

Physics Friday 149

December 31, 2010

For a block sliding down an inclined surface with angle of incline θ and with coefficient of kinetic friction μ. If we consider the forces, we see that the block can slide down the incline with constant velocity when the net forces are zero. Balancing forces perpendicular to the plane, the normal force is thus N=mg\cos\theta. The kinetic friction is thus f=\mu{N}=\mu{mg}\cos\theta, while the component of gravity parallel to the plane is thus mg\sin\theta. We see that these cancel when
\mu\cos\theta=\sin\theta, or when \mu=\tan\theta.

Now, suppose we have a large incline with \mu=\tan\theta, and we start our block sliding with a velocity v0 in a horizontal direction; that is to say, along the plane in a direction perpendicular to the direction of the slope. What, then, will be the speed a long time later?
Answer:

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Monday Math 148

December 27, 2010

Find I=\int_{-1}^{1}\int_{\frac{x^2}2+x-\frac12}^{-\frac{x^2}2+x+\frac12}\frac{x^5-y^3}{x^2+y^2}\,dy\,dx.
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Physics Friday 148

December 24, 2010

A thin bimetallic strip of thickness d is straight at a temperature T0, with length L0. The two metals have coefficients of linear thermal expansion α1 and α2, with α2>α1. If the temperature is raised to a temperature T not significantly greater than T0, what is the angle θ through which the strip bends?
Solution:

Total Lunar Eclipse Monday Night

December 20, 2010

Update Sunday: This post was supposed to be pre-scheduled for tomorrow (Monday), but I hit the wrong button.

Here is NASA’s page on the total lunar eclipse tonight, which should be visible throughout North America. The moment of greatest eclipse will be at 08:16:57 UT (that’s 11:16 PM for my fellow Alaskans and me); the penumbral eclipse begins at 05:29 UT and ends at 11:04 UT

Monday Math 147

December 20, 2010

Given two non-zero complex numbers z1 and z2 such that \left|z_1+z_2\right|=\left|z_1-z_2\right|, show that the arguments of z1 and z2 differ by π/2.
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Go and Read

December 19, 2010

Go and read this:
Finally, A Hamas Leader Admits That Israel Killed Mostly Combatants In Gaza” by Alan M. Dershowitz

The key point:

The Israel Defense Force put the total number of known combatants killed at 709 and the number of known civilian deaths at 295, with 162 (mostly men of fighting age) “unknown.” Such a ratio, if true, would be far better than that achieved by any other nation in a comparable conflict. Not surprisingly, Israel’s enemies initially disputed this ratio and claimed that the number of combatants killed was far lower and the number of civilians far higher. The United Nations, the Goldstone Report, various “human rights” organizations and many in the media automatically rejected Israel’s documented figures, preferring the distorted numbers offered by Hamas’ and other Palestinian sources.

But a statement recently made by a Hamas leader confirms that Israel was correct in claiming that approximately 700 combatants were killed.

Micro-credit

December 19, 2010

The BBC News reports on the epidemic of suicides and stress-related deaths in southeast India due to pressure arising from inability to repay micro-loans. According to the article, the government of the Indian state of Andhra Pradesh is reporting over eighty suicides in the past few months after defaulting on loans from micro-finance companies. Further, banks have stopped lending to the micro-credit institutions due to fears that large portions of the money loaned may be unrecoverable, in a situation similar to the subprime mortgage crisis.
So, it seems that micro-credit hasn’t lived up to all the talk about how it would help the poor improve their lives

More from Mexico

December 19, 2010

Continuing in the vein of this post, another Huffington Post report from Mexico: Mexico Mom Killed Demanding Justice For Slain Teen Daughter.

The brutal killing of activist Marisela Escobedo Ortiz stunned people across Mexico, and a group of women angrily demanding justice gathered outside the state prosecutors’ office in this border city, where the victim’s daughter was killed.

Escobedo’s slaying “shows that in Mexico, it is the victim who suffers,” anti-crime activist Alejandro Marti said.

The uproar resulted in the suspension of three state judges who had ordered the freeing of the main suspect in the slaying of Escobedo Ortiz’s daughter – the same man who was identified as a chief suspect in the mother’s death.

Prison Break (no, not the TV show)

December 19, 2010

141 inmates have escaped a Mexican prison near the border with Laredo, Texas; authorities suspect that prison employees helped. According to the Huffington Post:

The public safety department of Tamaulipas state, where the prison is located near the border with Laredo, Texas, said 141 inmates got out through a service entrance used by vehicles, “presumably with the assistance of the prison staff.”

The department said the prison’s director could not be located, adding that he and other officials were under investigation.

Eighty-three of the prisoners were being held for trial or had been convicted of crimes like theft, assault and other state offenses, while 58 were being held on federal charges, which include weapons possession and drug trafficking.

Here’s one for the holidays

December 19, 2010

Christmas trees depress religious minorities, LiveScience reports.

When people who did not celebrate Christmas or who did not identify as Christian filled out surveys about their moods while in the same room as a small Christmas tree, they reported less self-assurance and fewer positive feelings than if they hadn’t been reminded of the holiday, according to a new study.

The university students didn’t know the study was about Christmas, said study researcher Michael Schmitt, a social psychologist at Simon Fraser University in British Columbia, Canada. Nonetheless, he said, the presence of the tree caused non-celebrators and non-Christians to feel subtly excluded.

“Simply having this 12-inch Christmas tree in the room with them made them feel less included in the university as a whole, which to me is a pretty powerful effect from one 12-inch Christmas tree in one psychology lab,” Schmitt told LiveScience.