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More physics help (friction)?

A block of mass m rests on a rough horizontal surface. Coefficient of friction is u. A traction F = mg acts on angle θ with the vertical slide of the block. Find da block pulled across the floor. (A) Cot θ ≥ u (b) tan θ ≥ u What are the limits of cot θ in the form of u, if the force is pushing instead of pulling? If θ is smaller than a certain angle α, can block not move no matter what force. Find α in the form of arccot u

F makes θ with the vertical. Therefore, horizontal component of F = Fsinθ and vertical component = Fcosθ After breaking F in these two elements, we find that the forces on the block is 1 Fsinθ send = mgsinθ forward 2nd Fcosθ upward = mgcosθ upward (since F = mg) 3 Friction f backwards 4th Normal force N upward 5. Weight mg downward, there is no acceleration in vertical direction. Therefore the total force in vertical direction = 0 or, mgcosθ + N-mg = 0 or N = mg-mgcosθ Or, N = mg (1-cosθ) f = Un = umg (1-cosθ) Block can be drawn when the horizontal component of F excess friction. Or, mgsinθ> umg (1-cosθ) Divide by mg sinθ> u (1-cosθ) Do we have to choose between a and b? Or a and b are two different issues?

Tan Darius – Pushing the limits

Whitbread 97-98: Pushing the Limits - $29.99 Whitbread 97-98: Pushing the Limits -

Pushing The Limits $11.1 In a new collection of incisive essays, the author of The Evolution of Useful Things offers a close-up look at a variety of major projects that set the stage for bold new challenges in engineering, art, and architecture, assessing the achievements and risks associated with pushing the limits of technology, including the collapse of the Twin Towers on September 11th.

Pushing the Limits $13 This book is in Like New condition

No Limits $9.75 A brutal crash transformed this young man who loved life, had a god job, and was engaged to be married into a bitter, brain damaged and paralyzed person who hated life until he discovered there are no limits except those we create for ourselves. Today, Al Foxx delights audiences as an award-winning stand-up comic and a national motivational speaker.The reason his disability is so popular with audiences is because everyone has had their own version of his motorcycle crash. Al says accepting your disabilities means not only accepting your limitations, but accepting responsibility for making the most of the abilities you still have. Winners don”t quit pushing the limits until there are NO LIMITS.

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Human Body Pushing The Limits (Blu-Ray) $20.66 Rated: NR Synopsis: Human Body: Pushing the Limits takes you across continents and introduces you to people who have pushed their bodies to the max. This groundbreaking program uses CGI technology and hi-tech camera work to examine their physical ordeals in vivid detail both externally and internally!

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Human Body: Pushing the Limits DVD Set $29.95 Explore the human body like you never have before in this groundbreaking series.Features:4 complete episodes2 discsHuman Body: Pushing the Limits takes you across continents and introduces you to people who have pushed their bodies to the max. Using CGI technology and hi-tech camera work, see their physical ordeals in vivid detail both externally and internally.SightSight is the king of the senses. More than 80% of what we know of the world comes through our eyes – without it we’re lost. See our vision system, in living color, from the inside out.StrengthThe human body is engineered for strength, power and endurance. Learn how bone is as sturdy as concrete but flexible enough to resist breaking.SensationBelow the skin’s surface are the antennae that allow us to sense the world around us. Learn how this vital layer is the gateway to the original information superhighway – the nervous system.Brain PowerUncover the most powerful organ in the natural world – the human brain. Learn how this central processing unit generates as many electrical impulses in a single day as all the telephones in the world put together. Human Body: Pushing the Limits takes you across continents and introduces you to people who have pushed their bodies to the max.

Human Body: Pushing the Limits – Widescreen $14.99 Computer generated imagery and cutting edge photography combine to offer unparalleled insight into the extreme capabilities of the human body in this groundbreaking series originally aired on the Discovery channel. This collection, featuring the episodes “Sight,” “Strength,” “Sensation,” and “Brain Power,” offers vivid insight into the body’s inner and outer workings. ~ Jason Buchanan, Rovi

Whitbread 97/98: Pushing The Limits (DVD) $31.18 Founded in 1972, the Whitbread Round the World Race is a prestigious yet grueling yachting competition held every four years. Travelling southeast from England into the Atlantic, Indian, and Pacific Oceans and back to its British home port via South America`s Cape Horn, the nine-month-long race exposes competitors to some of the harshest weather conditions imaginable–including 100-foot waves, 60-knot winds, and subzero temperatures–as well as the round-the-clock rigors of sailing 30,000 miles of open water. This documentary recounts the travails of the 1997-1998 Whitbread race through remarkable action footage and interviews with crew members of the winning EF Language team, including skipper Paul Cayard and sailor Magnus Olsson.