Phys2A_F07_Lecture_14b

Phys2A_F07_Lecture_14b - Example: A Block on a Vertical...

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W. P. Beyermann Fall 2007 1 y x A 3.0 kg block is pressed against a vertical wall by a force that makes an angle of 30° from the horizontal. The kinetic coefficient of friction between the block and wall is 0.40. What magnitude of force is being applied if the block is sliding down the wall with an acceleration of 2.0 m/s 2 ? a F Example: A Block on a Vertical Wall with Friction G a F G w G Weight 3 kg 30° w G f G Friction n G Normal f G n G net F G ax F ay F
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W. P. Beyermann Fall 2007 2 x x x x ax x x net ma w n f F F F = + + + = = ) ( y y y y ay y y net ma w n f F F F = + + + = = ) ( From the free-body diagram θ cos a ax F F = sin a ay F F = n n x = 0 = y n 0 = x w 0 = x f mg w w y = = n f k y μ = 0 = x a 2 m/s 0 . 2 = y a (1) (2) 0 0 0 cos = + + + n F a cos a F n = (3) Eq. (1) becomes
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W. P. Beyermann Fall 2007 3 Eq. (2) becomes y k a ma mg n F = + + 0 sin μ θ (4) Two unknowns, F a & n , and two Eqs. Substituting Eq. (3) into Eq. (4) yields y a k a ma mg F F = + cos sin Solving for F a ) ( ) cos (sin g a m F y k a + = + θμ cos sin ) ( k y a g a m F + + = N 28 ) 30 cos( 40 . 0 ) 30 sin( ) m/s 8 . 9 m/s 2.0 kg( 0 . 3 2 2 = + + = D D a F
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W. P. Beyermann Fall 2007 4 Conceptual Example Rank in order from largest to smallest, the size of the friction forces for these different situations. The box and floor are made of the same materials in all cases. 0 = > = = > a e d c b f f f f f G G G G G
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W. P. Beyermann Fall 2007 5 You and a friend have just loaded a 200 kg crate filled with priceless art objects into the back of a 2000 kg truck. As you start to accelerate, the force , which is the static frictional force of the earth pushing back on the truck, propels the truck forward. The static coefficient of friction between the truck and the crate is 0.8, and rolling friction is negligible. What is the maximum magnitude of F T that will keep the crate from slipping?
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This note was uploaded on 04/07/2008 for the course PHY 2A taught by Professor Beyermann during the Fall '08 term at UC Riverside.

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Phys2A_F07_Lecture_14b - Example: A Block on a Vertical...

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