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exam_1_eqsheet_Fall06

# exam_1_eqsheet_Fall06 - t = 0 respectively • Freely...

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Some Equations for Exam 1 sin 30 = 1 2 = 0 . 50; cos 30 = 3 / 2 = 0 . 87 sin 60 = 3 / 2 = 0 . 87; cos 60 = 1 2 = 0 . 50 sin 45 = 2 / 2 = 0 . 71; cos 45 = 2 / 2 = 0 . 71 For vectors A = A x ˆ i + A y ˆ j + A z ˆ k and B = B x ˆ i + B y ˆ j + B z ˆ k : | A | = A = A 2 x + A 2 y + A 2 z ; A · B = AB cos θ = A x B x + A y B y + A z B z ; A × B = ( A y B z - A z B y ) ˆ i + ( A z B x - A x B z ) ˆ j + ( A x B y - A y B x ) ˆ k ; | A × B | = AB sin θ . For a function of the form f ( x ) = ax n , where n is an integer, df dx = nax n - 1 and f ( x ) dx = a n + 1 x n +1 + C . If a particle’s position is represented by r = r ( t ), v = d r dt and a = d v dt = d 2 r dt 2 . Therefore, v x ( t ) = a x ( t ) dt + C and x ( t ) = v x ( t ) dt + C , and similarly for y - and z -components. For a constant acceleration a , r ( t ) = r 0 + v 0 t + 1 2 a t 2 and v ( t ) = v 0 + a t where r 0 and v 0 are the position and velocity at time
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Unformatted text preview: t = 0, respectively. • Freely falling objects near the Earth’s surface accelerate downwards with g = 9 . 8 m/s 2 . For this exam , use the approximation that g = 10 m / s 2 . • Newton’s Second Law: F = m a . • Static friction: f s ≤ μ s N ; kinetic friction: f k = μ k N (where N is the magnitude of the normal force)....
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