212-SampleSolnW18.pdf

# F m a and in doing so will use path coordinates to

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F = m a and in doing so will use path coordinates to represent a . Then write what is given ( GIVEN =radius, angle, constant speed, lateral friction=0) and what is to be found ( FIND =speed). Finally, list any ASSUMPTIONS . Step 2: Write an equation, in vector form if possible, for the required unknown(s). Since we actually want to find the speed, we will use the acceleration equation in path coordinates: a = a t e t + a n e n = v e t + v 2 ρ e n Step 3: Count the number of non-trivial scalar equations and the number of scalar unknowns. That vector equation represents 2 scalar equations ( a t = v , a n = v 2 / ρ ) but the first ( a t = v ) is trivial because v =0. Thus, we have 1 non-­‐trivial equation a n = v 2 / ρ (1) with 2 unknowns ( a n , v 2 ). Step 4: Repeat steps 2-3 to find scalar unknowns until the number of non-trivial scalar equations from step 2 balances the number of non-trivial unknowns from step 2. We now use Newton’s 2 nd law, so we first want to drawa FBD and a Kinetic diagram (KD) with a coordinate system to represent F = m a as follows.

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Let’s assume the car is moving out of the page in the + k direction. Relating the unit vectors gives e n = i , e t = k .
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• Spring '05
• staff
• Force, Velocity, Euclidean vector, scalar equations, non-trivial scalar equations

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