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solution_pdf - chaney(glc568 Review and Motion in 1D...

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chaney (glc568) – Review and Motion in 1D – murthy – (21118) 1 This print-out should have 27 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A gram is what part of a kilogram? 1. 0.01 2. 0.5 3. 0.001 correct 4. 0.1 Explanation: 002 10.0 points Liquid volume can best be measured in 1. grams. 2. cubic centimeters. 3. liters. correct 4. meters. Explanation: 003 10.0 points Which unit would be best for filling your gas tank? 1. liters correct 2. meters 3. milliliters 4. kiloliters Explanation: /* If you use any of these, fix the comment symbols. 004 10.0 points What would equal 10 km? 1. 1000 m 2. 100 m 3. 10,000 m correct 4. 100,000 m Explanation: (10 km) · 1000 m 1 km = 10000 m 005 (part 1 of 4) 10.0 points It is given that r and s are distances with unit [L], t is a time with unit [T] and θ is an angle in radians. What are the required dimensions for the quantity c in the expression s = c t 1. [ c ]=[L]/[T] correct 2. [ c ]=[L 2 ] 3. [ c ]=1/[T] 4. [ c ]=[L] [T] 5. [ c ]=1/[L] 6. [ c ]=[T]/[L] 7. [ c ]=[L]/[T 2 ] 8. [ c ]=[T] 9. [ c ]=[L] 10. [ c ]=[L] [T 2 ] Explanation: c = s t = [ c ] = [ s ] [ t ] = [ L ] / [ T ] . 006 (part 2 of 4) 10.0 points
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chaney (glc568) – Review and Motion in 1D – murthy – (21118) 2 What are the required dimensions for the quantity c in the expression s = c t 2 1. [ c ]=1/[T] 2. [ c ]=[L] 3. [ c ]=[L]/[T] 4. [ c ]=[L 2 ] 5. [ c ]=[T]/[L] 6. [ c ]=[T] 7. [ c ]=[L] [T 2 ] 8. [ c ]=1/[L] 9. [ c ]=[L] [T] 10. [ c ]=[L]/[T 2 ] correct Explanation: c = s t 2 = [ c ] = [ s ] [ t 2 ] = [ L ] / [ T 2 ] . 007 (part 3 of 4) 10.0 points What are the required dimensions for the quantity c in the expression s = r cos( c t ) 1. [ c ]=[L]/[T] 2. [ c ]=[L]/[T 2 ] 3. [ c ]=1/[T] correct 4. [ c ]=1/[L] 5. [ c ]=[L] [T 2 ] 6. [ c ]=[L] 7. [ c ]=[L 2 ] 8. [ c ]=[T]/[L] 9. [ c ]=[T] 10. [ c ]=[L] [T] Explanation: The argument of a triangular function is dimensionless (radians), and the result of the triangular function is also dimensionless. For the equation s = r cos( c t ), we have [ c ] = 1 [ t ] = 1 / [ T ] . 008 (part 4 of 4) 10.0 points What are the required dimensions for the quantity c in the expression θ = s c 1. [ c ]=[L]/[T 2 ] 2. [ c ]=[T]/[L] 3. [ c ]=[L]/[T] 4. [ c ]=1/[T] 5. [ c ]=[T] 6. [ c ]=[L 2 ] 7. [ c ]=[L] [T] 8. [ c ]=1/[L] 9. [ c ]=[L] correct 10. [ c ]=[L] [T 2 ] Explanation:
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chaney (glc568) – Review and Motion in 1D – murthy – (21118) 3 c = s θ = [ c ] = [ s ] [ θ ] = [ L ] . 009 10.0 points This problem shows how dimensional analysis helps us check our work and sometimes even help us find a formula. A rope has a cross section A = 12 m 2 and density ρ = 2430 kg / m 3 . The “linear” density of the rope μ , is defined to be the mass per unit length, in the form μ = ρ x A y . Based on dimensional analysis, find the powers x and y . 1. x = - 2 , y = 1 2. x = 1 , y = 2 3. x = - 1 , y = 1 4. x = - 2 , y = 2 5. x = 1 , y = 1 correct 6. x = - 2 , y = - 1 7. x = - 1 , y = - 1 8. x = - 1 , y = 2 9. x = 1 , y = - 1 Explanation: Kilogram (kg): a unit of mass ( M ). Meter (m): a unit of length ( L ). [ x ] means ”the units of x ”. The units of both sides of any equation must be the same for the equation to make sense. The units of the left hand side (LHS) are given as [ μ ] = M L = ML - 1 and the right hand side has [ ρ x A y ] = parenleftbigg M L 3 parenrightbigg x × ( L 2 ) y = M x L - 3 x L 2 y = M x L 2 y - 3 x The powers on the units of mass and length need to be the same as for the LHS above, so x = 1 2 y - 3 x = - 1 2 y = - 1 + 3 = 2 y = 1 Thus the answer is ( x, y ) = (1 , 1).
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