• Toronto Metropolitan University

• PCS 211

Check the name of your professor: Read the following attentively • This test consists of 15 multiple-choice questions. • Each question is out of 2 points. In order to score 2 points, you should both select a correct answer and reasonably justify your selection in the space provided with maximum clarity and detail. If you only select a correct answer without meaningful justification you can only score 1 point. • For the multiple-choice questions select the option that is closest to the correct answer. Circle it in this booklet and fill in the appropriate bubble on the bubble sheet. The bubbles must be filled using a pencil. • This is a closed book test; pens, pencils, erasers, calculators (Sharp EL-546 and the Casio FX-991 only) and your Ryerson University ID are the only allowed items on your desk. • Show all your work in this booklet. We will check your work for all questions, and if your choice is not justified by the work done on this booklet, credit will not be given. • All electronic devices INCLUDING WATCHES must be turned off and placed out of reach. • Coats, jackets and bags must be placed out of reach (under the seats). • Your TMU photo ID must be on your desk at all times. Perform ALL your calculations to an accuracy of 5 significant figures and provide your final answer to an accuracy of 3 significant figures. Sign here to signify you read the instructions Please Print Clearly: Student: Last Name First Name Student Number: _ _ Section: Please insert in the circle the initial of your last name 2 1. An intravenous saline drip has 9.00 g of sodium chloride per liter of water. By definition, . Express the salt concentration in kg/m3 . a) 18.00 kg/m3 b) 9.00 kg/m3 c) 90.0 kg/m3 d) 0.90 kg/m3 e) 1.80 kg/m3 Solution: 3 3 3 g 1 kg 1 L 1 mL 100 cm 9.0 g/L 9.0 9.0 kg/m L 1000 g 1000 mL 1 cm 1 m         =   =               2. The energy of a particle moving with a speed of 10 m/s can be calculated using the equation: E = p2 /(2m) , where p = mv, m is the mass of the particle, and v is the speed. You can find that the dimension of energy is [E] = M∙L2 ∙T-2 and the corresponding SI unit is Joule: J = kg∙m2 ∙s-2. In the case of a particle moving with a speed greater than 10% of the speed of light this equation becomes inaccurate and should be replaced by an equation (derived by Albert Einstein) containing the speed of light c. Which is that equation? a) E = pc + mc b) E2 = pc2 + mc2 c) E2 = p2 c2 + m2 c4 d) E = p2 c + mc2 e) E = p2 c2 + m2 c4 Solution: Only equation (c) is dimensionally correct with the same dimension of the energy as in the equation E = p2 /(2m). 3. Five employees were told to measure the length of a hallway. Each of them performed the measurement independently from the others. This group produced 5 independent measurements: 4.402 m, 4.217 m, 4.345 m, 4.372 m, 4.289 m. What is the best estimate of the length of the hallway using all five independent measurements? a) L = 4.33 ± 0.3 m b) L = 4.43 ± 0.25 m c) L = 4.325 ± 0.073 m d) L = 4.425 ± 0.104 m Solution: The best estimate of the length of the hallway is L = 4.325 ± 0.073 m because this is the average and standard deviation of the individual measurements. This option is also properly rounded. 3 4. Three ropes support the lamp of weight W as shown in the figure. Find the force developed in the cable AD for equilibrium. Given: W = 800 N; b = 4 m; a = 4 m; c = 2 m a) 400 N b) 600 N c) 800 N d) 1000 N e) 1200 N Solution: ?????? = ??√??2 + ??2 + ??2 ?? = 800 ?? ∙ 6 4 = 1200 ?? 5. A skater moving to the left on the frictionless ice at 8.0 m/s hits a 5.0-m-wide patch of rough ice. The skater slows steadily, then continues on at 6.0 m/s. What is the acceleration on the rough ice? a) 0.20 m/s2 to the right b) 0.20 m/s2 to the left c) 1.00 m/s2 to the right d) 2.80 m/s2 to the right e) 2.80 m/s2 to the left Solutio