Physics 4C Spring 2017 Test 1

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1 Physics 4C Spring 017 Test 1 Name: April 19, 017 Please show your work! Answers are not complete without clear reasoning. When asked for an expression, you must give your answer in terms of the variables given in the question and/or fundamental constants, including g. Answer as many questions as you can, in any order. Calculators are allowed. Books, notes, and internet-connected devices are not allowed. Use any blank space to answer questions, but please make sure it is clear which question your answer refers to. g = 9.8 ms atmospheric pressure P 0 = Pa density of water ρ w = 1000 kg/m 3 sin θ + cos θ = 1 sin(θ) = sin(θ) cos(θ) cos(θ) = cos θ sin θ sin(α ± β) = sin α cos β ± cos α sin β cos(α ± β) = cos α cos β sin α sin β cos α cos β = 1 [cos(α β) + cos(α + β)] sin α sin β = 1 [cos(α β) cos(α + β)] sin α cos β = 1 [sin(α + β) + sin(α β)] sin ( θ + π ) = cos θ cos ( θ + π ) = sin θ sec θ := 1 cos θ csc θ := 1 sin θ cot θ := 1 tan θ Trigonometric Identities 1

2 1. The gravitational force exerted on a solid object is F 1. A cylindrical container with cross sectional area A holds a liquid of density ρ which has a depth h. Now consider, the object is suspended from a spring scale and submerged into the liquid in the container and the scale reads F (see figure). The atmospheric pressure is P 0. scale and submerged in water, the scale reads 3.50 N (Fig. P14.6). Find the density of the object. Scale a (a) Find the volume of the object. [4 pts] Figure P14.6 Problems 6 and A 10.0-kg block of metal measuring 1.0 cm by 10.0 cm by 10.0 cm is suspended from a scale and immersed in water as shown in Figure P14.6b. The 1.0-cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water. (a) What are the magnitudes of the forces acting on the top and on the bottom of the block due to the surrounding water? (b) What is the reading of the spring scale? (c) Show that the buoyant force equals the difference between the forces at the top and bottom of the block. 8. A light balloon is filled with 400 m 3 of helium at atmospheric pressure. (a) At 0 C, the balloon can lift a pay- W load of what mass? (b) What If? In Table 14.1, observe that the density of hydrogen is nearly half the density of helium. What load can the balloon lift if filled with hydrogen? b (b) Find the absolute pressure at the very bottom of the container of liquid. [4 pts]

sure the flow rate of gasoline (r 5 7.00 3 10 kg/m 3 ) through a hose having an outlet radius of 1.0 cm. If an open top,. conwater can drain the pipe1.0 has akpa density and ρ.

through a section 1 P of pipe. 5 The fluid eter 6.60 cm. The A and the is outlet.40 has cm, a cross find sectional (a) the speed area a.

3 sure the flow rate of gasoline (r kg/m 3 ) through a hose having an outlet radius of 1.0 cm. If an open top,. conwater can drain the pipe1.0 has akpa density and ρ. the The radius inlet toof the the Venturi inlet tube tube has to the a cross meter sectional area the difference in pressure is measured to be P A Venturi tube is used to measure the flow rate through a section 1 P of pipe. 5 The fluid eter 6.60 cm. The A and the is outlet.40 has cm, a cross find sectional (a) the speed area a. of If the pressure gasoline atas the it inlet leaves is measured.0 cm. A rubber to be P 1, and the the hose volume and rate (b) of the flowfluid through flow the rate tube in is cubic r, findmeters an expression per for P, The water level in the pressure second. at the outlet. [8 pts] zzle. (a) Calculate per by the nozzle. P 1 P ass of water flows te the gauge presse just behind the nd by plugging a with his finger. If e of the North Sea e force on his finf the hole, during d water fill 1 acre he hole remained h a mass flow rate nd. (a) Show that Figure P Review. Old Faithful Geyser in Yellowstone National Park erupts at approximately one-hour intervals, and the height of the water column reaches 40.0 m (Fig. P14.50). (a) Model the rising stream as a series of separate droplets. Analyze the free-fall motion of Q/C. (b) Each hydrom takes in water at ht of 87.0 m. The er is converted to 85.0%. How much ic unit produce? rado River to supon the rim of the of 564 m, and the m. Imagine that long pipe 15.0 cm p at the bottom sure at which the Figure P14.50 Videowokart/Shutterstock.com 3

4 3. Consider a siphon being used in air with atmospheric pressure P 0. Let ρ be the density of water. (a) In terms of the constants shown in the diagram, give an expression for the speed of the water as it emerges from the tube. You may assume that the cross sectional area of the container of water is very large. [4 pts] (b) Find an expression for the pressure in the tube at point B. [4 pts] (c) Will changing the value of h 1 affect the flow of the water through the tube, or can h 1 take any (positive) value? Explain your reasoning. [3 pts] (d) Suppose the cross sectional area of the container of liquid is α and the cross sectional area of the tube is a (α >> a). Let x be the height of the water s surface above the end of the siphon at time t. Then dx is the rate of change of dt height of water in the tank. Find a differential equation for dx, but you do not dt need to solve it. You may use your answer to part (a) if it is useful. [3 pts] 4

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Physics 4B Winter 2018 Test 2

Physics 4B Winter 2018 Test 2 Physics 4B Winter 018 Test Name: Feb 15, 018 Please show your work! Answer as many questions as you can, in any order. Calculators are allowed. Books, notes, and internet connected devices are not allowed.