True-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 111. The exam period was 90 minutes; the average score was 90.4; the median score was 93. Click here to see page1 page2 of the formula sheet that came with the exam.

Oil (ρ_{o} = 920 kg/m^{3}) flows through a horizontal cylindrical pipe of radius R_{1} = 12 cm with a speed of v_{1} = 2 m/s. Along the flow direction the pipe widens to a radius R_{2} = 24 cm (as shown in the figure), the speed of the oil is then equal to v_{2}.

What is the speed of the water in the wide part of the pipe?

(a) v_{2} = 0.5 m/s (b) v_{2} = 1.0 m/s (c) v_{2} = 2.0 m/s (d) v_{2} = 4.0 m/s (e) v_{2} = 8.0 m/s

(a) ΔP = 660 Pa (b) ΔP = 1185 Pa (c) ΔP = 1520 Pa (d) ΔP = 1725 Pa (e) ΔP = 1950 Pa

(a) less than ΔP. (b) equal to ΔP. (c) larger than ΔP.

A block of mass 20 kg is resting on a horizontal frictionless surface and is attached to a spring with a force constant k = 270 N/m. A force of F is applied to the block in the x-direction, thereby compressing the spring from its equilibrium length by 0.2 m.

What is the magnitude of the force F?

(a) 33 N (b) 49 N (c) 54 N

(a) 0.33 sec (b) 1.71 sec (c) 2.51 sec (d) 3.69 sec (e) 4.76 sec

(a) 0.24 m/s (b) 0.73 m/s (c) 1.31 m/s (d) 1.64 m/s (e) 2.28 m/s

(a) 0.14 (b) 0.22 (c) 0.31 (d) 0.45 (e) 0.52

A 50-kg child rides on a merry-go-round that has a radius of 3 meters. When the child is 1 meter from the center, the merry-go-round spins with an angular frequency of 12 rad/s. The moment of inertia of the merry-go-round alone is I = 250 kg m^{2}.

If the child slides to the outer edge of the merry-go-round, what will the new angular velocity be?

(a) ω = 1.3 rad/s (b) ω = 5.1 rad/s (c) ω = 12 rad/s (d) ω = 28 rad/s (e) ω = 110 rad/s

(a) increases. (b) remains the same. (c) decreases.

A person steps onto a spring scale in the bathroom, and the spring compresses by 0.57 cm. The spring constant is 1100 N/cm.

What is the mass of the person?

(a) 30 kg (b) 57 kg (c) 64 kg (d) 77 kg (e) 81 kg

(a) smaller than 0.57 cm. (b) equal to 0.57 cm. (c) larger than 0.57 cm.

A scuba diver swims 50 meters below the surface of the ocean (ρ = 1020 kg/m^{3}). Her facemask has a surface area of 0.06 m^{2}, her volume (including equipment) is 0.070 m^{3} and her mass (including equipment) is 80 kg.

What is the increase in force of the water on her face mask when she is 50 meters below the surface compared with when she is at the surface of the water?

(a) 6,000 N (b) 18,000 N (c) 30,000 N

(a) 700 N (b) 780 N (c) 810 N

(a) g/4 (b) g/2 (c) g (d) 2g (e) 4g

An object of mass 5 kg is hung on a vertical spring and set into vertical simple harmonic motion with an amplitude of 2 m and an angular frequency, ω = 25 radians/s.

What is the spring constant?

(a) 752 N/m (b) 1333 N/m (c) 2024 N/m (d) 2890 N/m (e) 3125 N/m

(a) smaller than 25 radians/s. (b) equal to 25 radians/s. (c) larger than 25 radians/s.

A hydraulic lift with a rectangular platform of length 1.5 m and width 0.8 m is used to raise cars above the ground. The cross-sectional area of the narrow, fluid-filled tube connected to the lift-platform is 0.06 m^{2} (as shown in the figure).

If a 500-kg car is placed on the lift-platform what force, F, must be applied to the small piston to balance the weight of the car?

(a) 6240 N (b) 4960 N (c) 1150 N (d) 245 N (e) 85 N

(a) 25 m (b) 10 m (c) 0.5 m

A 3 kg solid plastic cylinder (I = (1/2) M R^{2}) with radius 0.15 meters starts from rest at the top of a 1.44-meter ramp. It rolls without slipping down to the bottom of the ramp and has a final speed of 3.2 m/s.

Calculate the angular acceleration of the disk as it rolls down the ramp.

(a) α = 18.1 rad/s^{2} (b) α = 22.1 rad/s^{2} (c) α = 23.7 rad/s^{2}

(a) τ = 0.8 N-m (b) τ = 1.2 N-m (c) τ = 1.6 N-m

(a) f = 5.3 N (b) f = 6.1 N (c) f = 8.3 N

(a) a cylinder made out of the same material, but with twice the radius (b) a metal cylinder with the same dimensions but with twice the mass of the original (c) a hoop made out of the same material with radius 0.15 meters (d) a sphere made out of the same material with radius 0.15 meters (e) They all reach the bottom at the same time.

A wooden raft of length 2 m, width 1.5 m, and height 0.25 m, is floating in water. (The density of water is 1000 kg/m^{3}). When there is nothing on the raft it is found to float in the water such that it is submerged to a depth of 0.15 m, as shown in the figure.

What is the density of the wood?

(a) 400 kg/m^{3} (b) 600 kg/m^{3} (c) 1,600 kg/m^{3}

(a) 0.12 m (b) 0.15 m (c) 0.17 m (d) 0.21 m (e) 0.23 m