Physics 1401V October 28, 2016 Prof. James Kakalios Quiz No. 2

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1 This is a closed book, closed notes, quiz. Only simple (non-programmable, nongraphing) calculators are permitted. Define all symbols and justify all mathematical expressions used. Make sure to state all of the assumptions used to solve a problem. Credit will be given only for a logical and complete solution that is clearly communicated with correct units. Partial credit will be given for a well-communicated problem solving strategy based on correct physics. Only one solution can be turned in and only one solution will be graded. The multiple choice problems are worth a total of 30 points (6 points each) and only the answers entered on the separate bubble sheet will be graded.

2 Useful Mathematical Relationships: θ c b a Equation Sheet For a right triangle: sin θ = c a, cos θ = c b, tan θ = b a, a 2 + b 2 = c 2, sin 2 θ + cos 2 θ = 1 For a circle: C = 2πR, A = πr 2 If Ax 2 + Bx + C = 0, then x = B ± 2 B 4AC 2A d(z n ) = nz n 1, d(cosz) = sin z, d(sinz) = cosz, d(eaz ) = ae az, df(z) dt = df(z) dt, Useful constants: 1 mile = 5280 ft g = 9.8 m/s 2 = 32 ft/s cm = 1 inch 1 m = 3.3 feet Fundamental Concepts, Principles, and Definitions: v 2 = v o + 2 a (x-x o ) v = v 0 +at KE = mv 2! x = x 0 +v 0 t+at 2 F ma /2! = m ρ = V Δx dx V avg = distance/δt v x av = v x = Δt dt Under Certain Conditions:! m1m F = 0 F = mg F = G 2 F = -kx 2 r!! W = F dr E f F = µ kn E i = E in dv a x x = dt E out Centripetal acceleration a c = v 2 /R W NET = ΔK Power = Work/Δt ΔP = Δ (mv) = Force x time If F net = 0, then MV cm = constant

3 Physics 1401V September 30, 2016 Prof. James Kakalios Quiz No. 1 Problem 1 (35 points): A 1.0 kg steel ball and a 2.0 meter long cord of negligible mass make up a simple pendulum that can pivot without friction about the point O. This pendulum is released from rest in a horizontal position and when the ball is at its lowest point it strikes a 1.0 kg block sitting at rest on a long shelf. After the perfectly elastic collision the block moves to the right on the shelf. Assume and that the coefficient of kinetic friction between the square block and the shelf is µ k = 0.2. (a) (b) (c) (d) (e) What is the tension in the cord at the moment right before the steel ball collides with the block? What is the Work done on the ball by the cord, as it swings to its lowest point, right before it collides with the block? Justify your answer. What is the velocity of the block just after impact with the steel ball? How far does the block slide before coming to rest, assuming that the shelf is long enough? What is the average power expended, in Watts, by the frictional force as the block slides on the shelf?

4 Problem 2: 2a (18 points); 2b (8 points); 2c (9 points): A diver with a mass of 50 kg jumps from a high diving board 12 meters above the pool s surface. The board has a spring constant of k = 8 x 10 4 N/meter and has a deflection just before the diver launches herself of 10 centimeter. When the board releases its energy it propels the diver upwards. She successfully completes a famed Triple Lindy, and then reaches the water s surface. (a) What is her velocity when she first reaches the water s surface? (b) Two seconds after she dives into the water, her downward motion is arrested and she comes to rest. What is the average force exerted on her by the water as she slows down? You may consider the acceleration due to gravity g = 10 m/sec 2 for this problem. Ignore any effects due to air resistance, and you may consider her motion to be completely in the vertical direction. (c) In an attempt to model the air drag more realistically, you recognize that the force of air resistance on the diver depends on the velocity, the mass density of the air and the surface area of the stuntman. If the force of air drag is measured in Newtons, using the metric system, use dimensional analysis to determine how the Force varies with velocity v, the mass density ρ and surface area A. That is, if F = k ρ a v b A c, where k is a dimensionless constant, then determine the values of the power law exponents a, b and c.

5 Multiple Choice Questions Each Problem Worth 6 Points 1) Three 2 kg masses are located along the x-axis. One is located at the origin, the second is at x = 3 cm and the third is at x = 9 cm. Where is the center of mass of this system located, in cm? (a) 0 (b) 2 (c) 4 (d) 6 (e) 8 2) You throw a stone downward into some nice soft gushy mud and it penetrates into the muck by one inch from the top surface. If you wanted the stone to penetrate four inches, you would have to throw it into the mud (a) (b) (c) (d) (e) twice as fast three times as fast four times as fast eight times as fast sixteen times as fast 3) A 1 kg block rests on an inclined plane, where the coefficient of static friction between the block and the plane is µ s = What is the largest angle the plane can make with the horizontal, and still keep the block from sliding down? (a) 15 (b) 30 (c) 45 (d) 60 (e) 75 4) How much Work, in Joules, is done by a force F = 4i - 3j in Newtons displacing a mass over a distance ΔR = 4i + 2j measured in meters, and what is the angle θ between F and ΔR? (a) 0, 90 (b) 22.36, 63 (c) 22.36, 45 (d) 10, 63 (e) 10, 27 5) A baseball is thrown vertically upward and feels no air resistance. As the baseball is rising (a) its gravitational potential energy is not conserved, but its momentum is conserved. (b) both its momentum and its total energy are conserved. (c) both its momentum and its kinetic energy are conserved. (d) its kinetic energy is conserved, but its momentum is not conserved. (e) its momentum is not conserved, but its total energy is conserved.

6 Problem 1 ID No. Name Discussion Section

7 Problem 2 ID No. Name Discussion Section