S19_2211_Test1_BLANK

Please remove this sheet before starting your exam. Things you must have memorized The Momentum Principle The Energy Principle The Angular Momentum Principle Definition of Momentum Definition of Velocity Definition of Angular Momentum Definitions of angular velocity, particle energy, kinetic energy, and work Other potentially useful relationships and quantities γ ⌘ 1 s 1 - ✓ | ~ v | c ◆ 2 E 2 - ( pc ) 2 = ( mc 2 ) 2 d ~ p dt = d | ~ p | dt ˆ p + | ~ p | d ˆ p dt ~ F k = d | ~ p | dt ˆ p and ~ F ? = | ~ p | d ˆ p dt = | ~ p | | ~ v | R ˆ n ~ F grav = - G m 1 m 2 | ~ r | 2 ˆ r U grav = - G m 1 m 2 | ~ r | ~ F grav ⇡ mg near Earth’s surface Δ U grav ⇡ mg Δ y near Earth’s surface ~ F elec = 1 4 ⇡✏ 0 q 1 q 2 | ~ r | 2 ˆ r U elec = 1 4 ⇡✏ 0 q 1 q 2 | ~ r | ~ F spring = k s s U spring = 1 2 k s s 2 U i ⇡ 1 2 k si s 2 - E M Δ E thermal = mC Δ T ~ r cm = m 1 ~ r 1 + m 2 ~ r 2 + . . . m 1 + m 2 + . . . I = m 1 r 2 1 ? + m 2 r 2 2 ? + . . . K tot = K trans + K rel K rel = K rot + K vib K rot = L 2 rot 2 I K rot == 1 2 I ! 2 ~ L A = ~ L trans,A + ~ L rot ~ L rot = I ~! ! = r k s m v = d r k si m a Y = F/A Δ L/L (macro) Y = k si d (micro) ⌦ = ( q + N - 1)! q ! ( N - 1)! S ⌘ k ln ⌦ prob( E ) / ⌦ ( E ) e - E kT E N = - 13 . 6eV N 2 where N = 1 , 2 , 3 . . . E N = N ~ ! 0 + E 0 where N = 0 , 1 , 2 . . . and ! 0 = r k si m a (Quantized oscillator energy levels)

Moment of inertia for rotation about indicated axis The cross product ~ A ⇥ ~ B = h A y B z - A z B y , A z B x - A x B z , A x B y - A y B x i Constant Symbol Approximate Value Speed of light c 3 ⇥ 10 8 m/s Gravitational constant G 6 . 7 ⇥ 10 - 11 N · m 2 /kg 2 Approx. grav field near Earth’s surface g 9 . 8 N/kg Electron mass m e 9 ⇥ 10 - 31 kg Proton mass m p 1 . 7 ⇥ 10 - 27 kg Neutron mass m n 1 . 7 ⇥ 10 - 27 kg Electric constant 1 4 ⇡✏ 0 9 ⇥ 10 9 N · m 2 /C 2 Proton charge e 1 . 6 ⇥ 10 - 19 C Electron volt 1 eV 1 . 6 ⇥ 10 - 19 J Avogadro’s number N A 6 . 02 ⇥ 10 23 atoms/mol Plank’s constant h 6 . 6 ⇥ 10 - 34 joule · second hbar = h 2 ⇡ ~ 1 . 05 ⇥ 10 - 34 joule · second specific heat capacity of water C 4 . 2 J/g/K Boltzmann constant k 1 . 38 ⇥ 10 - 23 J/K milli m 1 ⇥ 10 - 3 kilo k 1 ⇥ 10 3 micro μ 1 ⇥ 10 - 6 mega M 1 ⇥ 10 6 nano n 1 ⇥ 10 - 9 giga G 1 ⇥ 10 9 pico p 1 ⇥ 10 - 12 tera T 1 ⇥ 10 12

Problem 1 [25 pts] The code below models the motion of the moon orbiting the Sun and Earth. The code is similar to the one you completed in lab except some of the lines of code are missing. Note that in this problem the Sun is assumed to be stationary. Add in the missing lines of code below to complete the program. GlowScript 2.7 VPython G = 6.7e-11 mSun = 2e30 #in kg mEarth = 6e24 #in kg mMoon = 7.35e22 #in kg ## OBJECTS with radii are not to scale and are exaggerated Sun = sphere(pos=vector(0,0,0), radius=7e8*5e1, color=color.yellow) Earth = sphere(pos=vector(1.5e11,0,0), radius=6.4e6, color=color.blue,make_trail=True) Moon = sphere(pos=vector(1.5e11,384472282,0), radius=1736482, color=color.green) t = 0 Earth.p = mEarth*vector(0, 29951.68, 0) Moon.p = mMoon*vector(-1023.056, 29951.68, 0) Sun.p = vector(0,0,0) deltat = 60*60 ## CALCULATIONS while True: A. [13 pts] Add the missing lines of code to calculate the net force on the Moon and Earth. B. [6 pts] Add the missing lines of code to update the momentum of the Moon and Earth. C. [6 pts] Add the missing lines of code to update the position of the Moon and Earth. t = t + deltat

Problem 2 [25 pts] A tennis ball, with mass 0.5 kg, flies toward Serena Williams with velocity < 40 , 5 , 0 > m/s. She hits it; contact with the racket is maintained for 0.01 seconds. After contacting the racket, the ball’s velocity is < - 40 , - 5 , 0 > m/s, and its position is ~ r = < 0 , 1 , 0 > m. Neglect any air resistance, friction, etc. A. [10 pts] What is the contact force of the racket on the ball during this short time interval?

Problem 3 [25 pts] You are playing a game where a ball of mass m , attached to two identical springs, can slide back and forth on a frictionless surface. The base for one spring is located at position h 0 , 0 , 0 i . The base of the other spring is located at position h 2 L 0 , 0 , 0 i as indicated in the diagram. The springs are identical with a rest length L 0 and spring con- stant k s . Using your hand you move ball to position h d, 0 , 0 i while you hold the ball motionless. This position is such that d > L 0 . A. [5 pts] Calculate the net spring force acting on the ball while you hold it motionless. Your answer should be a vector. B. [10 pts] You release the ball and it begins to move under the influence of the springs. After a short time Δ t , determine the new location of the ball. Your answer should be a vector.

C. [10 pts] Determine the net force acting on the ball at the new location you found in the previous part of this problem. Your answer should be a vector.

C. [5 pts] In the cubic lattice of our ball and spring model, determine the sti ↵ ness k s,i of the bond between two zinc atoms. D. [5 pts] An African bush elephant with a mass of 5,900 kg steps on the zinc penny. The Young’s modulus for zinc is 1 . 08 ⇥ 10 11 N/m 2 . By what percentage does the penny compress if the elephant presses down on the penny with all of his weight? E. [5 pts] Ten pennies are stacked on top of each other (face to face) and the elephant steps on this stack. By what percentage does the stack of pennies compress if the elephant presses down on them with all of his weight?

This page is for extra work, if needed.