Physics 218: Midterm#1 February 25 th, 2015 Please read the instructions below, but do not open the exam until told to do so. Rules of the Exam: 1. You have 75 minutes to complete the exam. 2. Formulae are provided on the last page. You may NOT use any other formula sheet. 3. You may use any type of handheld calculator. However, you MUST show your work. If you do not show HOW you integrated or HOW you took the derivative or HOW you solved a quadratic or system of equations, etc you will NOT get credit. 4. Cell phone use during the exam is strictly prohibited. 5. Be sure to put a box around your final answers and clearly indicate your work. 6. Partial credit can be given ONLY if your work is clearly explained and labeled. No credit will be given unless we can determine which answer you are choosing, or which answer you wish us to consider. If the answer marked does not follow from the work shown, even if the answer is correct, you will not get credit for the answer. 7. You do not need to show work for the multiple choice questions. 8. Have your TAMU ID ready when submitting your exam to the proctor. 9. Check to see that there are 10 pages + 1 formula sheet (11 in all) 10. If you need extra space, indicate/ mark on the main page of the problem that you are continuing on another page. 11. DO NOT REMOVE ANY PAGES FROM THIS BOOKLET except the formula sheet and scratch paper. Sign below to indicate your understanding of the above rules. Full name (in CAPS): UIN Section Number: Instructor s Name: Your Signature: Page 1 of 10
Short Problems (20) Problem 2 (20) Problem 3 (20) Problem 4 (20) Problem 5 (20) Total Score (100) Page 2 of 10
Short Problems (Circle the correct option) [NO Partial Credit] (20 points) A) [5 points] Making preparations for a party, you hang wrapped gift on an inflated foil balloon and notice that the assembly starts descending at a constant 2.8m/s 2. If you hang a glow stick instead, which is k times lighter than the wrapped gift, the balloon starts accelerating upwards with 4.2m/s 2. Assume that the lift produced by balloon stays unchanged and standard gravitation. What is the value of k? a) k=1.4 b) k=1.5 c) k=2.0 d) k=2.5 e) k=3.0 f) k=3.5 g) k=5.0 B) [5 points] A spelunker is surveying a cave. Starting from the entrance, she follows a passage straight towards East, then 106m towards South East until she reaches a cascade. The cascade is at 125m distance from the entrance. What was the length of the first passage towards East? a) 19.0m b) 25.0m c) 66.2m d) 88.4m e) 164m f) 175m g) 200m C) [5 points] A golfer standing at the bottom of a very long ramp tilted at 15 o from the horizontal sends a golf ball along the ramp. The ball goes uphill 100m then comes back. Assume no friction. What was the initial uphill velocity of the ball? a) 4.43m/s b) 4.59m/s c) 10.2m/s d) 20.4m/s e) 22.5m/s f) 31.3m/s g) 44.3m/s D) [5 points] A rotor blade is 10.0 ft long from central shaft to tip and rotates at 550rpm. What is the speed of the tip of this blade? a) 55.0m/s b) 62.8m/s c) 91.7m/s d) 168m/s e) 176m/s f) 192m/s g) 303m/s Page 3 of 10
Problem 2 (20 points) The equation of motion for an object in 2D is given by: 2 r( t) [ A t B t ] iˆ C t ˆj where r is a position vector whose magnitude is given in meters, t is time which is given in seconds, A, B, and C are positive constants; î and ĵ are two orthogonal unit vectors. Find the following: (a) (b) (c) (d) The units of A and the units of B. Justify your choice. Velocity (vector) as function of time. Acceleration (vector) as function of time. The angle between velocity and acceleration vectors. Page 4 of 10
Problem 3 (20 points) During launches, rockets often discard unneeded parts. A rocket starts from rest on the launch pad and accelerates upward at a steady acceleration of 5 times that of g. When it is 300 m above the launch pad, it discards a used fuel canister by simply disconnecting it. Once disconnected, the only force acting on the canister is gravity. a. Determine the maximum height reached by the canister, after separating from the rocket b. What total distance did the canister travel between its release and its crash onto the launch pad? Page 5 of 10
Problem 4 (20 points) Please refer to the drawing above. A stunt artist launches his motorcycle from a ramp of height H tilted at angle θ above horizontal; his initial speed is v o. He is aiming to land in a bed of a moving truck at point P, at horizontal distance L from the ramp. The truck is moving in the same horizontal direction, with constant velocity v o (same magnitude as the motorcycle s initial speed). The acceleration due to gravity is g pointing down. You can ignore air resistance. Using the known variables, L, H, θ, and/or g, find: a. The required initial speed of the motorcycle, v o b. The distance the truck travels while the motorcycle is in flight. Hint: You need to find the distance P P such that the truck arrives at point P at the right time.] c. The relative speed of the motorcycle with respect to the truck (horizontal and vertical components) just before landing at point P. Page 6 of 10
Problem 5 (20 points) A spacecraft is attempting vertical descent near the surface of a planet X. When it applies an upward thrust of 25.0kN from its engines, it slows down at a rate of 1.20m/s 2. When it instead applies an upward thrust of 10.0kN, it speeds up at a rate of 0.80 m/s 2. a. Draw a free body diagram for the spacecraft for each case. b. In each case, draw and state in words what is the direction of the acceleration of the spacecraft. c. Apply Newton s second law to each case, slowing down or speeding up, and use this to determine the spacecraft s weight near the surface of planet X. Page 7 of 10
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Phys 218 Exam I Formulae Trigonometry and Vectors: h adj = h cos θ = h sin φ h opp = h sinθ = h cos φ v = r2 r1 t 2 t 1 a = v2 v1 t 2 t 1 v = d r dt a= d v dt = d2 r dt 2 r(t) = r 0 + t 0 v(t )dt v(t) = v 0 + t 0 a(t )dt r(t) = r 0 + v 0 t + 1 2 at2 v(t) = v 0 + at v 2 x = v 2 x,0 + 2a x (x x 0 ) (and similarly for y and z) r(t) = r 0 + 1 2 ( v i + v f )t h 2 = h 2 adj + h 2 opp tan θ = hopp h adj Law of cosines: C 2 = A 2 + B 2 2AB cos γ sin α Law of sines: A = sinβ B = sin γ C A = A x î + A y ĵ + A zˆk  = A A Kinematics: constant acceleration only h φ θ h adj A B = A x B x + A y B y + A z B z = AB cos θ = A B = AB A B = (A y B z A z B y )î + (A z B x A x B z )ĵ + (A x B y A y B x )ˆk h opp A B = AB sin θ = A B = AB (direction via right-hand rule) A β γ C α B Quadratic: ax 2 + bx + c = 0 x 1,2 = b ± b 2 4ac 2a Derivatives: d dt (atn ) = nat n 1 Constants/Conversions: g = 9.80 m/s 2 = 32.15 ft/s 2 (Earth, sea level) 1 mi = 1609 m 1 lb = 4.448 N 1 ft = 12 in 0.454 kg (Earth, sea level) 1 in = 2.54 cm Circular motion: a rad = v2 a tan = d v R dt T = 2πR v Relative velocity: v A/C = v A/B + v B/C v A/B = v B/A Forces: Newton s: d dt d dt sin at = acos at cos at = asin at Integrals: { t2 t 1 f(t)dt = a n+1 (tn+1 2 t n+1 if f(t) = at n, then f(t)dt = a n+1 tn+1 + C (n 1) sinat dt = 1 a cos at cos at dt = 1 a sin at 1 ) F = m a, FB on A = F A on B