EF 151 Final Exam, Fall, 2011 Page 1 of 11

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1 EF 5 Final Exam, Fall, 0 Page of Instructions Do not open or turn over the exam until instructed to do so. Name, and section will be written on the st page of the exam after time starts. Do not leave your seat if there is less than 5 minutes to go in the exam. When time is called, immediately stop writing, remain seated, and pass your exam to the center aisle. Do not stand up or leave the room until all exams have been collected. ssume 3 significant figures for all given numbers unless otherwise stated Show all of your work no work, no credit Write your final answer in the box provided Include units for all answers Include directions for all vectors Geometry/Trig a c rea of a circle = r Volume of a cylinder = r h Law of Sines sin sin sinc a b c Law of Cosines c a b ab cos C Useful Conversions gallon = 3 cubic inches gallon = 4 quarts gallon = 8 fluid ounces m 3 = 000 L acre = 43,560 ft mile = 8 furlongs mile = 580 ft fathom = 6 ft rod = 6.5 ft chain = yards inch = 5.4 mm watt = N m/sec hp = watts (approx.) hp = 550 ft lb / sec lb = 4.45 N (approx.) m = 000 mm g = 3. ft/sec = 9.8 m/sec smoot = 67 inches C b Constant cceleration v s s s Circular Motion s arc length v speed a n normal acceleration a t tangential acceleration ρ radius of curvature angle ω angular speed α angular acceleration T period f frequency s v a t v at v v s t s v t a t v v s a a v n T f T f Projectile Motion g y y 0 x x0 tan tan x x 0 v0 θ launch angle v 0 launch velocity x 0, y 0 launch position, positive up Relative Motion v v v v v G v G G v Friction F max N s v G Force and cceleration F net ma F kinetic Work W F r Fr cos Power P F v P dw dt Spring force F kx N k

2 EF 5 Final Exam, Fall, 0 Page of Conservation of Energy mgh0 mv 0 kx0 W Rocket Propulsion m0 v uex ln gt m t thrust = u ex (dm/dt) in mgh f mv f kx m 0 : initial mass m t : final mass = m 0 (dm/dt)t dm/dt : rate of fuel burn u ex : exhaust speed of gases relative to the rocket. f E loss Impulse / Momentum / Restitution m m v mv t t v mv mv mv ( v v ) F dt e (line of impact) v v Constant ngular cceleration t t t t Center of Mass m r mr mnr R m m m Parallel xis Theorem I I Md cm n n Torque Fr sin r F Torque and cceleration I net ngular Impulse / Momentum I I I I t I L r p I p linear momentum o dt L angular momentum Work and Power W P KE I

3 EF 5 Final Exam, Fall, 0 Page 3 of Name: Section: Clearly write your name and section above. Tear off the cover page so you have easy access to the equations.. ( pt) What is the y component of the 0 lb force? a. -0cos(30 ) b. -0sin(30 ) c. -0cos(40 ) 0 lb x 40 y 30 d. -0sin(40 ). ( pt) The normal force on a 74 kg person when they are at the top of a m radius Ferris Wheel spinning at 4 rpm is: a. greater than their weight b. equal to their weight c. less than their weight 3. ( pt) Objects and collide and stick together. What it the x velocity of the objects after the collision? The mass and speed of each object before the collision is given below. m = 0 kg v = (0i j)m/s m = 0 kg v = (-0i + j)m/s a. positive b. zero c. negative y 4. ( pt) The net torque about the origin in the system shown is: (CCW is positive) a. 40()cos(30 ) b. 40()sin(30 ) + ft 40 lb 30 x c. (40)()cos(30 ) d. (40)()sin(30 )

4 EF 5 Final Exam, Fall, 0 Page 4 of 5. (6 pts) Hubble-arn is a unit of volume equivalent to 3. liters. Determine the volume of a cylinder with a diameter of 8 inches and a height of 4 inches? Give your answer in hubble-barns. One liter is equivalent to 000 cm (6 pts) object has a constant acceleration of (i 5j)m/s. What is its speed after 4 seconds if it starts with a velocity of (6i + 3j) m/s?

5 EF 5 Final Exam, Fall, 0 Page 5 of 7. (6 pts) soccer ball is kicked straight up from a point 3 ft above the ground. It hits the ground 3.5 seconds later. What was the initial speed of the ball? 8. (6 pts) What is the magnitude of the sum of these two vectors? N N

6 EF 5 Final Exam, Fall, 0 Page 6 of 9. (6 pts) pumpkin is launched at an angle of 35 from the horizontal with a speed of 94 ft/sec. What is the maximum height the pumpkin reaches above its launch point? 0. (6 pts) n airplane can fly at 00 mph with respect to the air. It needs to fly to a point 600 miles due north. The wind is coming from the west at 60 mph. How long will it take the airplane to complete its flight?

7 EF 5 Final Exam, Fall, 0 Page 7 of. (6 pts) Determine the acceleration of the cart. (FD = KD required) 4 lb 56 lb 8. (6 pts) The box just starts to move when a force is applied as shown. What is the static coefficient of friction between the box and the floor? (FD required) 40 lb 0 60 lb

8 EF 5 Final Exam, Fall, 0 Page 8 of 3. (6 pts) How long does it take a 0 hp engine that is 85% efficient to hoist a 08 lb professor 57 feet in the air? ssume a constant velocity. 4. (6 pts) 6 gram ball on a Rube Goldberg device is to be shot straight up with a spring powered lever as shown. How much should the spring (k=790 N/m) be stretched in in order to shoot the ball 3 meters high? ssume the air resistance force is a constant.5 N, that the ball goes straight up, and that all of the energy in the spring is transferred to the ball.

9 EF 5 Final Exam, Fall, 0 Page 9 of 5. (6 pts) tennis ball is thrown straight down from a height of 4.5 meters towards the ground with an initial speed of m/s. What coefficient of restitution is required so that the maximum height after the bounce is equal to the original height? 6. (6 pts) 500 lb cannon is mounted on wheels so it can roll freely. 30 lb cannon ball is shot with a speed of 0 ft/s at an angle of 40 above horizontal. What is the final velocity of the cannon?

10 EF 5 Final Exam, Fall, 0 Page 0 of 7. (6 pts). Determine the x-coordinate of the center of mass using the given coordinate system. ssume uniform thickness and density. ll dimensions are in cm. y 6 x (6 pts) Determine the angular acceleration of the solid uniform 40 pound disk. 8 inch 5 lb

11 EF 5 Final Exam, Fall, 0 Page of 9. (6 pts) 0.6 kg, 0.05 m radius solid sphere is moving along a track with a speed of 3.5 m/s. It goes up a hill and the speed at the top of the hill is.5 m/s. How high is the hill? 0. (6 pts) 0.8 kg ball is thrown with a speed of 4 m/s. It bounces off the hanging board with a speed of 3 m/s. Determine the angular velocity of the hanging board after the collision. The hanging board is initially at rest and has a mass moment of inertia about the pivot point of.8 kg-m. 4 m/s 0.6 m