v 1 v 2 direction of v? D 1 of 15 ReviewII-1. Consider the vectors V 1 and V 2 shown. What is the direction of V = V 2 V 1, V 1 + V = V 2

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1 1 of 15 ReviewII-1. Consider the vectors V 1 and V shown. What is the direction of V = V V 1, V 1 + V = V v 1 v C direction of v? D A B Answer: B, downward ReviewII-. A heavy-duty truck pulling a light trailer is accelerating forward. How does the magnitude of the force on the truck F ontruck from the trailer compare to the magnitude of the force on the trailer F ontrailer from the truck? a A) F ontruck > F ontrailer B) F ontrailer > F ontruck C) F ontrailer = F ontruck Answer: F ontrailer = F ontruck by Newton s III Law regardless of acceleration of truck.

2 of 15 ReviewII-3. A box of mass m is sitting in an elevator which is moving upward, and the speed is decreasing. The magnitude of the acceleration of the elevator is a. The magnitude of the normal force on the box from the floor is N. What is the correct expression for the magnitude of the normal force N on the box? N = A) m(g+a) B) m(g a) C) m(a g) D) mg Moving upward, slowing m Answer: N = m(g-a) You really can t answer this without first drawing a F.B.D. and then choosing a coordinate system (choose down as the +y direction, since that is direction of the acceleration.) ReviewII-4. Consider the vector A Which equation is correct? A) A x = +A cos B) A x = A cos C) A x = +A sin D) A x = A sin y A x Answer: A x = A sin

3 3 of 15 ReviewII-5. A mass m is lowered on a string. The mass is moving downward but it is slowing down. How does the magnitude of the tension T in the string compare to the magnitude of the net force, F net, on the mass? A) F net = T B) F net >T C) F net < T D) Impossible to tell from the information given. m moving downward, and slowing Answer: Draw the FBD: F net < T ReviewII-6. The graph shows velocity vs. time for a train moving along a straight track. The graph shows that the train is A) speeding up all the time. B) slowing down all the time. C) speeding up initially, but then slows down. D) slowing down initially, but then speeds up. E) changing direction. v Answer: speeding up all the time. (Note the plot is v vs. t, NOT x vs. t ) t

4 4 of 15 ReviewII-7. The free-body diagram for a car rounding a banked curve is shown. The car is going so fast that it is about to slip. The coordinate system has been chosen as shown. a x y N S N mg What is the correct y-equation? A) N sin + s N cos mg = 0 B) N s N sin mg cos = 0 C) N mg cos = 0 D) N cos s N sin mg = 0 E) None of these Answer: N cos s N sin mg = 0 ReviewII-8. A crate of mass m is accelerated to the left with a string at an angle above the horizontal. The coefficient of kinetic friction is K. The coordinate system has been chosen as shown. What is the correct x equation? a F x K A) F N mg 0 B) Fcos KN ma C) Fsin N mg 0 Fcos N mg N ma D) k E) None of these Answer: Fcos KN ma

5 v = constant 5 of 15 ReviewII-9. A block of mass m on a table is pulled along the table by an external horizontal force of F ext magnitude F ext, as shown. The table has a rough surface so there is a frictional force of magnitude F fric on block. The block is moving at constant speed v. How do the magnitudes of the external force F ext and the friction force F fric compare? A) F ext = F fric B) F ext > F fric C) F ext < F fric Answer: F ext = F fric Constant velocity means zero acceleration, which means the net force must be zero. ReviewII-10. Consider the following two situations: Situation I: A car on Earth rides over the top of a round hill, with radius of curvature = 100 m, at constant speed v = 35 mph. Situation II: A monorail car in intergalactic space (no gravity) moves along a round monorail, with radius of curvature = 100 m, at constant speed v = 35 mph. Which car experiences larger acceleration? A) Earth car B) Space car C) Both cars have the same acceleration. I II Answer: Both cars have the same acceleration. The presence of gravity doesn t change the fact that the acceleration for circular motion, constant speed, has magnitude a = v /r.

6 6 of 15 ReviewII-11. A rider in a "barrel of fun" finds herself stuck with her back to the wall. The free-body diagram is shown. Is the following statement definitely true for this situation? s N = mg A) Yes, it is certainly true. B) No, it might not be true. Answer: No, it might not be true. Only true if F fric = s N. Static friction F fric can have any value 0 < F fric < s N

7 7 of 15 ReviewII-1. A box of mass m is resting stationary on a board which is tilted at an angle from the horizontal. The coefficient of static friction between the box and the board is s. The angle is rather shallow and the friction is large, so the box is not about to slip. What is the magnitude of the force of friction between the board and the box? (A) (C) S Smg mg (B) cos mgcos S (D) mgsin (E) None of these. Answer: mgsin s N The box is not about to slip, so the force of static friction is NOT

8 8 of 15 ReviewII-13. The tip of the nose of a pogo stick rider moves along the path shown. The maximum compression of the pogo stick spring is A B C D shown. x At what point(a, B, C or D) is the elastic potential of the spring energy a maximum? At what point is the gravitational potential energy a maximum? At what point is the kinetic energy a maximum? Answers: PE elas is max at D, PE grav is max at A. Of these 4 points, KE is largest at C (just before the spring starts to compress)

9 9 of 15 ReviewII-14. A projectile is fired straight up and then it comes back down to its original height. There is non-negligible air resistance as the projectile is moving. During the entire flight of the projectile, the work done by the force of gravity is.. A) zero. B) positive C) negative During the entire flight of the projectile, the work done by the force of air resistance is... A) zero. B) positive C) negative Answer: W grav = 0 (negative on the way up, positive on the way down) W drag = negative (drag force is always opposite the displacement) ReviewII-15. A pendulum is launched in two different ways. During both launches, the bob is given an initial speed of 3.0 m/s and the same initial angle from the vertical. On launch 1, the speed is upwards, on launch, the speed is downwards. Assume no friction. 1 Which launch will cause the pendulum to swing the largest angle from the equilibrium position on the left side? A) Launch 1 B) Launch C) Both launches give the same maximum displacement. Answer: Both launches give the same maximum displacement, if no friction

10 10 of 15 ReviewII-16. A mass m is dropped from rest from a height h i above a table top on which sits on a spring with spring constant k. Just before the mass hits the spring the mass has speed v. The mass compresses the spring by a maximum amount x and stops for an instant at a height h f. There is no friction in this problem. Which of the following equations correctly expresses conservation of energy and allows one to solve for the compression x of the spring? 1 1 A) mgh mv kx m i 1 i 1 i B) mgh kx mgh C) mgh kx mgh mg h h kx mv 1 1 D) f i E) None of these equations is correct. f f k hi x hf 1 Answer: mgh kx mgh i f

11 11 of 15 ReviewII-17. A planet is in elliptical orbit around the Sun. The zero of potential energy U is chosen at r =, so GMm U(r). r How does the magnitude of U ( U = U) compare to the KE? A) U > KE B) U < KE C) U =KE D) depends on the position in the orbit. Answer: U > KE Bound orbit, so E tot < 0, which means KE is less than U. ReviewII-18. The gravitational potential energy of a rock near a star is shown in the diagram. When the rock is at the position shown, it has a kinetic energy of 5MJ. Will the rock escape to infinity or is it bound in orbit about the star? A) Escape B) in bound orbit C) impossible to tell -10MJ -0MJ U(r) 0 r -40MJ Answer: in bound orbit, since E tot = KE + PE +5MJ + ( 30MJ) = 5MJ < 0

12 1 of 15 ReviewII-19.A block of mass m with initial speed v slides up a frictionless ramp of height h inclined at an angle as shown. Assume no friction. m v h True A) or False B) : Whether the block makes it to the top of the ramp depends on the mass of block and on the angle. Answer: False. In the conservation of energy equation, the mass m cancels out and the angle does not appear. Suppose now that there is friction between the block and the ramp surface. True A) or False B) : Whether the block makes it to the top of the ramp depends both on the mass of block and on the angle. Answer: True. Word done by friction depends on mass and on length of travel ReviewII-0. What is the magnitude of the force of gravity exerted on the Earth by an apple that is falling from a tree to the ground? A) mg B) > mg C) < mg m Answer: mg By NIII, force on Earth by apple is same magnitude as force on apple by Earth.

13 13 of 15 ReviewII-1. For a small mass m on the surface of a (non-rotating) planet of mass M and radius R, is it always true that GMm mg R? A) Yes, this is always true regardless of whether the mass m is in free-fall or not. B) No, this is not always true. Answer: Yes, this is always true ReviewII-. Recall that Kepler's nd law says that planets move faster when closer to the Sun. (KII: A line drawn from the sun to the planet sweeps out equal areas in equal times). A small planet of mass m is in elliptical orbit about a large star of mass M. Which of the following statements is always true as the planet orbits the star? M m 1. The direction of the acceleration of the planet is toward the star.. The magnitude of the acceleration of the planet is a = v /r,where v is the speed of the planet and r is the distance between the planet and the star. 3. The magnitude of the force between the planet and the star is constant. 4. The speed of the planet is constant. A) All are true always. B) None are true always. C) Only 1 and are true always. D) Only 1 is true always. E) Some other combination. Answer: Only 1 is true always. The formula a = v /r is only true for circular motion with constant speed.

14 14 of 15 ReviewII-3. A hockey puck which was recently hit by a stick, slides up and over an icy (frictionless) round hill. At the moment the puck is at the top of the hill, the speed is A) increasing B) decreasing C) constant, non-zero D) zero Answer: constant, non-zero The puck is slowing on the way up, and speeding up on the way down. At the instant at the top, it is switching between slowing down and speeding up, and it is neither slowing nor speeding.

15 15 of 15 CTGravity-4. A projectile is fired with initial speed v 0 at radius r 0 from the center of an airless planet of mass M (r 0 is significantly greater than the radius of the planet). The projectile rises to a maximum distance r max and then falls back down to earth, and achieves a final speed v final just before it hits the ground. R r 0 v 0 r max M v final A student wishes to compute r max. What is the correct Conservation of Energy equation, she should start with? A) B) C) D) 1 GMm mv0 r Max 1 GMm 1 GMm m v m v r r 0 final 0 Max 1 GMm GMm mv0 r r 0 Max GMm GMm r r 0 Max E) None of these Answer: 1 GMm GMm mv0 (v is zero at r max ) r r 0 Max