Score_____/141 Points (3 Points Each+ 3Pts of Extra Credit )
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2011 AP Physics
2011 Break Work Name______Score_____/141 points (3 points each+ 3pts of extra credit ) g= -10 m/s2 Please SHOW WORK for relevant equations 1. If air resistance is neglected, a 1-kilogram projectile has an escape speed of about 11 km/s at the surface of the Earth. If the mass of the projectile is doubled, the escape speed is (A) 22 km/sec (B) 11√2 km/sec (C) 11 km/sec
(D) 11/√2 km/sec (E) 5.5 km/sec
Derive the formula for escape speed below:
2. An unstable nucleus has mass M and is initially at rest. It ejects a particle of mass m with speed V0. The remaining nucleus recoils in the opposite direction with a speed
a. v0b. mvo/M c. mvo/(M+m) d. (m+M)v0/m e. mvo /(M-m) Show work: Don’t forget momentum is a vector!!!
3. As a drag car moves from rest at time t = 0, its velocity varies as the square of the elapsed time according to the equation v = bt2, where b is a constant. The expression for the distance traveled by the car from its position at t = 0 is a. bt3 b. bt3/3 c. 4bt2 d. 3bt2 e. bt2/3 Show Work: Show that integral sign with dt for practice. 2011 AP Physics
4. For a block of mass m to slide without friction up a rise of height h, the minimum initial speed of the block must be gh gh a. b. c. 2gh d. 2 gh e. 2 2gh 2 2 Show Work:
5. An ice skater starts a spin with kinetic energy ½ . As she pulls her arms in, her moment of inertia decreases to 1/3 Io. Her angular speed then becomes a. 0 b. 0 c. d. 3 e. 3 3 3 o 0 0 Show Work: Remember energy is NOT conserved, because the ice skater is doing work.
A B C
6. Three blocks. A. B. and C, each have mass M and are connected by massless strings as shown above. Block C is pulled to the right by a force F causing the entire three-block system to accelerate. Assuming frictionless contact between the blocks and the level table beneath them, what is the net force experienced by block B ? a. 0 b. F/3 c. F/2 d. 2F/3 e. F Show Work: 2011 AP Physics
7. A mass m on the end of a string moves in a circle on a horizontal frictionless table as shown above. If the string is pulled through a hole in the table, the (A) angular momentum of m remains constant (B) angular momentum of m Increases (C) angular momentum of m decreases (D) kinetic energy of m remains constant (E) kinetic energy of m decreases Justify your reasoning: (Remember what it means for angular momentum to be conserved in terms of torques)
8. A cart of mass 5.0 kilograms is moving horizontally in a straight line at 6.0 meters per second. In order to change its speed to 10.0 meters per second, the work done on the cart must be (A) 40 joules (B) 90 joules (C) 160 joules (D) 400 joules (E) 550 joules Show Work:
9. An automobile of mass m is proceeding around a highway curve of 30.5 m (100 ft) radius. The surface of the roadway is horizontal, and the coefficient of friction between the tires and the roadway is 0.50. The maximum speed with which the car can round the curve without slipping is (A) 3.05 m/sec (B) 4.88 m/sec (C) 9.75 m/sec (D) 12.3 m/sec (E) 13.4 m/sec
Show Work: 2011 AP Physics
Questions 10-12 relate to five particles that start at x=0 at t=0 and move in one dimension independently of one another. Graphs of the velocity of each particle versus time are shown below.
10. Which particle is farthest from the origin at 2 seconds? (A) A (B) B (C) C (D) D (E) E Explain reasoning:
11. Which particle moves with a constant nonzero acceleration? (A) A (B) B (C) C (D) D (E) E Explain Reasoning:
12. Which particle is in its initial position at t=2 seconds? (A) A (B) B (C) C (D) D (E) E Explain Reasoning: 2011 AP Physics
13. A flywheel rotating at 12 revolutions per second can be brought to rest in 6 seconds. The average angular acceleration during this time interval is equal in magnitude to 1 (A) radians/sec2 (B) 2 radians/sec2 (C) 4 radians/sec2 (D) 4 radians/sec2 (E) 72 radians/sec2 Show Work:
14. A cart of mass 2m has a velocity V0 before it strikes another cart of mass 3m at rest. The two carts couple and move off together with a velocity
(A) (1/5) vo (B) (2/5) vo (C) (3/5)vo (D) 2 / 5vo (E) (2/3) v0 Show Work:
15. When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude F=ax + bx2. The work done by an outside agent in changing the stretch from x = 0 to x = ℓis ax2 bx 3 aℓ2 b ℓ 3 (A) (ax+bx2) ℓ (B) a+2bx (C) a+2b ℓ (D) (E) 2 3 2 3 Show Work: Remember W=1/2 kx2 is only for Hooke’s Law, this is NOT a Hook’s Law rubber band. 2011 AP Physics
1 16. The potential energy of a body of mass m is given by mgx kx2 . The force acting on the body 2 at position x is mgx2 kx 3 mgx2 kx 3 1 (A) (B) (C) mg+ kx (D) -mg+kx (E) mg-kx 2 6 2 6 2 Show Work:
17. A block starting from rest slides down a frictionless inclined plane of length L. When the block has attained one-half its final speed, the distance it has traveled along the plane is L L L 3L (A) (B) L( 2 1) (C) (D) (E) 4 2 2 4 Show Work (Use multiple equations):
18. extra credit: 3 pts dv The motion of a certain object is described as follows: kv2 t, where k is a constant dt
The initial velocity is v0, when time t=0. The expression involving the velocity v as a function of time t is kt 2 1 kt 2 1kt 2 1 1 kt 2 1kt 2 1 (A) v v0 (B) v0 (C) (D) (E) 2 v 2 v2 v0 v 2 v2 v0 Show Work: Can disprove wrong answers here or write out integration for correct answer. 2011 AP Physics
19. The forces produced by two springs as they are stretched are shown in the graph above. Spring 1 indicated by the dashed line is linear but spring 2 is not. The period of oscillation for a mass attached to spring 2 is (A) dependent on amplitude but never greater than for spring 1 (B) dependent on amplitude but never less than for spring 1 (C) dependent on amplitude but always equal to that of spring 1 (D) Independent of amplitude and never greater than for spring 1 (E) Independent of amplitude and never less than for spring 1 Explain Reasoning:
20. A spaceship of mass m is returning to the Earth with its engine turned off. It can be assumed to move in the Earth's gravitational field only. In moving from a distance R1 to a distance R2 from the center of the Earth of mass Me, the increase in kinetic energy of the spaceship, where G is the universal gravitational constant, is (A) GM m1 e R2
(B) GMem1 2 R2
(C) GMemR1 R 2 2 R1
(D) GM mR1 R 2 e R1 R 2
(E) GMemR1 R 2 2 2 R1 R 2 Show Work: 2011 AP Physics
21. The path traced out by a particle on the rim of a wheel that rolls without slipping is a cycloid (You should look up this work if you don’t know what it means). The coordinates of the path can be written x Rt Rsin t y R Rcos t where R and are constants and t is time. The magnitude of the acceleration of the particle is (A) 2 / R (B) R 2 (C) 2 R 2 (D) 2 R 2 (E) 2 / 2R Show Work:
22. A man pulls a 20 N crate up a frictionless 30° slope 15 meters high. (I know pic uses pounds and feet, but this test is really old and that’s what they did back then). If the crate is moved from rest at the bottom to rest at the top of the slope, the work done by the man is (A) +300 J (B) +150 J (C) zero (D) –150 J (E) –300 J Show Work: 2011 AP Physics
23. A spring which does not obey Hooke’s law supplies a force of magnitude ax2, where x is measured downward from the equilibrium position of the unloaded spring and a is a constant. A mass m is attached to the end of the spring and is released from rest at x=0. What is its maximum downward displacement? (A) mg/ a (B) 3mg / a (C) mg/a (D) 2mg/a (E) 3mg/a Show Work: Be careful to find maximum displacement, NOT where the equilibrium point is. Also, this is NOT Hooke’s law so ½ kx2 does NOT apply.
24. A ball of mass m at one end of a string of length R rotates in a vertical circle just fast enough to keep the string from going slack when the ball is at the top of the circle. The ball's speed when it is at the bottom of the circle is
(A) 2gR (B) 3gR (C) 4gR (D) 5gR (E) 7gR Show Work: (Remember that the ball does not stop dead at the top of the swing) 2011 AP Physics
25. A force acting in a straight line on an object of mass 5 kilograms is plotted as a function of time in the graph above. The change in the velocity of the object is
(A) 0.8 m/sec
(B) 1.1 m/sec
(C) 1.6 m/sec
(D) 2.3 m/sec
(E) 4.0 m/sec This one is a tough mathematically so it is OK to estimate the answer based on the graph (remember on the exam you have 1.28 minutes per question). Still show work below.
26. A ball starts from rest at the top of an inclined plane and rolls without slipping down the plane. The ratio of the angular velocity of the ball at the end of the plane to its angular velocity as it passes the center point C of the plane equals (A) 4 (B) 2 (C) 3 (D) 2 (E) 5/ 2 Show Work: (think multiple equations) 2011 AP Physics
27. A small satellite is in an elliptical orbit around the Earth. The distances RA and RB, are the maximum and minimum distances, respectively, of the satellite from the Earth's center. Let L be the angular momentum and K the kinetic energy of the satellite. A quantity with subscript A or B denotes the instantaneous value of the quantity at the position A or B, respectively. Which of the following must be true?
(A) LB>LA and KB>KA
(B) LB>LA and KB=KA
(C) LB=LA and KB=KA
(D) LB (E) LB=LA and KB>KA Explain reasoning: Make sure you tell me why angular momentum is conserved. 28. A block attached to a spring of negligible mass undergoes simple harmonic motion on a frictionless surface. The potential energy of the system is zero at the equilibrium position and has a maximum value of 50 joules. When the displacement of the block is half the maximum value, its instantaneous kinetic energy is A) zero (B) 12.5 joules (C) 25 joule (D) 37.5 joules (E) 50 joules Show Work (Pretest question!): 2011 AP Physics Questions 29-30 A block slides down a frictionless incline as indicated in the figure above. Let y = 0, x = 0, and t = 0 just as the block is released from rest at the top of the incline. Let the positive sense for y be up and the positive sense for x be to the right. 29. Which of the following graphs best represents the x component of the velocity of the block as a function of time? Explain your reasoning: 30. Which of the following graphs best represents the x component of the position of the block as a function of time? Explain your reasoning: 2011 AP Physics 31. Suppose the force required to tow a canal barge is directly proportional to the speed. If it takes 4.0 horsepower to tow the barge at a speed of 2.0 miles per hour, what horsepower is required to move the barge at a speed at a speed of 6.0 miles per hour? (A) 8.0 hp (B) 12 hp (C) 24 hp (D) 32 hp (E) 36 hp Show Work: 32. When a thin stick of mass M and length L is pivoted about one end, its moment of inertia is 2 I = ML /3. When the stick is pivoted about its midpoint, its moment of inertia is (A) ML2/12 (B) ML2/5 (C) ML2/3 (D) 7ML2/12 (E) ML2 Show Parallel axis theorem. I’ll give you extra credit if you integrate to find the answer. 2011 AP Physics 33. A projectile has an initial velocity of magnitude V0 which makes an angle 0 with the horizontal. Neglecting air friction, all of the following are true at point P, the highest point of its trajectory, EXCEPT: (A) The time t required to reach P is given by t=v0cos0/g (B) The horizontal displacement has been v0tcos0, where t is the time required to reach P. 2 (C) hmax=(v0sin0) /2g (D) The speed is v0 cos 0 (E) the acceleration is g Explain why your choice is not true. 34. An object is suspended from a spring whose mass is negligible compared to that of the object. The object is displaced slightly, and the period of its motion is observed to be T seconds. The spring is then cut in half and the object suspended from one of the halves. The object is displaced slightly, and its period is observed to be T' seconds. The ratio T'/T is (A) 1/2 (B) 1/ 2 (C) 1 (D) 2 (E) 2 Show Work: -kx 35. A particle is acted upon by a net force F=F0e . If the particle has velocity equal to zero at x = 0, then the maximum kinetic energy that the particle can attain is k 2 k (A)F0/k (B) F0/e (C)kF0 (D) (kF0) (E)ke F0 Show Work 2011 AP Physics 36. A bowling ball of mass 6.0 kg is released from rest from the top of a slanted roof that is 4.0 m long and angled at 30° , as shown above. The ball rolls along the roof without slipping. The rotational inertia of a sphere of mass M and radius R about its center of mass is MR2. (a) On the figure below, draw and label the forces (not components) acting on the ball at their points of application as it rolls along the roof. (b) Calculate the force due to friction acting on the ball as it rolls along the roof. If you need to draw anything other than what you have shown in part (a) to assist in your solution, use the space below. Do NOT add anything to the figure in part (a). (c) Calculate the linear speed of the center of mass of the ball when it reaches the bottom edge of the roof. 2011 AP Physics (d) A wagon containing a box is at rest on the ground below the roof so that the ball falls a vertical distance of 3.0 m and lands and sticks in the center of the box. The total mass of the wagon and the box is 12 kg. Calculate the horizontal speed of the wagon immediately after the ball lands in it. 37. If a particle’s position is given by x=4-12t+3t2 ( where t is in seconds and x is in meters) a. What is the average velocity during the time interval t=2 s and t= 3 s? b. What is the instantaneous velocity when the particle is midway between its positions at t=2 s and t=3s? c. What is the instantaneous acceleration at t= 3s? d. What is the average acceleration during the time interval t=2 s and t=3s? 2011 AP Physics 38. A particle has the position function: r= R(ωt-sinωt)i + R(1-cosωt)j where R and ω are constants. a. Determine the velocity and acceleration of the particle at any time t. b. For what values of time is the particle momentarily at rest? 39. A particle glued to the rim of a wheel with a radius of 20 cm has an angular position with respect to a fixed reference line given by θ(t)=2t3-3t2+π/2 radians. a. Find the angular frequency and angular acceleration of the particle. b. At what time t the resultant acceleration entirely radial? c. At what time t is the resultant acceleration entirely tangential? 2011 AP Physics