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1 OPEN ONLY WHEN INSTRUCTED Name: Hr: AP Physics C Mechanics Final Semester Examination Instructions: Write your name on the exam as well as scantron before you begin This exam consists of Section 1) Multiple Choice 20 multiple choice questions, each of equal value. 18 best answers will be considered. For this section place your answers on the scantron sheet using a #2 pencil. Erase mistakes completely. Section 2) Free Response 3 Free Response Questions Write detailed steps to complete this part. Space provided in this packet to finish this part. If you require additional sheets, please ask. Please copy this statement of academic honesty and Sign before you begin. On my personal integrity, I will not share any part of this exam, questions, answers or hints with any one else till Semester 1 exams are over. I understand that failure to comply will lead to the cancellation of my score (Sign here 1

2 SECTION 1 Multiple Choice POINTS A 0.50 kg object moves in a horizontal circular track with a radius of 2.5 m. An external force of 3.0 N, always tangent to the track, causes the object to speed up as it goes around. If it starts from rest its speed at the end of one revolution is: (A) 15 m/s (B) 19 m/s (C) 9.8m/s (D) 21m/s (E) 14m/s 2. A particle starts from rest and is acted on by a net force that does work at a rate that is proportional to the time t. The speed of the particle is proportional to: (A) 1/t 1/2 (B) t (C) t 1/2 (D) 1/t (E) t 2 3. The figure below shows a cold package of hot dogs sliding rightward across a frictionless floor through a distance d = 19.5 cm while three forces are applied to it. Two of the forces are horizontal and have the magnitudes F 1 = 5.00 N and F 2 = 1.00 N; the third force is angled down by θ = 60.0 and has the magnitude F 3 = 4.00 N. If the package has a mass of 2.1 kg and an initial kinetic energy of 0, what is its speed at the end of the displacement? (A) 2.12 m/s (B) 1.06 m/s (C) 3.12 m/s (D) 4.00 m/s 4. An object of mass 10 Kg starts from rest at time t = 0 and moves in a straight line. For time t > 0, the object s velocity v as a function of time t is given by v = 2t + 3t 2, where v is in m/s and t is in seconds. How much work is done by the net force between t = 0 and t = 1s? (A) 5J (B) 50J (C) 125J (D) 250J (E) 500J 2

3 5. A block of mass m is pulled along a rough horizontal floor by an applied force T as shown. The vertical component of the force exerted on the block by the floor is: (A) mg +TSinθ (B) mg (C) mg TSinθ (D) mg TCosθ (E) mg +TCosθ 6. A 5.0 kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is After one end of the plank is raised so the plank makes an angle of 25 with the horizontal, the force of friction is: (A) 18N (B) 21N (C) 0 N (D) 44N (E) 24N 7. A block of mass m is pulled across a rough horizontal surface at a constant speed by a force of magnitude F, which acts at an angle of θ to the horizontal, as shown above. The coefficient of kinetic friction between the block and the surface is 8. Block A, with mass m A, is initially at rest on a horizontal floor. Block B, with mass m B, is initially at rest on the horizontal top surface of A. The coefficient of static friction between the two blocks is µ s. Block A is pulled with an increasing force. It begins to slide out from under B when its acceleration reaches: (A) (m B /m A )/μ s g (B) μ s g (C) (m A /m B )/μ s g (D) m B μ s g (E) g 3

4 9. An object is released from rest from a great height and reaches its terminal velocity. Which of the following statements is true of the object while it is falling with terminal velocity? (A) There is no longer a gravitational force on it (B) There is no longer a drag ( air resistance) force on it. (C) Its acceleration is upward (D) The magnitudes of the gravitational and drag forces on it are equal. 10. Two blocks are connected by a string and pulley as shown. Assuming that the string and pulley are massless, the magnitude of the acceleration of each block is: (A) 0.98 m/s 2 (B) m/s 2 (C) 0.54 m/s 2 (D) m/s 11. Three books (X, Y, and Z) rest on a table. The weight of each book is indicated. The net force acting on book Y is: (A) Zero (B) 5N Up (C) 9N Down (D) 4N Down (E) None of these 12. Two blocks with masses m and M are pushed along a horizontal frictionless surface by a horizontal applied force F as shown. The magnitude of the force that either of these blocks exerts on the other is: (A) mf/m (B) mf/(m+m) (C) mf/m- m) (D) MF/m (E) MF/(M+m) 4

5 13. Two 4 Kg blocks hang froma rope that passes over 2 frictionles pulleys, as shown in the figure here. What is the tension in the horizontal portion of the rope if the blocks are not moving and the two pulleys have negligible mass? (A) 4N (B) 8B (C) 20N (D) 40N (E) 80N 14. The acceleration of an object, starting from rest, is shown in the graph below. Other than at t = 0, when is the velocity of the object equal to zero? (A) At t = 4.0 s (B) At t = 5.0 s (C) During the interval from 1.0s to 3.0s (D) At no other time on this graph (E) At t =3.5 s 15. A person throws a ball of mass 0.20 Kg. The ball starts from rest, accelerates horizontally and uniformly through a distance of 0.90 m, and leaves the person s hand at 30 m/s. The average horizontal force applied to the ball by the person s hand is (A) 3.3 N (B) 16.7 N (C) 81 N (D) 100 N 16. Ball 1 is dropped from rest at time t = 0 from a tower of height h as shown in the figure. At the same instant, ball 2 is launched upward form the ground with initial speed v 0. If the air resistance is negligible, at what time t will the two balls pass each other? (A) 0.25*h/ v 0 (B) 0.5 *h/ v 0 (C) h/v 0 (D) 2 *h/ v 0 (E) 4 *h/ v 0 5

6 17. A small particle starts from rest from the origin of an xy- coordinate system and travels in the xy- plane. Its acceleration in the x- direction is 2.0m/s 2, and its acceleration in the y- direction is 1.0 m/s 2. What is the x- coordinate of the particle when its y- coordinate is 12m? (A) 3.0 m (B) 6.0 m (C) 12 m (D) 24 m (E) 48 m 18. A toy raft shown in the top view above is sliding due east on frictionless ice at a constant speed v 0 whena fan blows on its sail, producing a constant acceleration a directed to the north. Which of the following could indicate the path of the raft while the fan is blowing. 19. A 20.0 kg box slides up a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 150 N is applied to the box to pull it up the incline. The applied force makes an angle of 10.0 degrees to the incline and above the incline. If the incline has a coefficient of kinetic friction of 0.100, then the increase in the kinetic energy of the box is (A) 424 J (B) 395 J (C) 344 J (D) 297 J (E) 250 J 20. An airplane has a mass of 30,000 kg and travels at 300 m/s. If the drag force is 1000 N, then the power the engines have to provide to keep flying is (A) 6.0 X 10 5 Watts (B) 5.5 X 10 5 Watts (C) 4.9 X 10 5 Watts (D) 4.2 X 10 5 Watts (E) 3.0 X 10 5 Watts 6

7 SECTION 2 FREE RESPONSE (Answer in the spaces given below. Ask for blank sheets if needed) (TOTAL PTS 18) - Express Answers in 2-3 Sig Figs 1. This graph shows the potential energy U(x) of a particle as a function of its position x. a. Identify all points of equilibrium for this particle (Show on the graph) (1 pt) Suppose the particle has a constant total energy of 4.0 joules, as shown by the dashed line on the graph. b. Determine the kinetic energy of the particle at the following positions (2 pts) i. x = 2.0 m ii. x = 4.0 m c. Can the particle reach the position x = 0.5 m? Explain. (1 pt) d. Can the particle reach the position x = 5.0 m? Explain. (1 pt) e. On the grid below, carefully draw a graph of the conservative force acting on the particle as a function of x, for 0 < x < 7 meters. (1 pt) 7

8 2. The figure below shows an 80- kilogram person standing on a 20- kilogram platform suspended by a rope passing over a stationary pulley that is free to rotate. The other end of the rope is held by the person. The masses of the rope and pulley are negligible. You may use g = 10 m/ s 2 a. Draw the free body diagram of person + platform (Considering them as one object) (1 pt) b. If the platform and the person are at rest, what is the tension in the rope? (1 pt) Assume that friction is negligible, and the parts of the rope shown remain vertical. c. Draw the free body diagram of the person alone. (1 pt) d. The person now pulls on the rope so that the acceleration of the person and the platform is 2 m/s 2 upwards. What is the tension in the rope under these new conditions? (1 pt) e. Under these conditions, what is the force exerted by the platform on the person? (1 pt) d. After a short time, the person and the platform reach and sustain an upward velocity of 0.4 m/s. Determine the power output of the person required to sustain this velocity. (1 pt) 8

9 3. A 0.1- kilogram block is released from rest at point A as shown above, a vertical distance h above the ground. It slides down an inclined track, around a circular loop of radius 0.5 meter, then up another incline that forms an angle of 30 with the horizontal. The block slides off the track with a speed of 4 m/s at point C, which is a height of 0.5 meter above the ground. Assume the entire track to be frictionless and air resistance to be negligible. a. Determine the height h. (1 pt) b. On the figure below, draw and label all the forces acting on the block when it is at point B. which is 0.5 meter above the ground. (1 pt) c. Determine the magnitude of the force exerted by the track on the block when it is at point B. (1 pt) d. Determine the maximum height above the ground attained by the block after it leaves the track. (1 pt) e. Another track that has the same configuration, but is NOT frictionless, is used. With the track it is found that if the block is to reach point C with a speed of 4 m/s, the height h must be 2 meters. Determine the work done by the frictional force. (2 pts) 9