Sample Final Examination

Transcription

1 Dawson College Physics 203-NYA-05 Mechanics Sample Final Examination This exam is divided into two parts: Part I: Problems (10 marks each) Solve all seven problems. Show all of your work, clearly and in order, to receive full marks. If you use a formula not given on the formula sheet, a derivation must be shown. Part II: Multiple Choice Questions (2 marks each) Answer all fifteen questions. Circle the best response from the choices given. If your final selection is unclear you will not be given the marks. No marks will be awarded for diagrams, calculations, or reasoning. Additional instructions: 1. The time allotted for this examination is three hours. 2. Answer directly on the question sheet. If you need extra room, you may use the back of another page. 3. Use g = 9.80 m/s When finished, return this entire package and the formula sheet to your instructor. Good luck! P1 P2 P3 P4 P5 P6 P7 MC Total / NYA Sample Final Page 1 of 14

2 Part I: Problems (10 marks each) Solve all seven problems. Show all of your work, clearly and in order, to receive full marks. If you use a formula not given on the formula sheet, a derivation must be shown. 1. The initial position of a particle at t = 0 is x = 10 m. The figure shows the velocity-time graph for the particle. v x (m/s) t (s) -10 (a) Draw the corresponding position-time graph (with numerical values). (4 marks) (b) Draw the corresponding acceleration-time graph (with numerical values). (4 marks) (c) During which time interval(s) is the particle speeding up? (2 marks) 203-NYA Sample Final Page 2 of 14

3 2. A ball is thrown towards a cliff with an initial speed of 30.0 m/s directed at an angle of 60.0 above the horizontal. The ball lands on the edge of the cliff 4.00 s after it is thrown. (a) What is the height of the cliff? (3 marks) (b) What is the maximum height reached by the ball? (4 marks) (c) What is the ball s impact velocity? (3 marks) 203-NYA Sample Final Page 3 of 14

4 3. A 40.0N force pushes two masses, m 1 = 8.00kg and m 2 = 4.00kg, across a horizontal surface. The force is directed 30.0 below the horizontal, as shown in the figure. The coefficient of kinetic friction between both masses and the surface is N 30.0 m 1 m 2 (a) Draw a free body diagram for each mass. (3 marks) (b) What is the acceleration of the masses? (5 marks) (c) What is the force that m 2 exerts on m 1? (2 marks) 203-NYA Sample Final Page 4 of 14

5 4. A ball of mass m 1 = 4.00 kg is tied to another ball of mass m 2 = 3.00 kg by a string of length m. The two balls are swung in a vertical circle by a second string of length m connected to m 2. As the balls rotate, the strings remain parallel. At the top if the circle, m 2 is moving at 4.00 m/s. m m m m/s m (a) Draw a free-body diagram for each mass at this instant. (3 marks) (b) What is the tension in the string connecting the two balls at this instant? (4 marks) (c) What is the tension in the string connecting m 2 to the centre of the circle at this instant? (3 marks) 203-NYA Sample Final Page 5 of 14

6 5. The spring shown in the figure is compressed 50.0 cm and is used to launch the block, which has a mass of 100 kg. The surface is frictionless except for the final 30.0 incline, where the coefficient of kinetic friction is k = N/m 10.0 m 30.0 (a) What is the speed of the block when it reaches the valley below its starting point? (4 marks) (b) What distance does the block slide along the 30.0 incline before stopping? (6 marks) 203-NYA Sample Final Page 6 of 14

7 6. A 1000kg car, travelling east at 30.0m/s, collides with a 3000kg truck, travelling north. After the collision, the vehicles stick together and the combined wreckage moves at 55.0 north of east. N N car 30.0 m/s E wreck 55.0 E truck (a) What is the speed of the truck before the collision? (7 marks) (b) What percentage of the initial kinetic energy of the system is lost during the collision? (3 marks) 203-NYA Sample Final Page 7 of 14

8 7. A solid wheel (made of two disks of different size) has a moment of inertia I = kg m 2. The wheel can rotate about a frictionless axle passing through its centre. A rope wrapped around the outer radius of the wheel exerts a tangential force of magnitude 9.00N at a distance r 1 = m from the axle. A second rope, wrapped around the inner radius of the wheel exerts a tangential force of magnitude 12.0 N at a distance r 2 = m from the axle. r 2 r N 9.00 N (a) What is the torque due to each force and the net torque acting on the wheel? (5 marks) (b) What is the angular acceleration of the wheel? (2 marks) (c) If the wheel starts from rest, how many revolutions does it make in 12.0 seconds? (3 marks) 203-NYA Sample Final Page 8 of 14

9 Part II: Multiple Choice Questions (2 marks each) Answer all fifteen questions. Circle the best response from the choices given. If your final selection is unclear you will not be given the marks. No marks will be awarded for diagrams, calculations, or reasoning. 1. The motions of a car and a truck along a straight road are represented by the velocity-time graph below. The two vehicles are side-by-side at time t = 0. At time t f, which of the following statements is correct? v car truck t f t (a) Both vehicles have travelled the same distance. (b) The truck has not moved at all. (c) The car has travelled further than the truck. (d) The truck has travelled further than the car. (e) No information about the distances travelled can be determined from this graph. 2. A package is dropped from a helicopter while the helicopter is moving upwards at 15 m/s. If it takes 25 s before the package strikes the ground, how high above the ground was the package when it was released? (a) 2.7 km (b) 3.4 km (c) 2.2 km (d) 3.2 km (e) None of the above. 3. If the scalar (dot) product of two vectors is negative, which of the following statements is correct? (a) There was a calculator error. (b) The angle between the vectors is between 0 and 90. (c) The angle between the vectors is exactly 90. (d) The angle between the vectors is between 270 and 360. (e) The angle between the vectors is between 90 and NYA Sample Final Page 9 of 14

10 4. A physics student jumps up into the air off of a horizontal floor. How does the force exerted on the student by the floor compare to the student s weight? (a) The force of the floor is equal to the weight and in the same direction. (b) The force of the floor is equal to the weight and in the opposite direction. (c) The force of the floor is less than the weight and in the same direction. (d) The force of the floor is less than the weight and in the opposite direction. (e) The force of the floor is greater than the weight and in the opposite direction. 5. A cyclist rides up a 30 slope with a constant speed. Which of the following statements is correct? (a) The net force acting on the bike (due to gravity, the normal force, and friction) points opposite to the direction of motion. (b) The net force acting on the bike (due to gravity, the normal force, and friction) points in the direction of motion. (c) The net force acting on the bike (due to gravity, the normal force, and friction) is zero. (d) None of the above statements is correct. 6. Three blocks are pushed across a frictionless surface. If the force P = 6.0 N, what is the magnitude of the force that the 3.0 kg block exerts on the 2.0 kg block? P 2.0 kg 3.0 kg 5.0 kg (a) 8.4 N (b) 7.2 N (c) 6.4 N (d) 5.6 N (e) 4.8 N 7. A car drives around a circular curve on a level road. Which of the following statements is correct? (a) The friction force of the road on the car is zero, and the car naturally follows the road. (b) The friction force of the road on the car increases when the car s speed is lower. (c) The friction force of the road on the car increases when the car s speed is higher. (d) The friction force of the road on the car increases when the car moves to the outside of the curve. (e) There is no net friction force because the road and the car exert equal and opposite forces on each other. 203-NYA Sample Final Page 10 of 14

11 8. The only force acting on a 2.0 kg body as it moves along the x axis is shown in the figure. At x = 0 the body is already moving at 3.0 m/s in the positive x direction. At what value of x will the body momentarily come to rest? F x (N) x (m) 3 (a) 3.0 m (b) 5.0 m (c) 7.0 m (d) 9.0 m (e) 12 m 9. A 40 g ball is launched at an unknown angle from point A at the top of a 30 m tall cliff. The ball reaches a maximum height of 10 m above the top of the cliff before falling to the ground at point B. Neglecting air resistance, what is the change in kinetic energy from point A to point B? A 10 m 30 m B (a) 12 J (b) 32 J (c) 20 J (d) 12 J (e) 20 J 203-NYA Sample Final Page 11 of 14

12 10. A box slides along the frictionless surface shown in the figure. At the position shown, the box is already moving down the slope. At which level on the other side will the box stop? III II I (a) Level III. (b) Level II. (c) Level I. (d) The box will stop at the lowest point in the valley and never make it to the other side. (e) It depends on the mass of the box. 11. Two objects of different mass collide. How do the impulses they exert on each other during the collision compare? (a) They are are equal in magnitude and in direction. (b) They are equal in magnitude and opposite in direction. (c) They are equal in magnitude and opposite in direction, but only if it was an elastic collision. (d) They are equal in magnitude and opposite in direction, but only if it was an inelastic collision. (e) They are equal in magnitude and opposite in direction, but only if the objects have the same initial speed. 12. Car A is moving with a speed v when it rear ends Car B, which has twice the mass of A and is initially at rest. The collision occurs on an icy road at a speed slow enough that the collision is elastic. After the collision, which of the following scenarios is possible? (a) Both cars are moving with a speed v. (b) Car A is at rest and car B is moving with a speed v/2. (c) Car A is at rest and car B is moving with a speed v. (d) Car A is moving with a speed v/3 and car B is moving with a speed 2v/3. (e) Car A is moving with a speed v/ 2 and car B is moving with a speed v/ NYA Sample Final Page 12 of 14

13 13. A rigid body is rotating with a uniform angular velocity. Which of the following statements is correct? (a) All points on the body have the same angular velocity and the same linear velocity (b) All points on the body have the same angular velocity, but different linear velocities (c) All points on the body have different angular velocities, but the same linear velocity (d) All points on the body have different angular velocities and different linear velocities 14. A child of mass 20 kg sits 140 cm to the left of the pivot point of a see-saw. Another child of mass 35 kg sits 80 cm to the right of the pivot point. Assuming the see-saw itself is massless, how will the see-saw rotate? (a) Counterclockwise. (b) Clockwise. (c) The see-saw will not rotate at all. (d) Not enough information is given to determine the sense of rotation. 15. The figure below shows a plate with a circle cut out of it. The dimensions have been measured to be: l = (5.12 ± 0.04) cm, w = (3.10 ± 0.03) cm, r = (0.52 ± 0.01) cm. Accounting for the uncertainties in the measurements, how should the area of the plate be reported? l w r (a) A = (15.02 ± 0.05) cm 2 (b) A = (15.02 ± 0.09) cm 2 (c) A = (15.0 ± 0.2) cm 2 (d) A = (15.0 ± 0.3) cm 2 (e) A = (15.0 ± 0.8) cm NYA Sample Final Page 13 of 14

14 Answers Problems 1. (a) x (m) t (s) (c) 0 4 s and 5 6 s (b) a x (m/s 2 ) t (s) (a) y = 25.5 m (b) y max = 34.4 m (c) v = 20.0 m/s at 41.4 below the horizontal 3. (a) m 1 : f k1 F 21 n 1 m 2 : f k2 n 2 F 12 (b) a = 1.17 m/s 2 (c) F 21 = 10.5 N (left) w 1 40 N w 2 m 1 : m 2 : 4. (a) T 1 (b) T 1 = 217 N (c) T 2 = 284 N T 1 w 1 T 2 w 2 5. (a) v = 19.9 m/s (b) d = 32.1 m 6. (a) v T = 14.3 m/s (north) (b) 54.8% 7. (a) τ 1 = 2.25 N m, τ 2 = 1.20 N m, Στ = 1.05 N m (b) α = 2.63 rad/s 2 (c) θ = 30.1 rev Multiple Choice 1. (d) 2. (a) 3. (e) 4. (e) 5. (c) 6. (e) 7. (c) 8. (b) 9. (a) 10. (a) 11. (b) 12. (d) 13. (b) 14. (c) 15. (d) 203-NYA Sample Final Page 14 of 14