Physics 1000 Final Examination. December A) 87 m B) 46 m C) 94 m D) 50 m

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1 Answer all questions. The multiple choice questions are worth 4 marks and problems 10 marks each. 1. You walk 55 m to the north, then turn 60 to your right and walk another 45 m. How far are you from where you originally started? A) 87 m B) 46 m C) 94 m D) 50 m 2. If the eastward component of vector A is equal to the westward component of vector B and their northward components are equal. Which one of the following statements about these two vectors is correct? A) Vector A is perpendicular to vector B. B) The magnitude of vector A is twice the magnitude of vector B. C) Vectors A and B point in opposite directions. D) The magnitude of vector A is equal to the magnitude of vector B. E) Vector A is parallel to vector B. 3. A box of mass m is pulled with a constant acceleration a along a horizontal frictionless floor by a wire that makes an angle of 15 above the horizontal. If T is the tension in this wire, then A) T = ma. B) T < ma. C) T > ma. 4. Two weights are connected by a massless wire and pulled upward with a constant speed of 1.50 m/s by a vertical pull P. The tension in the wire is T (see figure). Which one of the following relationships between T and P must be true? A) T > P B) T = P C) P = T N D) P + T = 125 N E) P = T + 25 N

2 5. Two unequal masses M and m (M > m) are connected by a light cord passing over a pulley of negligible mass, as shown in the figure. When released, the system accelerates. Friction is negligible. Which figure below gives the correct free-body force diagrams for the two masses in the moving system? A B C D 6. A brick is resting on a rough incline as shown in the figure. The friction force acting on the brick, along the incline, is A) less than the weight of the brick. B) greater than the weight of the brick. C) zero D) equal to the weight of the brick 7. A 4.0-kg object is moving with speed 2.0 m/s. A 1.0-kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping? A) the 1.0-kg object B) the 4.0-kg object C) Both objects travel the same distance. D) It is impossible to know without knowing how long each force acts.

3 8. Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. When they hit the ground A) the heavier one will have 2 times the kinetic energy of the lighter one. B) both of them will have the same kinetic energy. C) the heavier one will have four times the kinetic energy of the lighter one. D) the heavier one will have twice the kinetic energy of the lighter one. 9. A 3.00-kg ball swings rapidly in a complete vertical circle of radius 2.00 m by a light string that is fixed at one end. The ball moves so fast that the string is always taut and perpendicular to the velocity of the ball. As the ball swings from its lowest point to its highest point A) the work done on it by gravity and the work done on it by the tension in the string are both equal to -118 J. B) the work done on it by gravity and the work done on it by the tension in the string are both equal to zero. C) the work done on it by gravity is +118 J and the work done on it by the tension in the string is -118 J. D) the work done on it by gravity is -118 J and the work done on it by the tension in the string is zero. E) the work done on it by gravity is -118 J and the work done on it by the tension in the string is +118 J. 10. Swimmers at a water park have a choice of two frictionless water slides as shown in the figure. Although both slides drop over the same height, h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the end of slide 1 compares with v2, the speed of a swimmer reaching the end of slide 2? A) v1 < v2 B) v1 > v2 C) v1 = v2 D) No simple relationship exists between v1 and v2 because we do not know the curvature of slide Two identical balls are thrown directly upward, ball A at speed v and ball B at speed 2v, and they feel no air resistance. Which statement about these balls is correct? A) At its highest point, ball B will have twice as much gravitational potential energy as ball A because it started out moving twice as fast. B) Ball B will go four times as high as ball A because it had four times the initial kinetic energy. C) The balls will reach the same height because they have the same mass and the same acceleration. D) At their highest point, the acceleration of each ball is instantaneously equal to zero because they stop for an instant. E) Ball B will go twice as high as ball A because it had twice the initial speed. 12. A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment but instead compress the spring a distance of 2x

4 A) just as it moves free of the spring, the box will be traveling four times as fast as before. B) just as it moves free of the spring, the box will have twice as much kinetic energy as before. C) just as it moves free of the spring, the box will be traveling twice as fast as before. D) just before it is released, the box has twice as much elastic potential energy as before. E) the box will go up the incline twice as high as before. 13. You are standing on a skateboard, initially at rest. A friend throws a very heavy ball towards you. You can either catch the object or deflect the object back towards your friend (such that it moves away from you with the same speed as it was originally thrown). What should you do in order to MINIMIZE your speed on the skateboard? A) Deflect the ball. B) Catch the ball. C) Your final speed on the skateboard will be the same regardless whether you catch the ball or deflect the ball. 14. In a collision between two objects having unequal masses, how does magnitude of the impulse imparted to the lighter object by the heavier one compare with the magnitude of the impulse imparted to the heavier object by the lighter one? A) The heavier object receives a larger impulse. B) The lighter object receives a larger impulse. C) Both objects receive the same impulse. D) The answer depends on the ratio of the masses E) The answer depends on the ratio of the speeds. 15. In a perfectly ELASTIC collision between two objects A) the momentum of the system is conserved but the kinetic energy of the system is not conserved. B) both the momentum and the kinetic energy of the system are conserved. C) the kinetic energy of each object is conserved. D) the kinetic energy of the system is conserved, but the momentum of the system is not conserved.

5 Problems 1. A load of bricks with mass m 1 = 14.0kg hangs from one end of a rope that passes over a small, frictionless pulley. A counterweight of mass m 2 = 27.4kg is suspended from the other end of the rope, as 2 shown in the figure. The system is released from rest. Use g = 9.80m/ s for the magnitude of the acceleration due to gravity. (a) What is the magnitude of the upward acceleration of the load of bricks? (b) What is the tension in the rope while the load is moving? 2. A small toy airplane is flying in the xy-plane parallel to the ground. In the time interval t=0 to t=2.00 seconds its velocity as a function of time is given as v = 1.20t iˆ + ( t) ˆj m/s. Find the acceleration and position of the airplane at time t=1.00 s. At time t=0 the airplane is at the origin, x=0 and y=0. 3. In a Giant Swing the seat is connected to two cables, as shown, one of which is horizontal. The seat swings in a horizontal circle with a velocity of m/s. If the seat has a mass of kg and an 84-kg person is sitting in it, find the tension in each cable. 15 marks 4. A 350kg roller coaster starts from rest at point A and slides down the frictionless loop-the-loop shown in the accompanying figure. How fast is this roller coaster moving at point B? How hard does it press against the track at point B? (Hint: use conservation of energy).

6 5. A 6.0-kg box moving at 3.0 m/s on a horizontal, frictionless surface runs into a light spring of force constant k=75 N/cm. What is the maximum compression of the spring? 6. Two identical masses are released from rest in a smooth hemispherical bowl of radius R, from the positions shown in the figure. Ignore friction between the masses and the surface of the bowl. If they stick together when they collide, how high above the bottom of the bowl will the masses go after colliding? 7. An elevator has mass 600-kg, not including passengers. The elevator is designed to ascend, at constant 2 acceleration of a y = 2m / s for 4 meters and then with constant speed. It is driven by a motor that can provide up to 40 hp to the elevator. What is the maximum number of passengers that can ride in the elevator? Assume that the average passenger has a mass of 65 kg. 8. A force parallel to the x-axis acts on a particle moving along the x axis. This force produces a potential energy 4 given by U ( x) = 1.20x J. What is the magnitude and direction of the force when x= m? 9. A 45.0-kg woman stands up in a 60.0-kg canoe 5.00 m long. She walks from a point 1.00 m from one end to a point 1.00 m from the other end (the figure below). If you ignore resistance to motion of the canoe in the water, how far does the canoe move during this process? (Hint: use conservation of momentum and then relate the velocities to displacements). 10. A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force F = 25iˆ 38 ˆj N to the cart as it undergoes a displacement s = 9.2ˆ i 2.6 ˆj m. How much work does the force you apply do on the grocery cart? Bonus question: When a large nucleus splits during a nuclear reaction, the daughter nuclei of the fission fly apart with enormous kinetic energy. Explain why. (5 marks)

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