Name: Student #: BROCK UNIVERSITY Page 1 of 12 Final Exam: July 2016 Number of pages: 12 (+ formula sheet) Course: PHYS 1P21/1P91 Number of students: 104 Examination date: 9 July 2016 Number of hours: 3 Time of Examination: 16:00 19:00 Instructor: S. D Agostino A formula sheet is included at the end of the test paper. No other aids are permitted except for a non-programmable, non-graphing calculator (this regulation does not preclude special arrangements being made for students with disabilities). Translation dictionaries (e.g., English-French) or other dictionaries (thesaurus, definitions, technical) are not allowed. Use or possession of unauthorized materials or electronic devices will result in a charge of academic misconduct under the University s Academic Integrity Policy. A minimum score of 50 percent must be obtained on this final examination in order to earn a credit in the course. Solve all problems in the space provided. Before you leave the exam room, hand in this paper and your formula sheet at the completion of the exam. Total number of marks: 50 1 2 3 4 5 6 7 8 9 10 Total 5 5 5 5 4 4 4 4 4 10 50
PHYS 1P21/1P91 July 2016 Page 2 of 12 1. [5 marks] A car is travelling at a constant speed of 33 m/s on a highway. At the instant this car passes an entrance ramp, a second car enters the highway from the ramp. The second car starts from rest and has a constant acceleration. What acceleration must it maintain, so that the two cars meet for the first time at the next exit, which is 2.5 km away?
PHYS 1P21/1P91 July 2016 Page 3 of 12 2. [5 marks] A criminal is escaping across a rooftop and runs off the roof horizontally at a speed of 5.3 m/s, hoping to land on the roof of an adjacent building. Air resistance is negligible. The horizontal distance between the two buildings is D, and the roof of the adjacent building is 2.0 m below the jumping-off point. Determine the maximum value for D.
PHYS 1P21/1P91 July 2016 Page 4 of 12 3. [5 marks] A helicopter flies over the arctic ice pack at a constant altitude, towing an airborne 129-kg laser sensor that measures the thickness of the ice (see the drawing). The helicopter and the sensor both move only in the horizontal direction and have a horizontal acceleration of magnitude 2.84 m/s 2. Ignoring air resistance, determine the tension in the cable towing the sensor.
PHYS 1P21/1P91 July 2016 Page 5 of 12 4. [5 marks] A girl is sledding down a slope that is inclined at an angle of 30.0 with respect to the horizontal. The wind is aiding the motion by providing a steady force of 105 N that is parallel to the motion of the sled. The combined mass of the girl and the sled is 65.0 kg, and the coefficient of kinetic friction between the snow and the runners of the sled is 0.150. How much time is required for the sled to travel down a 175-m slope, starting from rest?
PHYS 1P21/1P91 July 2016 Page 6 of 12 5. [4 marks] A motorcycle is travelling up one side of a hill and down the other side. The crest of the hill is a circular arc with a radius of 45.0 m. Determine the maximum speed that the motorcycle can have while moving over the crest without losing contact with the road.
PHYS 1P21/1P91 July 2016 Page 7 of 12 6. [4 marks] A pitcher throws a 0.140-kg baseball, and it approaches the bat at a speed of 40.0 m/s. The bat does 70.0 J of work on the ball in hitting it. Ignoring air resistance, determine the speed of the ball after the ball leaves the bat and is 25.0 m above the point of impact.
PHYS 1P21/1P91 July 2016 Page 8 of 12 7. [4 marks] Starting with an initial speed of 5.00 m/s at a height of 0.300 m, a 1.50-kg ball swings downward and strikes a 4.60-kg ball that is at rest, as the drawing shows. (a) Determine the speed of the 1.50-kg ball just before impact. (b) Assuming that the collision is elastic, determine the velocities (magnitude and direction) of both balls just after the collision. (c) How high does each ball swing after the collision, ignoring air resistance?
PHYS 1P21/1P91 July 2016 Page 9 of 12 8. [4 marks] A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has a length of 64 cm and is wound around the top at a spot where its radius is 2.0 cm. The thickness of the string is negligible. The top is initially at rest. Someone pulls the free end of the string, thereby unwinding it and giving the top an angular acceleration of 12 rad/s 2. Determine the final angular velocity of the top when the string is completely unwound.
PHYS 1P21/1P91 July 2016 Page 10 of 12 9. [4 marks] A person is sitting with one leg outstretched and stationary, so that it makes an angle of 30 with the horizontal. The weight of the leg below the knee is 44.5 N, with the centre of gravity located below the knee joint. The leg is being held in this position because of the force M applied by the quadriceps muscle, which is attached 0.100 m below the knee joint (see the drawing). Determine the magnitude of M.
PHYS 1P21/1P91 July 2016 Page 11 of 12 10. [10 marks] Circle the letter labelling the best response in each case. DO NOT WRITE THE LETTERS CORRESPONDING TO YOUR ANSWERS FOR THE MULTIPLE-CHOICE QUESTIONS ON THE TEST PAPER. Do not use brightly coloured pens or highlighters to indicate your answers. (a) A straight-line segment of a position-time graph lies below the horizontal axis but is inclined upwards. The object i. moves in the negative direction and its speed is increasing. ii. moves in the negative direction and its speed is constant. iii. moves in the negative direction and its speed is decreasing. iv. moves in the positive direction and its speed is increasing. v. moves in the positive direction and its speed is constant. vi. moves in the positive direction and its speed is decreasing. (b) You throw Ball A horizontally from the top of a tall building, and at the same time you drop Ball B from the same starting position. Air resistance can be neglected. i. Ball A hits the ground first. ii. Ball B hits the ground first. iii. The two balls hit the ground at the same time. iv. [It depends on the relative masses of the balls.] v. [It depends on the initial speed of Ball A.] (c) Consider how the gravitational force exerted by the Sun on the Earth would change if the distance between the Sun and the Earth remained the same, the masses of the Sun and the Earth remained the same, but the radius of the Sun suddenly decreased by a factor of 2. The force would i. increase by a factor of 2. ii. increase by a factor of 4. iii. decrease by a factor of 2. iv. decrease by a factor of 4. v. remain unchanged. (d) An apple falls from a tree and hits the ground. The mass of the Earth is 6 10 24 kg and the mass of the apple is 0.1 kg. As the apple falls, the force that the Earth exerts on the apple is the force that the apple exerts on the Earth. i. greater than ii. equal to iii. less than iv. [The apple does not exert a force on the Earth, it just responds to the force that the Earth exerts on it.]
PHYS 1P21/1P91 July 2016 Page 12 of 12 (e) You are standing on a bathroom scale in an elevator when the cable holding the elevator suddenly breaks. The scale reading i. increases to a slightly larger value. ii. remains the same. iii. decreases to a slightly smaller value. iv. decreases abruptly to zero. (f) The mass of Object A is greater than the mass of Object B. The force that Earth exerts on Object A is the force that Earth exerts on Object B. i. greater than ii. equal to iii. less than iv. [It depends on whether the objects are at rest or moving.] (g) While you are running, how should you throw a ball so that you can catch it again yourself? Neglect air resistance. i. Slightly forward. ii. Straight up. iii. Slightly backward. iv. It can t be done. (h) Alice and Basil each throw a rock from the top of a cliff. The rocks have the same mass and the same initial speeds. Alice throws her rock horizontally and Basil throws his rock at a 32 above the horizontal. Ignoring air resistance, which rock has the greater impact speed upon hitting the ground? i. Alice s rock. ii. Basil s rock. iii. The impact speeds are the same. iv. [It depends on the masses of the rocks.] (i) Why is it difficult for a high-speed car to negotiate an un-banked curve? i. A large force is pushing the car outward. ii. The magnitude of the friction force may not be large enough to provide the necessary inward acceleration. iii. The kinetic friction force may be too large. iv. The faster the car moves, the harder it is to turn the steering wheel. (j) When a ball is thrown straight up, its acceleration i. is momentarily zero at its peak height. ii. gradually decreases until it reaches peak height, then gradually increases on the way down. iii. has a constant upward value on the ball s upward journey, and has a constant downward value on the ball s downward journey. iv. [None of the above.]