BROCK UNIVERSITY. Course: PHYS 1P21/1P91 Number of students: 234 Examination date: 5 December 2014 Number of hours: 3

Transcription

1 Name: Student #: BROCK UNIVERSITY Page 1 of 12 Final Exam: December 2014 Number of pages: 12 (+ formula sheet) Course: PHYS 1P21/1P91 Number of students: 234 Examination date: 5 December 2014 Number of hours: 3 Time of Examination: 8:00 11:00 Instructor: S. D Agostino A formula sheet is attached at the end of the test paper. No other aids are permitted except for a non-programmable, non-graphing calculator. Solve all problems in the space provided. Total number of marks: Total

2 PHYS 1P21/1P91 December 2014 Page 2 of [5 marks] A soccer ball is kicked from the ground so that it is projected at an initial angle of 39 relative to the ground and with an initial speed of 28 m/s. The ground is flat and horizontal, and there is no air resistance. (a) Determine the time that the soccer ball stays in the air until it hits the ground. (b) Determine how far from the kicking point the ball hits the ground. (c) Determine the ball s maximum height above the ground.

3 PHYS 1P21/1P91 December 2014 Page 3 of [5 marks] The Earth orbits the Sun once per year ( s) in an approximately circular orbit of radius m. With respect to the Sun, determine (a) the Earth s angular speed. (b) the Earth s tangential speed. (c) the magnitude of the Earth s centripetal acceleration.

4 PHYS 1P21/1P91 December 2014 Page 4 of [5 marks] A 40-kg child slides down a curved slide starting at the top with an initial speed of 4 m/s. (a) Suppose that the slide is frictionless. Determine the speed of the child when she is 3 m below her starting height. (b) Suppose that the slide has friction. Determine the speed of the child when she is 5 m below her starting height if she starts from rest and 300 J of thermal energy is dissipated during the motion.

5 PHYS 1P21/1P91 December 2014 Page 5 of [5 marks] Two pucks collide on an air-hockey table, where friction between the pucks and the table can be assumed to be zero. Puck A has a mass of kg and initially moves East with a speed of 5.5 m/s. Puck B has a mass of kg and is initially at rest. After the pucks collide, Puck A moves at an angle of 65 North of East and Puck B moves at an angle of 37 South of East. Determine the speeds of the two pucks just after the collision.

6 PHYS 1P21/1P91 December 2014 Page 6 of [4 marks] Two banked curves have the same radius. Curve A is banked at an angle of 13 and Curve B is banked at an angle of 19, where both angles are measured relative to the horizontal. A car can travel around Curve A without relying on friction at a speed of 18 m/s. Determine the speed at which the same car can travel around Curve B without relying on friction.

7 PHYS 1P21/1P91 December 2014 Page 7 of [4 marks] In the figure, the two strings pass over massless, frictionless pulleys. The coefficient of friction between the 80-kg block and the table top is 0.1. When the 80-kg block is released, all three blocks begin to move. 80 kg (a) Determine the blocks acceleration. (b) Determine the tension in each string. 10 kg 25 kg

8 PHYS 1P21/1P91 December 2014 Page 8 of [4 marks] A bowling ball rolls along a rack without slipping. At the bottom of the slope the ball s translational speed is 3.50 m/s. Determine the ball s translational speed after it reaches the top of the slope, which is 0.76 m above the bottom of the slope. Friction can be ignored and the ball s moment of inertia is 2 5 MR2, where R is the radius of the ball m

9 PHYS 1P21/1P91 December 2014 Page 9 of [4 marks] A 10-g bullet is fired into a 2.5-kg wooden block that is attached to one end of a massless spring that has stiffness constant 845 N/m. The other end of the spring is fixed in place, and the spring is initially unstretched. The block rests on a horizontal, frictionless surface. Once the bullet strikes the block it quickly stops and becomes embedded into the block, and the block + bullet system oscillates with an amplitude of 0.2 m. Determine the initial speed of the bullet.

10 PHYS 1P21/1P91 December 2014 Page 10 of [4 marks] A subatomic particle called a pion has mass kg. A short time after being formed (the pion s lifetime) the pion transforms into other particles. A pion moves at 99% of the speed of light relative to a laboratory. An observer who is stationary relative to the laboratory measures the lifetime of the pion as s. (a) Determine the pion s lifetime as measured by a hypothetical observer moving along with the pion. (b) According to the hypothetical observer in Part (a), how far does the laboratory move during the pion s lifetime? (c) Determine the pion s total momentum and total energy as measured by an observer stationary relative to the laboratory.

11 PHYS 1P21/1P91 December 2014 Page 11 of [10 marks] Circle the best response in each case. (a) You stand on a bathroom scale in an elevator, when the elevator suddenly begins accelerating upwards. The scale reading i. increases somewhat. ii. decreases somewhat. iii. does not change. iv. decreases suddenly to zero. v. [There is not enough information.] (b) You simultaneously release two balls from a height; one you drop straight down, and the other you throw horizontally. Which ball reaches the ground first? i. The ball dropped straight down reaches the ground first, because it travels a shorter distance. ii. The ball thrown horizontally reaches the ground first, because its speed is greater. iii. The two balls reach the ground at the same time, because their vertical motion is the same. iv. [It depends on the masses of the balls; the heavier ball falls faster.] v. [It depends on the masses of the balls; the heavier ball falls more slowly.] (c) Why is it difficult for a car to negotiate a curve at high speed? i. A huge force is pushing the car outward. ii. The sliding friction force is too large. iii. The faster the car moves, the harder it is for the driver to steer. iv. The magnitude of the friction force may not be large enough to provide the necessary acceleration. v. Because of Newton s third law, the car s reaction force may be too great. (d) How would the gravitational force exerted by the Sun on the Earth change if the distance between the Sun and the Earth suddenly shrank to half of its original distance, while the masses remained the same. 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. (e) Two satellites orbit the Earth in circular orbits. The radius of the orbit of Satellite A is smaller than the radius of the orbit of Satellite B. i. The speed of B is greater than the speed of A. ii. The period of A is greater than the period of B. iii. The speed of A is greater than the speed of B. iv. The angular speed of B is greater than the angular speed of A. v. [There is not enough information given.]

12 PHYS 1P21/1P91 December 2014 Page 12 of 12 (f) For an object moving in a circle at a constant speed, i. the net force on the object is zero, because the centripetal force exactly balances the centrifugal force. ii. the net force on the object is zero, because the angular acceleration is zero. iii. the net force on the object is directed towards the centre of the circle. iv. the net force on the object is directed away from the centre of the circle. v. the net force on the object is directed inwards, but not exactly towards the centre, because the object has a tangential velocity. (g) An object slides in a straight line on a horizontal frictionless surface. In order to continue its motion at a constant speed, i. a constant pushing force is needed. ii. a steadily increasing pushing force is needed. iii. a steadily decreasing pushing force is needed. iv. no external force is needed. v. no external force is needed only if the object contains its own force. (h) Object A has mass 10 kg and Object B has mass 2 kg. Object A collides with Object B and momentum is conserved in the collision. i. The force that object A exerts on Object B is greater than the force that Object B exerts on Object A. ii. The force that object A exerts on Object B is less than the force that Object B exerts on Object A. iii. The force that object A exerts on Object B is equal to the force that Object B exerts on Object A. iv. [It depends on whether the collision is elastic or inelastic.] (i) You pick up a book that is lying on the floor and place it on a desk. The total mechanical energy of the book i. has increased, because its potential energy has increased. ii. has decreased, because it is farther from the centre of the Earth. iii. remains the same, because it is still at rest. iv. remains the same, because no work is done on the book. v. remains the same, because the kinetic energy of the book does not change. (j) The laws of motion that form the core of this course are based on the work of i. Archaeopteryx of Jurassic. ii. Loki of Marvel. iii. Shaquille of Louisiana. iv. Monty of Python. v. Isaac Newton of Woolsthorpe.