Hints to help with selected problems. Draw a free-body diagram of the situation and then a component triangle. 1.5a

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1 Hints to help with selected problems 10. Determine the acceleration of a 34 kg block along a frictionless inclined plane with a 35.0 o slope (i.e., gradient). [5.6 m/s 2 down] Draw a freebody diagram of the situation and then a component triangle. 1.5a Use the information and diagram below to answer question 4. Cue balls on coin operated billiard tables are either larger than the numbered balls or are magnetic. This allows them to be returned for play in the event they are accidentally pocketed (i.e., scratched). 4. A 0.17 kg cue ball is moving at 4.0 m/s when it strikes a 0.16 kg stationary numbered ball (object ball). After the collision, the cue ball moves 60 o to the left of its original direction while the object ball moves 30 o to the right of the cue ball s original path. Determine the speed of the a. cue ball after the collision. [2.0 m/s] b. object ball after the collision. [3.7 m/s] Cue ball before collision Cue ball after collision Object ball after collision The sum of the two momentum vectors after the collision must be equal to the momentum of the cue ball before the collision. Make a rightangle triangle: 2.4a Copyright Kennedy,

2 6. Two identical 350 g toy cars with magnets on their ends are used to compress a spring at the bottom of a frictionless incline. Car 1 is moving with a speed of 0.25 m/s before rolling down the incline and connecting and sticking to car 2 that is initially at rest. a. Determine the velocity of the cars after they collide. [0.87 m/s to the right] b. Show that the collision is not elastic. [Appendix A] c. If the toy cars come to a stop by compressing the spring a distance of 1.50 cm, determine the spring s constant. [2.3 x 10 3 N/m] 1 v = 0.25 m/s 2.5.a 15.0 cm 2 Both the law of conservation of energy and the law of conservation of momentum are needed to solve this question. 8. A 25.0 g arrow is shot into a 1.00 kg block of Styrofoam. The Styrofoam absorbs the impact of the arrow and slides into a spring (140 N/m) compressing it 5.30 cm as shown in the diagram. As the Styrofoam and arrow compress the spring, 60 % of the energy is dissipated as heat. Calculate the speed of the arrow before it hit the Styrofoam [40 m/s] arrow Styrofoam & Spring 2.5.b First solve for the spring potential energy. Then use the 60 % dissipated (i.e.,, 40 % retained) to determine the kinetic energy of the arrow/styrofoam before it contacts the spring. Now the law of conservation of momentum is used to calculate the speed of the arrow before it collides with the Styrofoam block. Copyright Kennedy,

3 16. Determine the electric field strength at point P in the following situations if charge A is 4.00 µc and charge B is 3.00 µc. [1.12 x 10 7 N/C, 19.8 N of E] 3.3a 17. Determine the electric field strength at point P in the following situation if charge A is 4.00 µc and charge B is 3.00 µc. [3.44 x 10 6 N/C, 3.41 S of W] 3.3b Copyright Kennedy,

4 15. A 4.20 x 10 3 kg pith ball, having a charge magnitude of 2.40 µc, is suspended on a 90.0 cm long string between two oppositely charged parallel plates as shown in the diagram. The pith ball is 2.00 cm from its original vertical position before the plates were charged. [Appendix A] Draw a freebody diagram and a displacement triangle. Similar triangles are set up. 2.0 cm 3.0 cm 3.5a 5. Two charges are separated by a distance of 1.0 m as shown in the diagram below. A third charge of 2.0 nc is to be placed in line with the two fixed charges so that the net electrostatic force acting on the third charge will be zero. Determine the location on the line where this third charge should be located. 3.8a 1.0 nc 4.0 nc The third charge could possibly be located in one of three places (to the left, inbetween, or to the right). Draw a freebody diagram for the third charge in each of the three possible locations. For the net force to equal zero, the two forces acting on it must be equal and opposite. Write an equation to express this. A quadratic equation with two possible solutions should be obtained. Your freebody diagrams will help decide which is the correct solution. Copyright Kennedy,

5 7. At the equator, the Earth s magnetic field is nearly parallel to the surface with a magnitude of 4.45 x 10 5 T. A truck is driven due east starting from a point on the equator. Determine the electron flow direction through the truck s vertical antenna. [down, towards the ground] Draw a diagram that shows what is described in the question. Then use a hand rule to determine the flow of electrons. 4.5a 5. Cell phone tower A is at grid location I13 and tower B is at M3 on the map shown below. Tower A detects a signal coming from a bearing of 350 (80 N of W). Tower B detects the same signal coming from a bearing of 264 (84 W of S). Determine the most likely grid location of the cell phone. [Appendix A] 5.1a Use a ruler to draw lines representing the direction the signal comes from for each cell phone tower. Where the lines intersect is the location of the phone. Use the information below to answer question A certain compound microscope has two convex lenses that are 6.0 cm apart. The objective lens has a focal length of 1.0 cm, and the eyepiece has a focal length of 7.0 cm. The object under study is placed 1.5 cm from the objective lens as shown in the diagram below where 1 division = 1.0 cm. Determine the microscope s magnifying power. 5.5a First: Use the objective lens and its focal length draw a ray diagram to establish the location and height of the image. Second: Use the image that was drawn and use it as if it is an object for the eyepiece draw a ray diagram with the image from the objective lens as the object for the eyepiece lens. It can be useful to use two different colours to help interpret all the overlapping lines. Copyright Kennedy,

6 29. In a photoelectric experiment a variable frequency light source was incident upon a photoelectric metal and the following stopping voltages were recorded. Use the following data to a. graph the data. b. determine i. the threshold frequency of the metal. [~2.4 x Hz] ii. the work function of the metal. [~1.0 ev] iii. Planck s constant. [~7.2 x J s] 6.2a The slope of the line is Planck s constant. For this graph the units of the slope will be evs. Convert the ev to joules to be able to compare it to the accepted value of 6.63 x J s. 7. Electrons are accelerated from rest across a potential difference of 1200 V in a CRT. This beam of electrons then enter a magnetic field of T. Determine the radius of the beam s curvature (assume the beam and the magnetic field are perpendicular to each other). [2.60 mm] 7.1a Use the following force expression and energy expression. 7. Assume that each photon equally shares the rest masses of the positron and electron and their kinetic energies. Use the following expressions to start each section. 8.6a Copyright Kennedy,