UNIT B SUMMARY KEY CONCEPTS CHAPTER SUMMARY 4 Gravity extends throughout the universe. Fundamental forces Force Net force Gravitational force Gravitational field strength Newton s law of universal gravitation Calculating g anywhere in the universe Variations in g Free fall and weightlessness g F g _ mtest F g Gm Am B r 2 There are four fundamental forces: gravitational, electromagnetic, and strong and weak nuclear forces. (4.1) Force is a push or a pull on an object. Force is a vector quantity measured in newtons (1 N 1 kg m/s 2 ). (4.1) Net force is the vector sum of two or more forces acting simultaneously on an object. A free-body diagram helps you determine the net force acting on an object. (4.1) Gravitational force is a fundamental force, and can be described as an action-at-a-distance force or as a field. (4.2) Gravitational field strength is the ratio of gravitational force to mass at a specific location. The units of gravitational field strength are N/kg or m/s 2. (4.2) Newton s law of universal gravitation states that the gravitational force of attraction between any two masses is directly proportional to the product of the masses and inversely proportional to the square of the separation distance between the centres of both masses. (4.2) Newton s law of gravitation can be used to determine the magnitude of gravitational field strength anywhere in the universe. The magnitude of gravitational field strength at a location is equal to the magnitude of gravitational acceleration at that location. (4.3) The value of g at Earth s surface depends on latitude, altitude, the composition of Earth s crust, and Earth s rotation about its axis. (4.3) Free fall is the condition in which the only force acting on an object is the gravitational force. True weightlessness is the condition in which weight 0 for an object and F g 0 on the object. (4.3) 5 Forces can change velocity. Newton s first law of motion Newton s second law of motion Newton s third law of motion Types of friction Factors affecting friction Coefficients of static and kinetic friction F net m a F A on B F B on A (F f,static ) max μ s F N F f,kinetic μ k F N Newton s first law states that an object will continue being at rest or moving at constant speed in a straight line unless acted upon by a non-zero net force. (5.1) Newton s second law states that when a non-zero net force acts on an object, the object accelerates in the direction of the net force. The magnitude of the acceleration is directly proportional to the magnitude of the net force and inversely proportional to the mass of the object. (5.2) Newton s third law states that if object A exerts a force on object B, then B exerts a force on A that is equal in magnitude and opposite in direction. (5.3) Friction is a force that opposes either the motion of an object or the direction the object would be moving in if there were no friction. Static friction is present when an object is stationary but experiences an applied force. Kinetic friction is present when an object is moving. (5.4) The magnitude of the force of kinetic friction acting on an object is directly proportional to the normal force on the object. (5.4) The coefficient of kinetic friction is a proportionality constant that relates the magnitude of the force of kinetic friction to the magnitude of the normal force. The coefficient of static friction is a proportionality constant that relates the maximum magnitude of the force of static friction to the magnitude of the normal force. Temperature, moisture, the roughness of the contact surfaces, and the materials forming the contact surfaces are some factors that affect the values of the coefficients of friction. (5.4) 156 Unit B Summary
UNIT B REVIEW ACHIEVEMENT CHART CATEGORIES k Knowledge and understanding t Thinking and investigation c Communication a Application Key Terms Review 1. Using your own words, define these terms, concepts, principles, or laws. You may use additional terms to represent your understanding. c force normal force friction applied force gravitational force gravitational field strength weight mass Newton s law of universal gravitation free fall inertia Newton s first law of motion Newton s second law of motion action force reaction force Newton s third law of motion static friction kinetic friction coefficient of static friction coefficient of kinetic friction Key Concepts Review CHAPTER 4 2. Although there are many examples of forces, there are only four fundamental forces. k (a) List the 4 fundamental forces from weakest to strongest. (b) State which of these forces act at very small distances. (c) State which of theses forces may be repulsive or attractive. 3. A 45-kg parachutist is descending at constant speed. (a) Draw a free-body diagram of the situation. k (b) Explain why the parachutist is not accelerating. k (c) Explain why a free-body diagram is helpful to describe the situation. k 4. Compare the acceleration due to gravity and the gravitational field strength at the top of a tall skyscraper. k 5. Is an object in free fall weightless? Explain your reasoning. k 6. Calculate the gravitational force acting on a 251-kg satellite at an altitude of 1.2 10 4 km above Earth s surface. Use the data from Table 4.3 on page 117. k 7. Two bags, each containing ten oranges of equal mass, are hung 4.0 m apart. Describe two situations, one involving mass and the other involving separation distance, that would quadruple the gravitational force exerted by one bag on the other. Explain your answer. k 8. Calculate the gravitational field strength at an altitude of 1.5 10 4 km above Earth s surface. Use the data from Table 4.3 on page 117. k CHAPTER 5 9. An object experiences zero net force. Describe the possibilities for its motion. k 10. An object experiences three forces: F 1 is 60 N [E], F 2 is 36 N [W], and F 3 is 83 N [W]. Explain, using words and diagrams, how to calculate the net force on the object. What is the net force? k 11. Calculate the acceleration of a 1478-kg car if it experiences a net force of 3100 N [W]. k 12. What happens to the acceleration of an object if the mass is constant and the net force (a) quadruples? k (b) is divided by 4? k (c) becomes zero? k 13. A pencil exerts a force of 15 N [down] on a notebook. What is the reaction force? What object is exerting the reaction force? k 14. How does the ability of a car slowing down on wet asphalt compare to it slowing down on wet concrete? Use the data from Table 5.1 on page 148. k Unit B Review 157
Connect Your Understanding 15. A car is stopped at a stoplight facing due east. When the light turns green, the car gradually speeds up from rest to the city speed limit, and cruises at the speed limit for a while. It then enters a highway on-ramp and gradually speeds up to the highway speed limit all the while heading due east. Sketch a free-body diagram for the car during each stage of its motion (five diagrams in total). t 16. Use an example to explain the meaning of the statement: The gravitational force exerted by Mars on a space probe varies inversely as the square of the separation distance between the centre of Mars and the centre of the probe. a 17. Compare the gravitational force exerted by Earth (mass M) on two satellites (masses m and 2m) in orbit at the same altitude. a 18. Compare the magnitude of Earth s gravitational field strength at the equator and at the North Pole. Explain your answer to a classmate. c 19. On Earth, how does the mass of an object affect the value of each quantity? Explain your answers. (a) acceleration due to gravity t (b) gravitational field strength t 20. If the ski jumping and bobsled events at the 2010 Winter Olympics in Vancouver and Whistler, B.C. had been held near the top of the mountain rather than at the base, how might the results of these events have been affected? Whistler has an elevation of 2182 m at the top of the mountain and 652 m at the base. a 21. A student working on a satellite problem got an answer of 57.3 N s 2 /m. What physical quantity was the student solving for? a 22. The gravitational force on an object located 2r Earth from Earth s centre is 200 N [toward Earth s centre]. What is the gravitational force if the object is 10r Earth from Earth s centre? a 23. A spring scale is used to measure the gravitational force acting on a 4.00-kg silver block on Earth s surface. If the block and spring scale are taken to the surface of Mars, by how much does the reading on the spring scale change? Use the data from Table 4.3 on page 117. a 24. Suppose the mass of the person sitting next to you is 70 kg and the separation distance between you and that person is 1.0 m. The mass of Mars is 6.42 10 23 kg and the separation distance between Mars and Earth is 2.3 10 11 m. Compare the gravitational force exerted on you by Mars and the gravitational force exerted on you by the person sitting next to you. Assume the distance from Mars to you and to Earth is the same. t 25. Explain why the coefficients of static and kinetic friction are numerals without units (i.e. dimensionless). c 26. Consider the quantities gravitational force, mass, and gravitational field strength. Which of these quantities affects the inertia of an object? t 27. A person with a plaster cast on an arm or leg experiences extra fatigue. Use Newton s laws of motion to explain to a classmate the reason for this fatigue. c 28. Use inertia and Newton s first law to explain how the spin cycle in a washing machine removes water from wet clothes. t 29. A load is placed on a 1.5-kg cart. A force of 6.0 N [left] causes the cart and its load to have an acceleration of 3.0 m/s 2 [left]. What is the mass of the load? a 30. A book is at rest on a table. The table is exerting an upward force on the book that is equal in magnitude to the downward force exerted by the book on the table. What law does this example illustrate? t 31. Consider the motion of a rocket during lift off from a launch pad. A student says that the rocket pushes down against the launch pad during lift off. This causes the rocket to then move up. Another student says that the launch pad is not necessary to push against. Which student is correct? t Skills Practice 32. A 50-kg diver steps off a 9.0-m diving tower at the same time as a 100-kg diver. Work with a partner to compare the times taken for the two divers to reach the water. Ignore air resistance. a 158 Unit B Review
33. Skylab 1, the first American space station, had a mass of about 68 t. It was launched into orbit 435 km above Earth s surface. Calculate the gravitational field strength at the location of Skylab 1 at this altitude. Use the data from Table 4.3 on page 117. a 34. Consider a 5.0-kg and a 10-kg rock both freefalling from a low bridge into a river below. Neglecting air resistance, (a) Draw a free-body diagram for both rocks. t (b) What is the net force acting on each rock? a (c) What is the acceleration of each rock? a (d) Which rock would hit the water first? Explain your answer. c 35. A 2.0-kg mass is attached to a 3.0-kg mass by a string. The system is on a frictionless surface. If a force of 25 N is applied to the 3.0-kg mass, directed away from the 2.0-kg mass, calculate (a) the acceleration of the system a (b) the tension in the string a 36. A force acting on train A causes it to have an acceleration of magnitude 4.0 10 1 m/s 2. Train A has six cars with a total mass of 3.0 10 5 kg, and a locomotive of mass 5.0 10 4 kg. Train B has a locomotive of the same mass as train A, and four cars with a total mass of 2.0 10 5 kg. If the same force acts on train B, what will be its acceleration? Ignore friction. t 37. A submarine rescue chamber has a mass of 8.2 t and safely descends at a constant velocity of 10 cm/s [down]. If g 9.81 m/s 2, what is the upward force exerted by the cable and water on the chamber? a 38. A 240-kg motorcycle and 70-kg rider are travelling on a horizontal road. The air resistance acting on the rider-bike system is 1280 N [backward]. The road exerts a force of static friction on the bike of 1950 N [forward]. What is the acceleration of the system? a 39. The velocity of a 0.25-kg model rocket changes from 15 m/s [up] to 40 m/s [up] in 0.60 s. Calculate the force that the escaping gas exerts on the rocket. a 40. A 4.0-kg mass experiences a net force of 36 N for 3.1 seconds, in the direction in which it was already moving. If the mass s original speed was 2.7 m/s, calculate its speed after the force was applied. a 41. A 1.2-kg ball tossed at a velocity of 6.7 m/s vertically upward encountered a force of air resistance averaging 1.4 N. k (a) Draw a free-body diagram for this ball. (b) Calculate the average net force experienced by the ball. (c) Calculate the average acceleration of the ball. (d) How much height had the ball gained when its velocity was zero. (e) Can the ball reach a height greater than your answer in (d)? Explain. 42. Two boxes, A and B, are in contact and initially stationary on a horizontal, frictionless surface. Box A has a mass of 60 kg and box B a mass of 90 kg. A force of 800 N [right] acts on box A, causing it to push on box B. k (a) What is the acceleration of both boxes? (b) What is the magnitude of the action and reaction forces between the boxes? 43. A person exerts a force of 1.5 N [right] to pull a 2.0-kg block of glass at constant velocity along a horizontal surface on the Moon (g Moon 1.62 m/s 2 ). What is the coefficient of kinetic friction for the glass on the surface? k 44. Three oak blocks, m A 4.0 kg, m B 6.0 kg, and m C 3.0 kg, are positioned next to each other on a dry, horizontal oak surface. Use the data from Table 5.1 on page 148 to answer these questions. k (a) What horizontal force must be applied to accelerate the blocks at 1.4 m/s 2 [forward]. (Assume that the blocks are already moving at a constant velocity.) (b) Calculate the force exerted by m B on m C. (c) Calculate the force exerted by m B on m A. 45. A 60-kg student is standing on a scale in an elevator on Earth. What will be the reading on the scale when the elevator is t (a) moving down at constant speed? (b) at rest at a floor? (c) accelerating at 4.9 m/s 2 [up]? (d) accelerating at 3.3 m/s 2 [down]? 46. During the last seconds of a hockey game, the losing team replaces their goalie with a good shooter. The other team shoots the 150-g puck with an initial speed of 7.0 m/s directly toward the unguarded net from a distance of 32 m. The coefficient of kinetic friction for the puck on the ice is 0.08. (a) What is the force of kinetic friction acting on the puck? a (b) What is the acceleration of the puck? a Unit B Review 159
(c) How long does it take the puck to stop? a (d) Will the puck reach the net if no other player touches it? a 47. A 60-kg skydiver falls toward Earth with an unopened parachute. The air resistance acting on the skydiver is 200 N [up]. What is the acceleration of the skydiver? a 48. A group of tourists on a ledge overlooking Pulpit Rock, Northwest Territories, dislodge a 25-kg boulder. The rock takes 8.0 s to fall 3.00 10 2 m into the water below. At this location, the gravitational field strength is 9.81 N/kg [down]. (a) Calculate the average acceleration of the boulder. a (b) Calculate the average air resistance acting on the boulder. a 49. The G rocket of the former Soviet Union has a mass of about 3.8 10 6 kg and its first-stage engines exert a thrust of about 5.0 10 7 N [up]. (a) What is the weight of the rocket on Earth s surface? a (b) Calculate the net force acting on the rocket at liftoff. a (c) Calculate the initial acceleration of the rocket. a (d) What should happen to the acceleration if the force exerted by the engines remains constant as the fuel burns? c (e) Why is the first stage jettisoned after the fuel is consumed? c 50. A sliding object of mass m travelling at constant speed on a frictionless surface encounters a rough surface with a coefficient of kinetic friction k. Show that the acceleration of this object on the rough surface is a = k g. a 51. The value of g on the Moon is less than that on Earth. So a pendulum on the Moon swings slower than it would on Earth. Suppose a pendulum is 36 cm long. Use the equation T 2 l_ g to calculate the period, T, at the equator on Earth and on the Moon. Use the data from Table 5.1 on page 148. a 52. Construct a gathering grid to distinguish among Newton s three laws. In the left column, identify the criteria you will use to compare and contrast the laws. Add three additional columns, one for each law. Then place checkmarks in the appropriate columns to compare the laws. t Revisit the Big Ideas and Fundamental Concepts 53. Consider a space probe moving at constant speed in space. Explain what would happen to each of the quantities listed below as the probe approaches a massive planet. Use as many descriptive terms as you can in order to represent your understanding. c The probe s speed Its acceleration Its direction of travel 54. Write a blog entry listing simple safety checks that drivers can do before venturing on the road. c 55. A sailor is sitting in her sailboat. The wind has just died down and she wishes to return to shore. She decides to use a fan to blow air at the sail. What will happen when the fan is turned on? Will she reach the shore? a Science, Technology, Society, and the Environment 56. Look at the picture of a car being tested for a front-end collision. Discuss the markings on the car and their use to researchers trying to measure forces and accelerations. a Question 56 57. During the 2000 Sydney Olympics, some swimmers wore special swimsuits designed to reduce water resistance. Compare the arguments that people might make to defend or oppose the standardization of athletic equipment in the interests of fair play. c 58. Manufacturers of skis recommend different waxes for different snow temperatures. Design and carry out an experiment to test the recommendations for three different waxes. t 59. Wear is thought to be the largest limiting factor to the longevity of artificial joints. Describe how forces and lifestyle affect the longevity of these devices. a 160 Unit B Review
60. The process of walking involves all three of Newton s laws in some way. The forces applied to your foot help you move around by overcoming static friction, accelerate, stop, or stay in one location with all forces balanced. All of these forces are applied to a small area, your foot. Using the concepts learned in this unit, describe what you think a shoe manufacturer should consider when designing (a) an athletic shoe a (b) a casual shoe a Reflection 61. How has your understanding of forces changed after this unit? Identify three things that helped change your understanding of forces. 62. What are two questions you have about forces? B13 Unit Task PHYSICS SOURCE Tire Design, Stopping Distance, and Vehicle Mass Question How do tire tread, surface conditions, and vehicle mass affect the stopping distance of a vehicle? Task Overview Imagine that you work for the Ontario Ministry of Transportation. One section of highway has an abnormally large number of accidents. The surface of one lane of the highway is concrete and the other is surfaced in asphalt. You are a member of a research team formed to determine the stopping distances for different types of tires on vehicles of different masses on both wet and dry surfaces. Using a format of your choice, report on your findings to the Traffic Branch of the Ministry. Your teacher will give you a copy of the full Task. Figure 5.40 Unit B Review 161