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the water. The acceleration of the dolphin is 2.6 m/s2 [up]. 8. Two boxes, A and B, are touching each other and are at rest on a horizontal, frictionless surface. Box A has a mass of 25 kg and box B a mass of 15 kg. A person applies a force of 30 N [right] on box A which, in turn, pushes on box B. Calculate the accele... |
is large, a player will usually bump the ball to slow it down so that another player can redirect it over the net (Figure 3.51). At the instant the player bumps the ball, the ball exerts a large force on the player’s arms, often causing sore arms. Immediately after the interaction, the ball bounces upward. To explain ... |
) What evidence do you have that two forces were present? (c) What evidence do you have that a force was exerted on each cart? (d) How do the magnitudes and directions of the two forces compare? 3. Compare and contrast the results from steps 3 and 4. action force: force initiated by object A on object B reaction force:... |
reaction force is the downward force that the ball exerts on the player’s arms. During the collision, the ball accelerates upward and the player’s arms accelerate downward (Figure 3.54). e TECH Explore how a stranded astronaut can return to a spacecraft by throwing away tools. Follow the eTech links at www.pearsoned.c... |
exerted by Earth on apple Faction force exerted by apple on Earth Freaction Figure 3.56 The action-reaction forces when an apple falls toward Earth’s surface 162 Unit II Dynamics 03-Phys20-Chap03.qxd 7/24/08 10:37 AM Page 163 When a magnet is brought close to an iron nail, the action force is the magnetic force that t... |
xd 7/24/08 10:37 AM Page 164 Applying Newton’s Third Law to Situations Involving Frictionless Surfaces In Example 3.12, an applied force acts on box A, causing all three boxes to accelerate. Newton’s third law is used to calculate the force that box C exerts on box B. Example 3.12 Three boxes, A, B, and C, are position... |
Involving Friction In Example 3.13, a rough surface exerts a force of friction on two boxes. Newton’s third law is used to calculate the force exerted by box B on box A in this situation. Example 3.13 Two boxes, A and B, of identical material but different mass are placed next to each other on a horizontal, rough surf... |
kg is connected to log A by another light chain. (a) The horses can pull with a combined force of 2600 N. The ground exerts a force of friction of magnitude 2400 N on the logs. Calculate the acceleration of the logs. (b) If the force of friction on log A is 900 N, calculate the force exerted by log B on log A. Answer ... |
consumption. This allows greater payloads to be carried efficiently and safely through the sky. By 1925, Turnbull had perfected a propeller that used an electric motor to change its pitch. In 1927, the Canadian Air Force successfully tested the propeller at Borden, Ontario. Turnbull was later inducted into the Canadia... |
rocket when the rocket is released. • Explain the motion of the rocket, water, and air in terms of Newton’s third law. Include sketches showing at least three action-reaction pairs of forces. • How well did your results agree with your hypothesis? Chapter 3 Forces can change velocity. 167 03-Phys20-Chap03.qxd 7/24/08 ... |
on opposite sides, and another hole at the top. The box is hung from a rigid support with a string. Predict what will happen if the box is filled with water through the top hole and the holes at the bottom are open. Use Newton’s third law to explain your answer. Test your prediction. Cover the holes at the bottom with... |
xd 7/24/08 10:38 AM Page 170 In a sport such as curling, friction affects how far the stone will travel along the ice. Sweeping the ice in front of a moving stone reduces the force of friction acting on the stone (Figure 3.68). The result is that the stone slides farther. To better understand how the nature of a contac... |
, you discovered that the force of friction depends on the nature of the two surfaces in contact. If you drag an object on a smooth surface, the force of friction acting on the object is less than if you drag it on a rough or bumpy surface. If you drag a smooth block and a rough block on the same surface, the force of ... |
a force of ever-increasing magnitude, you will notice that the table remains at rest until you exceed a critical value. Because of Newton’s second law, the magnitude of the force of static friction must increase as the applied force on the table increases, if the forces are to remain balanced. Static Friction on a Hor... |
aphrase The force of static friction acting on the desk is 143 N [180]. Answer 1. FT Ffstatic FN FN Ffstatic Fg Static Friction on an Incline If an object is at rest on an incline, the net force acting on the object 0 N. Let’s first examine the forces acting on the object is zero, F net (Figure 3.74). FN Ffstatic Figur... |
exerted a force of static friction on the loonie, preventing the coin from sliding down the incline. Example 3.15 demonstrates how to calculate the force of static friction acting on a loonie at rest on an incline of 25.0. 174 Unit II Dynamics 03-Phys20-Chap03.qxd 7/24/08 10:38 AM Page 175 Example 3.15 A loonie with a... |
static prevents the loonie from sliding downhill. The positive value for Ffstatic indicates that the direction of F fstatic is uphill. 2.9 102 N [uphill] F fstatic Paraphrase The force of static friction acting on the loonie is 2.9 102 N [uphill]. Chapter 3 Forces can change velocity. 175 03-Phys20-Chap03.qxd 7/24/08 1... |
. So F a FN Ffkinetic Fg Fg θ Fg θ Figure 3.79 (left) Free-body diagram for an object accelerating downhill; (below) vector addition diagrams for the and forces Forces Forces Fg Fnet Ffkinetic Fg Ffkinetic Fnet Fnet 0 Fg FN Fg Fnet Fnet FN 0 The equation for the net force acting on the object parallel to the incline is... |
So the magnitude the object to accelerate uphill, F app must be greater than the sum of the magnitudes of F fkinetic. g and F of F Since the object is not accelerating perpendicular to the incline, the net force acting on the object in this direction is zero. The equation for the net force on the object in the perpend... |
hill] Paraphrase The acceleration of the block is 1.4 m/s2 [downhill]. Practice Problems 1. Determine the acceleration of the block in Example 3.16 if friction is not present. 2. A 55.0-kg skier is accelerating down a 35.0 slope. The magnitude of the skier’s acceleration is 4.41 m/s2. Calculate the force of kinetic fri... |
and (b)]. Da Vinci also discovered that the force of friction acting on an object depends on the normal force acting on that object. Find out what this relationship is by doing 3-11 Inquiry Lab. (a) (b) Figure 3.84 The force of friction acting on the box in each of these pictures is the same. For hard contact surfaces... |
the mass system increased, what happened to the maximum magnitude of the force of static friction? 3. What is the relationship between the maximum magnitude of the force of static friction and the magnitude of the normal force? Write this as a proportionality statement. Does this relationship agree with your hypothesi... |
of kinetic friction and the magnitude of the normal force acting on an object? Design and Conduct Your Investigation • State a hypothesis relating the magnitudes of F • Then use the set-up in Figure 3.85 on page 181 to design an experiment. List the materials you will use as well as a detailed procedure. You will need... |
temperature of the two contact surfaces, and other factors. Table 3.4 lists coefficients of friction between pairs of materials. Table 3.4 Approximate Coefficients of Friction for Some Materials Material Coefficient of Static Friction s Coefficient of Kinetic Friction k Copper on copper Steel on dry steel Steel on gre... |
improves the acceleration of the car. The amount of moisture on a road surface, the temperature of the road surface and tires, and the type of tire treads are some factors that determine if a vehicle will skid. For a given tire, the coefficients of static and kinetic friction are greater on a dry road than if the same... |
Fapp sFN sFN) vertical direction F F netv N FN Fnetv 0 FN FN mg FF g Fg (mg) mg FN mg into the equation for Fapp. Fapp Substitute FN smg Fapp sg m 46 N m (0.06)9.81 s2 46 kgm s2 (0.06)9.81 m s2 8 101 kg Paraphrase The mass of the sled is 8 101 kg. Fapp Ffstatic 0 Fneth FN forward Ffstatic Fapp Fg Figure 3.89 Practice ... |
toboggan to start moving, the surface of the incline is exerting the maximum magnitude of the force of static friction on the toboggan. u p p u h ill h ill o w n d o w n d θ 20.0° Figure 3.90 g 9.81 m/s2 u p p u h ill h ill o w n d o w n d Ffstatic FN Fg θ 20.0° θ 20.0° Fg Fg Answers 1. 0.58 2. (a) 0.47 (b) 3.3 102 N ... |
links at www.pearsoned.ca/school/ physicssource. Ffkinetic Ffkinetic Figure 3.92 Diagram showing the force of kinetic friction acting on the tires of a skidding car Safety features on vehicles such as anti-lock braking systems are designed to prevent the wheels of a vehicle from locking when a driver steps on the brak... |
the force of kinetic friction if the truck in Example 3.19 is skidding downhill at constant speed on a hill forming an angle of 15.0 with the horizontal. Answers 1. 4.59 102 2. 4.16 103 N [uphill] horizontal direction F F fkinetic neth Ffkinetic Fneth ma Ffkinetic kFN vertical direction FF F netv N FN Fnetv 0 FN FN mg... |
app Fnet Fapp ma Fapp Fapp F g Fg Fg Fg FF g F fkinetic Fg Ffkinetic Fg Ffkinetic ma Fg Ffkinetic Now, Fg mg cos So, FN (mg cos ) mg cos Also, Fg mg sin and kFN Ffkinetic Fapp ma (mg sin ) kFN) ( ma mg sin kFN Substitute FN mg cos into the equation for Fapp. Fapp ma mg sin ma mg(sin kmg cos kcos ) Practice Problems 1.... |
is weigh 15 N [down]. Calculate the difference in the maximum force of static friction for the skis on a wet and dry snowy, horizontal surface. Refer to Table 3.4 on page 183. 5. A force of 31 N [forward] is needed to start an 8.0-kg steel slider moving along a horizontal steel rail. What is the coefficient of static f... |
same road surface. Find out what hydroplaning is and how tires are designed to minimize this problem. Write a brief report of your findings, including diagrams where appropriate. Begin your search at www.pearsoned.ca/school/physicssource. 14. Design an experiment to determine the coefficients of static and kinetic fri... |
explain the motion of (a) a figure skater during a glide, and (b) a hockey puck during a cross-ice pass. Assume ice is frictionless. 3. (3.4) A transport truck pulls a trailer with a force of 1850 N [E]. What force does the trailer exert on the transport truck? 4. (3.5) An inexperienced driver, stuck in snow, tends to... |
truck hitched to a 453-kg trailer accelerates along a level road from a stoplight at 0.75 m/s2 [forward]. Ignore friction and air resistance. Calculate (a) the tension in the hitch, (b) the force of friction exerted by the road on the pickup truck to propel it forward, and (c) the force the trailer exerts on the picku... |
speed of 320 km/h in 6.50 s. The wheels of the car can exert an average horizontal force of 1.52 104 N [backward] on the pavement. If the force of air resistance on the car is 5.2 103 N [backward], what is the mass of the car? 15. A tractor and tow truck have rubber tires on wet concrete. The tow truck drags the tract... |
a free-body diagram for each type of friction. Think About It Review your answers to the Think About It questions on page 125. How would you answer each question now? e TEST To check your understanding of forces and Newton’s laws of motion, follow the eTest links at www.pearsoned.ca/school/physicssource. Chapter 3 For... |
drop two coins of different shapes and sizes from the same height. How do the rates of both coins falling compare? Materials variety of coins (penny, nickel, dime, quarter, loonie, and toonie) ruler Styrofoam™ disk (size of a loonie) Procedure 1 Choose any two different coins and place them at the edge of a table abov... |
together. Although this force is the weakest fundamental force, you can feel its effect when you interact with an object of very large mass such as Earth. When you slide down a waterslide, you can feel the gravitational force exerted by Earth pulling you downward toward the bottom of the slide (Figure 4.3). But if you... |
is the same, whether or not the object is at rest or is moving. This equation relates the gravitational force acting on an object, the so-called weight of the object, to its mass. g Fg Figure 4.6 Diagram showing the forces acting on an object that is suspended from a spring scale weight: gravitational force exerted on... |
-Phys20-Chap04.qxd 7/24/08 10:59 AM Page 199 Gravitational Mass mg is determined by finding the ratio of The mass in the equation F g the gravitational force acting on an object to the acceleration due to g and g are in the same direction, the scalar form of the gravity. Since F equation may be used: Fg mg m Fg g A pra... |
equivalent to gravitational mass. So it does not matter whether you determine the mass of an object using inertia or weight, because the numerical value of the mass is the same. Chapter 4 Gravity extends throughout the universe. 199 04-Phys20-Chap04.qxd 7/24/08 10:59 AM Page 200 action-at-a-distance force: force that ... |
to g. Figure 4.10 shows how the magnitude of Earth’s gravitational field strength changes as a test mass is moved farther away from Earth’s centre. The farther the test mass is moved, the more significant is the decrease in g. In fact, the graph in Figure 4.10 shows an inverse square relationship: g 1 r 2 Magnitude of... |
and differences among gravitational mass, inertial mass, and gravitational force. Gravitational Mass Inertial Mass Gravitational Force Definition SI Unit Measuring Instrument(s) How the Quantity Is Measured Factors It Depends On Variability with Location e TEST To check your understanding of gravitational force, weigh... |
proportional to the product of both masses: Fg mAmB Figure 4.11 shows the magnitude of the gravitational force acting on an object at Earth’s surface (rEarth), one Earth radius above Earth (2rEarth), and two Earth radii above Earth (3rEarth). If the separation distance from Earth’s centre to the centre of the object d... |
product of the two masses, and inversely proportional to the square of the separation distance. Experiments have shown that the magnitude of the gravitational force acting on any pair of objects does not depend on the medium in which the objects are located (Figure 4.14). In other words, given two fish, the gravitatio... |
that uses a sensitive fibre and a beam of light to measure very minute forces due to gravity, magnetic fields, or electric charges. Cavendish used a modified torsion balance invented by John Michell (1724–1793) to verify Newton’s law of gravitation. A modern torsion balance consists of a small, light, rigid rod with t... |
twists, and the greater the angle of rotation. By measuring the amount of deflection, the gravitational force exerted by M on m can be determined. Spheres M are then moved to a symmetrical position on the opposite side of m, and the procedure is repeated. Since the separation distance between m and M, the values of m ... |
Earth is equal to Earth’s equatorial radius. Base of mountain: rB rEarth 6.38 106 m Top of mountain: rT 6.38 106 m 5959 m The person’s weight is equal to the gravitational force exerted by Earth on the person, and is directed toward Earth’s centre both at the base and at the top of the mountain. Calculate Fg at the ba... |
A is to 6 5 halved, and mB increases to 4 of its original value Answer 1. (a) 2.5 1011 N (b) 1.3 109 N Analysis and Solution mAmB and Fg From Newton’s law of gravitation, Fg Figure 4.18 represents the situation of the problem. 1 r 2. before after mA mA Fg 1.3 1010 N mB r Fg? 2r Figure 4.18 Fg (6mA) mB 1 2 and Fg 1 (2r)... |
force on Earth (F g) Analysis and Solution Draw a free-body diagram for Earth (Figure 4.20). Practice Problems 1. During a solar eclipse, Earth, the Moon, and the Sun are aligned on the same plane as shown in Figure 4.21. Calculate the net gravitational force exerted by both the Moon and the Sun on Earth. 1.50 1011 m ... |
rase The net gravitational force on Earth due to the Sun and Moon during a lunar eclipse is 3.50 1022 N [toward Sun’s centre]. The Role of Gravitational Force on Earth’s Tides Newton used the concept of gravitational force to account for Earth’s tides. Although he correctly identified the gravitational force exerted by... |
The bulges at A and B are the high tides. The low tides occur at the midpoints of A and B. The bulge at B occurs because the land mass of Earth at B is pulled toward the Moon, leaving the ocean water behind. Next consider the fact that Earth rotates on its axis once every 24 h. As the bulges remain fixed relative to t... |
1.7374 106 m Required g) gravitational force exerted by Moon on water (F Analysis and Solution Draw a free-body diagram for the water showing only F g due to the Moon (Figure 4.26). away from Moon toward Moon Fg Figure 4.26 Practice Problem 1. Using the value of G given in Example 4.4, calculate the gravitational forc... |
assist, the flight time to Neptune was reduced from 30 to 12 years, and a minimum of onboard propellant on the spacecraft was required. Voyager 1 Voyager 1 Launch Launch Sept. 5, 1977 Sept. 5, 1977 Voyager 2 Voyager 2 Launch Launch Aug. 20, 1977 Aug. 20, 1977 Jupiter Mar. 5, 1979 Jupiter Mar. 5, 1979 Jupiter Jul. 9, 1... |
eventually Nicolaus Copernicus (1473–1543) proposed two different models of the solar system: one Earth-centred and the other Sun-centred. Later Johannes Kepler (1571–1630) developed three empirical laws describing planetary motion using astronomical data compiled by astronomer Tycho Brahe (1546–1601). Kepler’s laws c... |
Calculate the magnitude of the gravitational force exerted by (i) the Moon on a 100-kg astronaut standing on the Moon’s surface, and (ii) Earth on a 100-kg astronaut standing on Earth’s surface. (b) Explain why the values of Fg in part (a) are different. 5. Mars has two moons, Deimos and Phobos, each named after an at... |
itation, follow the eTest links at www.pearsoned.ca/school/physicssource. Chapter 4 Gravity extends throughout the universe. 215 04-Phys20-Chap04.qxd 7/24/08 10:59 AM Page 216 info BIT A g force is a force that causes an acceleration with a magnitude of some multiple of g. A force of 2g means the magnitude of the accel... |
value of the gravitational acceleration? Design and Conduct Your Investigation State a hypothesis. Then design an experiment. Identify the controlled, manipulated, and responding variables. Review the procedure in 4-2 QuickLab on page 198. List the materials you will use, as well as a detailed procedure. Check the pro... |
.38 106 1.74 106 3.40 106 7.15 107 6.03 107 2.56 107 2.48 107 *Source: Jet Propulsion Laboratory, California Institute of Technology (See JPL link at www.pearsoned.ca/school/physicssource.) Example 4.5 (a) Calculate the magnitude of the gravitational acceleration of an object at the equator on the surface of Earth and ... |
the surface of Earth is 9.78 m/s2 and of the Moon is 1.62 m/s2. Practice Problems 1. A satellite orbits Earth at a distance of 3rEarth above Earth’s surface. Use the data from Table 4.1 on page 218. (a) How many Earth radii is the satellite from Earth’s centre? (b) What is the magnitude of the gravitational accelerati... |
throughout the universe. 219 04-Phys20-Chap04.qxd 7/24/08 10:59 AM Page 220 Example 4.6 (a) What is the mass of a 60.0-kg student on Mars and on Earth? (b) What is the student’s weight at the equator on the surface of Mars and of Earth (Figure 4.33). Use the data from Table 4.1 on page 218. Fg? Mars Given (a) ms (b) m... |
magnitude of the weight. g will be toward the centre of each mg to find the Mars FgMars msgMars Earth FgEarth msgEarth N (60.0 kg)3.704 g k 222 N N (60.0 kg)9.783 g k 587 N 220 Unit II Dynamics 04-Phys20-Chap04.qxd 7/24/08 10:59 AM Page 221 Paraphrase and Verify (a) The mass of the student would be 60.0 kg on both Mar... |
that make up Earth’s crust are not uniformly distributed. Some materials, such as gold, are more dense than materials such as zinc. Earth’s rotation about its axis also reduces the measured value of g, but the closer an object is to the North or South Pole, the less effect Earth’s rotation has on g. Concept Check Leo ... |
moving at constant velocity, the scale reads 600 N. Fg 600 N 300 200 100 400 0 500 600 700 Figure 4.36 The elevator and student are either at rest or moving at constant velocity. Using the free-body diagram for the student (Figure 4.37), the equation for the net force on the student is F N F F FN F g net 0 F g 0 Fg 0 ... |
person during an elevator ride. Follow the eSim links at www.pearsoned.ca/school/ physicssource. 224 Unit II Dynamics w F N m(a g) m(g a ) Example 4.7 demonstrates how to calculate the true weight and apparent weight of an astronaut in a rocket during liftoff on Earth’s surface. Example 4.7 A 100.0-kg astronaut in a s... |
102 N [up], 9.81 102 N [down] N to find the astronaut’s apparent weight. w F N (2.94 103 N) 2.94 103 N Paraphrase During liftoff, the astronaut’s true weight is 9.81 102 N [down] and her apparent weight is 2.94 103 N [down]. In Example 4.8, an astronaut is accelerating in deep space, a location in which the gravitatio... |
224. Answers 1. (a) (F g) 1.30 102 N [down], (w) 1.15 103 N [down] F net b) (F 2. (a) (F (b) (F g) 0 N, (w) 1.02 103 N [down] g) 2.22 102 N [down], (w) 8.88 102 N [down] g) 2.22 102 N [down], (w) 6.65 102 N [down] Apply Newton’s second law. F N FN ma ma m (100.0 kg)19.6 s2 1.96 103 N Use the equation w F N to find the... |
but F 0. N N N g Observe the motion of water in a cup while in free fall by doing 4-4 QuickLab. 4-4 QuickLab 4-4 QuickLab Water in Free Fall Problem What is the motion of water in a cup when the cup is dropped from several metres above Earth’s surface? CAUTION: Do this activity outside. Have someone steady the ladder ... |
rocket is zero. The astronaut would experience no measurable gravitational forces from any celestial bodies, and the astronaut’s acceleration would be zero. In this situation, the astronaut would have a true weight of zero and an apparent weight of zero, a condition called true weightlessness. true weightlessness: sit... |
vs. rMoon. How is it similar to Figure 4.10 on page 201? (b) What is the value of g (i) on the surface? (ii) at 1 2 rMoon above the surface? (iii) at rMoon above the surface? the (c) At what distance is g 1 100 and apparent weight? 10. Calculate the acceleration of the elevator in Figures 4.38 and 4.40 on page 223. Ex... |
the chapter. gravitational force mass is one of two types Gravitation involves weight is gravitational field strength equation equation other examples inertial strong nuclear using exerted by a using celestial body where direction acceleration standard masses and a and a G is value 6.67 1011 N•m2/kg2 Figure 4.47 230 U... |
halved, mA increases by 8 times, and mB is reduced to 1 4 of its original value. 9. Suppose a 65-kg astronaut on Mars is standing on a scale calibrated in newtons in an elevator. What will be the reading on the scale when the acceleration of the elevator is (a) zero? (b) 7.2 m/s2 [up]? (c) 3.6 m/s2 [down]? 10. A 50-kg... |
and the other is asphalt. You are a member of a research team formed to determine the stopping distances in the summer for both wet and dry days for different types of tires and for different masses of vehicles. Your team is to prepare a written report on your findings for the Traffic Branch of the Ministry. Assume th... |
these tires. Remember that some drivers may lock their brakes while braking. 6 Determine the stopping distance for the different vehicles under different conditions. Remember to consider driver reaction time. 7 Write a report of your findings. Use graphs and tables where appropriate. Thinking Further Write a three-par... |
etic friction is present when an object is moving. The magnitude of the force of friction acting on an object is directly proportional to the normal force on the object. The coefficients of friction are proportionality constants that relate the magnitude of the force of friction to the magnitude of the normal force. Te... |
of the normal force acting on an object. Free fall is the condition where the only force acting on an object is the gravitational force. True weightlessness is the condition in which w 0 for an object and F 0 on the object. g Figures 4.11–4.13, 4.16, 4.24 Examples 4.1–4.4 4-3 Design a Lab Examples 4.5–4.6 Figures 4.34... |
less surface with two ropes. Person A applies a force [50] on one rope. Person B applies a force of 25 N [345] on the other rope. If the net force on the wagon is 55.4 N [26], calculate the magnitude of person A’s applied force. A θ 1 50º x θ 2 345º B 9. A book is at rest on a table. The table is exerting an upward for... |
quantity was the student solving for? 19. 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.” 20. Is an object in free fall weightless? Explai... |
cars with a total mass of 2.0 105 kg. If the same force acts on train B, what will be its acceleration? Ignore friction. 30. 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/s2, what is the upward force exerted by the cable and water on the chambe... |
pass over light, frictionless pulleys. The coefficient of kinetic friction for object B on the surface is 0.200. (a) What is the acceleration of object B? (b) What is the tension in each string? Explain why the tensions are different. (c) Draw a free-body diagram for object B. (d) Identify four action-reaction pairs a... |
? (ii) at rest at a floor? (iii) accelerating at 4.9 m/s2 [up]? (iv) accelerating at 3.3 m/s2 [down]? (b) What is the student’s apparent weight and true weight in all the situations in part (a)? 04-Phys20-Chap04.qxd 7/24/08 10:59 AM Page 237 44. A 60-kg skydiver falls toward Earth with an unopened parachute. The air re... |
suits 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. 50. List two different stakeholders in the airbag debate and describe how their positions on the issue compare. 51. The G rocket of the for... |
Circular Motion, Circular Motion, Work, and Work, and Energy Energy The International Space Station is a silent companion to Earth, placed into an orbit that is a precise balance of kinetic and gravitational potential energies. The International Space Station stays in orbit because physicists and engineers applied the... |
. The number of devices that make use of the properties of circular motion is almost too large to count. Bicycles, gears, drills, transmissions, clutches, cranes, watches, and electric motors are just a few examples. The wheel and the many technologies derived from it are a uniquely human creation (Figure 5.1). But the... |
the barrier (Figure 5.2). 2 You will be rolling a marble around inside the barrier. Before you do, predict where you think the marble will go when you remove the barrier. Now roll the marble around the inside rim of the barrier. 3 As the marble is rolling around the rim, lift the barrier and make a note of the directi... |
it is a very efficient form of transportation; and it is full of parts moving in circular motion. Perhaps most importantly for this lesson, it is easy for us to examine. When you pedal a bike, the force is transferred through the chain and the wheel turns (Figure 5.3). The wheel transmits the force to the road, which,... |
50 PM Page 243 PHYSICS INSIGHT A line tangent to the circle represents the velocity vector. It is perpendicular to the radial line at that point. v A r Figure 5.6 The velocity vector v shows the velocity of a particle at any instant as it moves on a circular path. A line drawn from point A in Figure 5.5 to the centre o... |
B. A short time has passed as the pebble moved from point A to point B. This small change in time is written as t. Chapter 5 Newton’s laws can explain circular motion. 243 05-Phys20-Chap05.qxd 7/24/08 12:50 PM Page 244 The pebble has experienced a very small displacement from point A to point B, which is written as d.... |
centripetal acceleration. If the circular motion is uniform, then so is the centripetal acceleration. According to Newton’s second law, if a mass is accelerating, it must also experience a non-zero net force. This non-zero net force is c ). In our example, the pebble stuck in the called the centripetal force (F wheel ... |
hole rubber stopper (mass 25 g) 1.5 m of string or fishing line small-diameter plastic tube 100-g mass metre-stick felt marker safety goggles stopwatch CAUTION: Remember to swing the rubber stopper over your head and in a place clear of obstructions. Table 5.1 Data for 5-2 Inquiry Lab Required Skills Initiating and Pla... |
stopwatch. While your partner does this, be sure to monitor the speed of the stopper so that the mark does not move off the lip. Record the time in the “Time 1” column of the table. 2. For each trial, divide the average time by the number of revolutions the stopper made. Record the values for the time it takes to make... |
third law states that for every action there is an equal and opposite reaction. If we apply this law to our example, then the action force is the hand pulling on the rope to make the object move in a circle. This is the centripetal force. The reaction force is the force the rope exerts on your hand. It is outward. Thi... |
INSIGHT Some texts refer to centrifugal force. This refers to the reaction force that exists as a result of centripetal force. If the centripetal force is removed, there is no centrifugal force. e SIM For an interactive demonstration that explores the relationship among centripetal acceleration, force, and velocity, v... |
of hitting the ball much more difficult (Figure 5.14). Figure 5.14 Pitchers can put a spin on a ball that causes it to curve. This curve is predictable. e WEB To learn more about the effect of putting a spin on a ball, follow the links at www.pearsoned.ca/school/ physicssource. In these sports and many others, putting... |
e) P v Figure 5.15 Point P on the spinning baseball makes one complete rotation from (a) to (e). The time for this is called the period and is measured in s/cycle. This is frequently abbreviated to s for convenience. If an object is spinning quickly, the period may be a fraction of a second. For example, a hard drive i... |
is its period? Answers 1. 5.00 Hz 2. 2.4 103 rpm 3. 1.0 103 Hz; 1.0 103 s Given T 0.00833 s Required frequency in Hz and rpm T 1 f f 1 0.00833 s 120 Hz hard drive case Now convert the SI units of frequency to rpm: Hz 60 s/min 60 s/min rpm Analysis and Solution The frequency is the inverse of the period. Solve the freq... |
s 1 0 0 10 1 s 00 1.07 105 km/h h Earth’s speed as it orbits the Sun is approximately 107 000 km/h. The speed of a planet as it rotates on its axis can be determined in the same way but varies depending on the latitude. We will explore the reasons for this later in “Centripetal Force, Acceleration, and Frequency” in s... |
accelerate at a greater rate. While the dragster performs the tire-spin, the tires change shape (Figure 5.18). The rear tires start off being fat and thick. During the spin they become thin and their diameter increases. Clearly, this must have something to do with the spinning motion of the wheel, and therefore centri... |
as Figures 5.9 and 5.10 in section 5.1. Using these figures, we can derive an equation for centripetal acceleration. vA B vB A d r r C vB –vA v C Figure 5.19 An object following in a circular path moves through a displacement as there is a change in velocity v. The triangles formed by these two vectors will d help us ... |
both experience a gravitational acceleration of 9.81 m/s2 [down]. Two objects of different masses moving in a circular path will experience the same centripetal acceleration if they have the same radius and speed. Mass does not affect centripetal acceleration, but companies that manufacture racing tires, jet engines, ... |
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