The velocity vector of a sprinting cheetah has x- and y-components vx = +16.4 m/s and vy = −26.3 m/s. (a) What is the magnitude of the velocity vector? (b) What angle does the velocity vector make with the +x- and −y-axes?
> A towline is attached between a car and a glider. As the car speeds due east along the runway, the towline exerts a horizontal force of 850 N on the glider. What is the magnitude and direction of the force exerted by the glider on the towline?
> An 85 kg skier is sliding down a ski slope at a constant velocity. The slope makes an angle of 11° above the horizontal direction. Ignore air resistance. (a) What is the force of kinetic friction acting on the skier? (b) What is the coefficient of kinet
> An 80.0 N crate of apples sits at rest on a ramp that runs from the ground to the bed of a truck. The ramp is inclined at 20.0° to the ground. (a) What is the normal force exerted on the crate by the ramp? (b) The interaction partner of this normal for
> Mechanical advantage is the ratio of the force required without the use of a simple machine to that needed when using the simple machine. Compare the force to lift an object with that needed to slide the same object up a frictionless incline and show tha
> (a) In Example 2.14, if the movers stop pushing on the safe, can static friction hold the safe in place without having it slide back down? (b) If not, what minimum force needs to be applied to hold the safe in place?
> Before hanging new William Morris wallpaper in her bedroom, Brenda sanded the walls lightly to smooth out some irregularities on the surface. The sanding block weighs 2.0 N and Brenda pushes on it with a force of 3.0 N at an angle of 30.0° with respect t
> A crate of artichokes is on a ramp that is inclined 10.0° above the horizontal. Give the direction of the normal force and the friction force acting on the crate in each of these situations. (a) The crate is at rest. (b) The crate is sliding up the ramp
> A crate of potatoes of mass 18.0 kg is on a ramp with angle of incline 30° to the horizontal. The coefficients of friction are μs = 0.75 and μk = 0.40. Find the normal force (magnitude) and the frictional force (magnitude and direction) on the crate if
> A crate of potatoes of mass 18.0 kg is on a ramp with angle of incline 30° to the horizontal. The coefficients of friction are μs = 0.75 and μk = 0.40. Find the normal force (magnitude) and the frictional force (magnitude and direction) on the crate if t
> A crate of potatoes of mass 18.0 kg is on a ramp with angle of incline 30° to the horizontal. The coefficients of friction are μs = 0.75 and μk = 0.40. Find the normal force (magnitude) and the frictional force (magnitude and direction) on the crate if
> A crate of potatoes of mass 18.0 kg is on a ramp with angle of incline 30° to the horizontal. The coefficients of friction are μs = 0.75 and μk = 0.40. Find the normal force (magnitude) and the frictional force (magnitude and direction) on the crate if
> Two of Robin Hood's men are pulling a sledge loaded with some gold along a path that runs due north to their hideout. One man pulls his rope with a force of 62 N at an angle of 12° east of north and the other pulls with the same force at an angle of 12°
> A book that weighs 10 N is at rest in six different situations. Blue arrows indicate forces exerted on the book by an object that is not shown. Rank the situations according to the magnitude of the normal force on the 10 N book due to the table, from sma
> A box sits on a horizontal wooden ramp. The coefficient of static friction between the box and the ramp is 0.30. You grab one end of the ramp and slowly lift it up, keeping the other end of the ramp on the ground. What is the angle between the ramp and t
> In the drawing, what is the vector sum of forces if each grid square is 2 N on a side? Problems 7, 8, 13, and 16
> A binary star system consists of two stars of masses M1 and 4.0M1 a distance d apart. Is there any point where the net gravitational field due to the two stars is zero? If so, where is that point?
> Rank the vectors /, and / in order of increasing magnitude. Explain your reasoning.
> Using the masses and mean distances found in Appendix B, calculate the net gravitational force on the Moon (a) during a lunar eclipse (Earth between Moon and Sun) and (b) during a solar eclipse (Moon between Earth and Sun).
> In the drawing, what is the vector sum of forces if each grid square is 2 N on a side? Problems 6, 12, and 15
> Find the ratio of Earth's gravitational force on a satellite when it is on the ground to the gravitational force exerted when the satellite is orbiting at an altitude of 320 km.
> Two vectors, each of magnitude 4.0 N, are inclined at a small angle α below the horizontal, as /
> (a) What is the magnitude of the gravitational force that Earth exerts on the Moon? (b) What is the magnitude of the gravitational force that the Moon exerts on Earth? See Appendix B for necessary information.
> A hummingbird is hovering motionless beside a flower. The blur of its wings shows that they are rapidly beating up and down. If the air pushes upward on the bird with a force of 0.30 N, what is the force exerted on the air by the hummingbird?
> Vectors /, and / are shown in the figure. (a) Draw vectors / and /, where / and /. (b) Show that / by graphical means.
> An astronaut stands at a position on the Moon such that Earth is directly over head and releases a Moon rock that was in her hand. (a) Which way will it fall? (b) What is the gravitational force exerted by the Moon on a 1.0 kg rock resting on the Moon'
> Rank the vectors / , And / in order of increasing magnitude. Explain your reasoning. Problems 3, 4, and 14
> How far above the surface of Earth does an object have to be in order for it to have the same weight as it would have on the surface of the Moon? (Ignore any effects from Earth's gravity for the object on the Moon's surface or from the Moon's gravity for
> Two objects, A and B, are acted on by the forces shown in the FBDs. Is the magnitude of the net force acting on object B greater than, less than, or equal to the magnitude of the net force acting on object A? Explain.
> During a balloon ascension, wearing an oxygen mask, you measure the weight of a 5.00 kg object and find that the value of the gravitational field strength at your location is 9.792 N/kg. How high above sea level, where the gravitational field strength wa
> A sailboat, tied to a mooring with a line, weighs 820 N. The mooring line pulls horizontally toward the west on the sailboat with a force of 110 N. The sails are stowed away and the wind blows from the west. The boat is moored on a still lake—no water cu
> At what altitude above Earth's surface would your weight be half of what it is at Earth's surface?
> A car is driving on a straight, level road at constant speed. Draw an FBD for the car, showing the significant forces that act on it.
> Find and compare the weight of a 65 kg man on Earth with the weight of the same man on (a) Mars, where g = 3.7 N/kg; (b) Venus, where g = 8.9 N/kg; and (c) Earth's Moon, where g = 1.6 N/kg.
> On her way to visit Grandmother, Red Riding Hood sat down to rest and placed her 1.2 kg basket of goodies beside her. A wolf came along, spotted the basket, and began to pull on the handle with a force of 6.4 N at an angle of 25° with respect to vertical
> A man is lazily floating on an air mattress in a swimming pool. If the weight of the man and air mattress together is 806 N, what is the upward force of the water acting on the mattress?
> Find the altitudes above Earth's surface where Earth's gravitational field strength would be (a) two-thirds and (b) one-third of its value at the surface. [Hint: First find the radius for each situation; then recall that the altitude is the distance fr
> A person stands on the ball of one foot. The normal force due to the ground pushing up on the ball of the foot has magnitude 750 N. Ignore the weight of the foot itself. The other significant forces acting on the foot are the tension in the Achilles tend
> What is the approximate magnitude of the gravitational force exerted by the Sun on the Voyager 1 spacecraft when they are separated by 17 billion kilometers? The spacecraft has a mass of 722 kg.
> Forces of magnitudes 2000 N and 3000 N act on five objects. The directions of the forces are shown in the sketches. Rank the objects according to the magnitude of the net force, from smallest to largest. Explain your reasoning.
> Vector / has magnitude 7.1 and direction 14° below the +x-axis. Vector has x-component cx = −1.8 and y-component cy = −6.7. Compute (a) the x- and y-components of /; (b) the magnitude and direction of / ; (c) the magnitude and direction of / .
> In each of these, the x- and y-components of a vector are given. Find the magnitude and direction of the vector. (a) x = −5.0 cm, y = +8.0 cm. (b) Fx = +120 N, Fy = −60.0 N. (c) vx = −13.7 m/s, vy = −8.8 m/s. (d) ax = 2.3 m/s2, ay = 6.5 cm/s2.
> (a) Calculate your weight in newtons. (b) What is the weight in newtons of 250 g of cheese? (c) Name a common object whose weight is about 1 N.
> Find the x- and y-components of the four vectors shown in the drawing. Problems 22–24
> A woman who weighs 600 N sits on a chair with her feet on the floor and her arms resting on the chair's armrests. The chair weighs 100 N. Each armrest exerts an upward force of 25 N on her arms. The seat of the chair exerts an upward force of 500 N. (a)
> A barge is hauled along a straight-line section of canal by two horses harnessed to tow ropes and walking along the tow paths on either side of the canal. Each horse pulls with a force of 560 N at an angle of 15° with the centerline of the canal. Find th
> Vector / has magnitude 4.0 units; vector / has magnitude 6.0 units. The angle between / And is 60.0°. What is the magnitude of
> A hanging plant is suspended by a cord from a hook in the ceiling. Draw an FBD for each of these: (a) the system consisting of plant, soil, and pot; (b) the cord; (c) the hook; (d) the system consisting of plant, soil, pot, cord, and1hook. Label each
> A vector is 20.0 m long and makes an angle of 60.0° counterclockwise from the y-axis (on the side of the −x-axis). What are the x- and y-components of this vector?
> Consider the skydiver and parachute to be a single system. Identify the external forces acting on this system and draw an FBD.
> (a) Identify the forces acting on the parachute. Describe each force as: (type of force) exerted on (object 1) by (object 2). (b) Draw an FBD for the parachute. (c) What are the magnitude and direction of the force on the parachute due to the skydiver?
> 1. You place two different coins on the cover of your physics book and then slowly lift the cover. Assuming the coefficients of static friction are the same, which is true? (a) The more massive coin starts to slide first. (b) The less massive coin starts
> 1. Interaction partners (a) are equal in magnitude and opposite in direction and act on the same object. (b) are equal in magnitude and opposite in direction and act on different objects. (c) appear in an FBD for a given object. (d) always involve gravit
> In Conceptual Example 2.13, a horse pulls a sleigh at constant velocity. Suppose the horse wants to speed up. If it pulls forward on the sleigh with a larger force to try to make the net force on the sleigh nonzero, the sleigh will simultaneously pull ba
> Which of the fundamental forces binds quarks together to form protons, neutrons, and many exotic subatomic particles?
> Rank, in order of increasing x-component
> Which of the fundamental forces has the shortest range?
> Which of the following forces bind electrons to nuclei to form atoms: strong force, contact force, electromagnetic force, gravitational force?
> Which of the following forces have an unlimited range: strong force, contact force, electromagnetic force, gravitational force?
> Which of the fundamental forces governs the motion of planets in the solar system? Is this the strongest or the weakest of the fundamental forces? Explain.
> The readings of the two spring scales shown in the drawing are the same. (a) Explain why they are the same. [Hint: Draw FBDs.] (b) What is the reading?
> Does the concept of a contact force apply to both a macroscopic scale and an atomic scale? Explain.
> A bird sits on a stretched clothesline, causing it to sag slightly. Is the tension in the line greatest where the bird sits, greater at either end of the line where it is attached to poles, or the same everywhere along the line? Treat the line as an idea
> For a problem about a crate sliding along an inclined plane, is it possible to choose the x-axis so that it is parallel to the incline?
> Pulleys and inclined planes are examples of simple machines. Explain what these machines do in Examples 2.4, 2.14, and (2.16) to make a task easier to perform.
> Compare the advantages and disadvantages of the two methods of vector addition (graphical and algebraic).
> (a) Identify the forces acting on the skydiver. Describe each force as: (type of force) exerted on (object 1) by (object 2). (b) Draw an FBD for the skydiver. (c) Find the magnitude of the force on the skydiver due to the air. (d) Identify the interac
> If two vectors have the same magnitude, are they necessarily equal? If not, why not? Can two vectors with different magnitudes ever be equal?
> You are standing on one end of a light wooden raft that has floated 3 m away from the pier. If the raft is 6 m long by 2.5 m wide and you are standing on the raft end nearest to the pier, can you propel the raft back toward the pier where a friend is sta
> An SUV collides with a Mini Cooper convertible. Is the force exerted on the Mini by the SUV greater than, equal to, or less than the force exerted on the SUV by the Mini? Explain.
> A heavy ball hangs from a string attached to a sturdy wooden frame. A second string is attached to a hook on the bottom of the lead ball. You pull slowly and steadily on the lower string. Which string do you think will break first? Explain.
> Can the x-component of a vector ever be greater than the magnitude of the vector? Explain.
> If a wagon starts at rest and pulls back on you with a force equal to the force you pull on it, as required by Newton's third law, how is it possible for you to make the wagon start to move? Explain.
> What is the distinction between a vector and a scalar quantity? Give two examples of each.
> (a) Does a man weigh more at the North Pole or at the equator? (b) Does he weigh more at the top of Mt. Everest or at the base of the mountain?
> A freight train consists of an engine and several identical cars on level ground. Determine whether each of these statements is correct or incorrect and explain why. (a) If the train is moving at constant speed, the engine must be pulling with a force g
> (a) What assumptions do you make when you call the reading of a bathroom scale your “weight”? What does the scale really tell you? (b) Under what circumstances might the reading of the scale not be equal to your weight?
> With the y-axis pointing north, rank vectors /
> (a) Is it possible for the sum of two vectors to be smaller in magnitude than the magnitude of either vector? (b) Is it possible for the magnitude of the sum of two vectors to be larger than the sum of the magnitudes of the vectors?
> Two cars are headed toward each other in opposite directions along a narrow country road. The cars collide head-on, crumpling up the hoods of both. Describe what happens to the car bodies in terms of the principle of inertia. Does the rear end of the car
> When a car begins to move forward, what force makes it do so? Remember that it has to be an external force; the internal forces all add to zero. How does the engine, which is part of the car, cause an external force to act on the car?
> In an attempt to tighten the loosened steel head of a hammer, a carpenter holds the hammer vertically, raises it up, and then brings it down rapidly, hitting the bottom end of the wood handle on a two-by- four board. Explain how this tightens the head ba
> A dog goes swimming at the beach and then shakes himself all over to get dry. What principle of physics aids in the drying process? Explain.
> An American visitor to Finland is surprised to see heavy metal frames outside of all the apartment buildings. On Saturday morning the purpose of the frames becomes evident when several apartment dwellers appear, carrying rugs and carpet beaters to each f
> Explain the need for automobile seat belts in terms of Newton's first law.
> Which item in the following list is not a scalar? temperature, test score, stock value, humidity, velocity, mass.
> Which item/s in the following list is/are a vector quantity? volume, force, speed, length, time.
> A person is standing on a bathroom scale. Which of the following is not a force exerted on the scale: a contact force due to the floor, a contact force due to the person's feet, the weight of the person, the weight of the scale?
> Margie, who weighs 543 N, is standing on a bathroom scale that weighs 45 N. (a) With what magnitude force does the scale push up on Margie? (b) What is the interaction partner of that force? (c) With what magnitude force does the floor push up on the
> Two forces of magnitudes 3.0 N and 4.0 N act on an object. How are the directions of the two forces related if (a) the net force has magnitude 7.0 N or (b) the net force has magnitude 5.0 N? (c) What relationship between the directions gives the small
> Badgers Ltd, a business that provides a market research service, operates a job costing system. Towards the end of each financial year, the overhead recovery rate (the rate at which indirect cost will be absorbed by jobs) is established for the forthcomi
> A business places substantial emphasis on customer satisfaction and, to this end, delivers its product in special protective containers. These containers have been made in a department within the business. Management has recently become concerned that th
> A hotel group prepares financial statements on a quarterly basis. The senior management is reviewing the performance of one hotel and making plans for next year. The managers have in front of them the results for this year (based on some actual results a
> The management of a business is concerned about its inability to obtain enough fully trained labour to enable it to meet its present budget projection, which is as follows: The amount of labour likely to be available amounts to £20,000. All
> A business in the food industry is currently holding 2,000 tonnes of material in bulk storage. This material deteriorates with time. In the near future, it will, therefore, be necessary for it to be repackaged for sale or sold in its present form. The ma
> SJ Services Ltd has been asked to quote a price for a special contract to render a service that will take the business one week to complete. Information relating to labour for the contract is as follows: A shortage of skilled labour means that the neces
> Delphi plc has recently decided to enter the expanding market for digital radios. The business will manufacture the radios and sell them to small TV and hi-fi specialists, medium sized music stores and large retail chain stores. The new product will be l
> International Electric plc at present offers its customers 30 days’ credit. Half of the customers, by value, pay on time. The other half takes an average of 70 days to pay. The business is considering offering a cash discount of 2 per cent to its custome
> AB Ltd operates retail stores throughout the country. The business is divisionalised. Included in its business are Divisions A and B. A centralised and automated warehouse that replenishes inventories using computer-based systems supports the work of the
> The University of Devonport consists of six faculties and an administration unit. Under the university’s management philosophy, each faculty is treated, as far as is reasonable, as an independent entity. Each faculty is responsible for
> Pieman Products Ltd makes road trailers to the precise specifications of individual customers. The following are predicted to occur during the forthcoming year, which is about to start: All direct labor is paid at the same hourly rate. A customer has as
