Question: How does the magnitude of the normal

> Prove that the product of two even (or two odd) functions is even.

> Evaluate the function at the given value(s) of the independent variable. Then find the domain and range. a. f (−3) b. f (0) c. f (5) d. f (10)

> Sketch the lines through the point with the indicated slopes. Make the sketches on the same set of coordinate axes. Point (3, 4) Slopes 1 -2 -(3/2)

> Find any intercepts. y2 = x3 − 4x

> Find any intercepts. y = x2 + x – 2  

> A skydiver, who weighs 650 N, is falling at a constant speed with his parachute open. Consider the apparatus that connects the parachute to the skydiver to be part of the parachute. The parachute pulls upward on the skydiver with a force of 620 N. (a) Id

> 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 sca

> 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?

> 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?

> 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?

> 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 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

> 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 smallest

> 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.

> 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

> The figure shows the quadriceps and the patellar tendons attached to the patella (the kneecap). If the tension T in each tendon is 1.30 kN, what are the magnitude and direction of the contact force F exerted on the patella by the femur? The weight of the

> 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.

> 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?

> 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

> 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 bac

> 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 b has magnitude 7.1 and direction 14° below the +x-axis. Vector c has x-component cx = −1.8 and y-component cy = −6.7. Compute: (a) the x- and y-components of b. (b) the magnitude and direction of c. (c) the magnitude and direction of c+b.

> 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.

> Find the x- and y-components of the four vectors shown in the drawing.

> Vector A has magnitude 4.0 units; vector B has magnitude 6.0 units. The angle between A and B is 60.0°. What is the magnitude of A+B?

> 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?

> A person is doing leg lifts with 3.00 kg ankle weights. The lower leg itself has a mass of 5.00 kg. When the leg is held still at an angle of 30.0° with respect to the horizontal, the patellar tendon pulls on the tibia with a force of 337 N at

> 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?

> Rank, in order of increasing x-component, A+B, B+C and A+C in Problem 4. The x-axis points to the right. Explain your reasoning.

> With the y-axis pointing north, rank vectors D, E and F in Problem 8 in order of increasing y-component. Explain your reasoning.

> Rank vectors A, B and C in Problem 6 in order of increasing x-component. The x-axis points east. Explain your reasoning.

> 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.

> A force of 20 N is directed at an angle of 60° above the x-axis. A second force of 20 N is directed at an angle of 60° below the x-axis. What is the vector sum of these two forces?

> Juan is helping his mother rearrange the living room furniture. Juan pushes on the armchair with a force of 30 N directed at an angle of 25° above a horizontal line while his mother pushes with a force of 60 N directed at an angle of 35° below the same

> 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°

> In the drawing, what is the vector sum of forces D+E+F if each grid square is 2 N on a side?

> Rank the vectors D, E and F in order of increasing magnitude. Explain your reasoning.

> A young boy with a broken leg is undergoing traction. (a) Find the magnitude of the total force of the traction apparatus applied to the leg, assuming the weight of the leg is 22 N and the weight hanging from the traction apparatus is also 22 N. (b) Wh

> In the drawing, what is the vector sum of forces A+B+C if each grid square is 2 N on a side?

> Two vectors, each of magnitude 4.0 N, are inclined at a small angle α below the horizontal, as shown. Let C = A + B. Sketch the direction of C and estimate its magnitude. (The grid is 1 N on a side.)

> Vectors A, B, and C are shown in the figure. (a) Draw vectors D and E, where D=A+B and E=A+C. (b) Show that by graphical means

> Rank the vectors A, B and C in order of increasing magnitude. Explain your reasoning.

> Your car won't start, so you are pushing it. You apply a horizontal force of 300 N to the car, but it doesn't budge. What force is the interaction partner of the 300 N force you exert? (a) the frictional force exerted on the car by the road (b) the force

> 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

> A friction force is (a) a contact force that acts parallel to the contact surfaces. (b) a contact force that acts perpendicular to the contact surfaces. (c) a scalar quantity since it can act in any direction along a surface. (d) always proportional to

> Within a given system, the internal forces (a) are always balanced by the external forces. (b) all add to zero. (c) are determined only by subtracting the external forces from the net force on the system. (d) determine the motion of the system. (e) can

> 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 gravitat

> How does the magnitude of the normal force N compare with the object's weight W? A passenger (weight W) rides in an elevator. The magnitude of the normal force on the passenger due to the floor is (a) equal to W (b) greater than W (c) less than W (d) Th

> An airplane is cruising along in a horizontal level flight at a constant velocity, heading due west. (a) If the weight of the plane is 2.6 × 104 N, what is the net force on the plane? (b) With what force does the air push upward on the plane?

> How does the magnitude of the normal force N compare with the object's weight W? A car (weight W) is parked on an incline. The magnitude of the normal force on the car is (a) equal to W (b) greater than W (c) less than W (d) The given information is ins

> How does the magnitude of the normal force N compare with the object's weight W? A child (weight W) sits on a level floor. The normal force on the child is (a) equal to W (b) greater than W (c) less than W (d) The given information is insufficient to det

> A woman stands on an airport's moving sidewalk and moves due west at constant velocity. The frictional force on the woman is _____. (Ignore air resistance.) (a) zero (b) kinetic and to the west (c) kinetic and to the east (d) static and to the west (e)

> A crate containing a new water heater weighs 800 N. Tim and a friend push horizontally on the water heater with a force of 600 N as it slides across the floor with constant velocity. What can you conclude about the coefficient of kinetic friction between

> A crate containing a new water heater weighs 800 N. The crate rests on the basement floor. Tim pushes horizontally on it with a force of 400 N, but it doesn't budge. What can you conclude about the coefficient of static friction between the crate and the

> Explain the need for automobile seat belts in terms of Newton's first law.

> 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 to

> Which vector sum is not equal to zero? (a) C+D (b) C+D+E (c) C+F (d) B+C (e) B+F

> Vector A in the drawing is equal to (a) C+D+E (b) B+C+F (c) D+F (d) A+B+F

> A roller coaster car is towed up an incline at a steady speed of 0.50 m/s by a chain parallel to the surface of the incline. The slope is 3.0%, which means that the elevation increases by 3.0 m for every 100.0 m of horizontal distance. The mass of the ro

> To make an object start moving on a surface with friction requires (a) less force than to keep it moving on the surface. (b) the same force as to keep it moving on the surface. (c) more force than to keep it moving on the surface. (d) a force equal to th

> Which of these is not a long-range force? (a) the force that makes raindrops fall to the ground (b) the force that makes a compass point north (c) the force that a person exerts on a chair while sitting (d) the force that keeps the Moon in its orbital pa

> When an object is in translational equilibrium, which of these statements is not true? (a) The vector sum of the forces acting on the object is zero. (b) The object must be stationary. (c) The object has a constant velocity. (d) The speed of the object i

> When a force is called a “normal” force, it is (a) the usual force expected given the arrangement of a system. (b) a force that is perpendicular to the surface of Earth at any given location. (c) a force that is always vertical. (d) a contact force perp

> 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?

> Which of the fundamental forces has the shortest range?

> Which item in the following list is not a scalar? temperature, test score, stock value, humidity, velocity, mass.

> 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?

> (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?

> 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. (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).

> If two vectors have the same magnitude, are they necessarily equal? If not, why not? Can two vectors with different magnitudes ever be equal?

> Which item/s in the following list is/are a vector quantity? volume, force, speed, length, time.

> 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

> You want to push a 65 kg box up a 25° ramp. The coefficient of kinetic friction between the ramp and the box is 0.30. With what magnitude force parallel to the ramp should you push on the box so that it moves up the ramp at a constant speed?

> 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.

> You want to lift a heavy box with a mass of 98.0 kg using the two ideal- pulley system as shown. With what minimum force do you have to pull down on the rope in order to lift the box at a constant velocity? One pulley is attached to the ceiling and one t

> A boy has stacked two blocks on the floor so that a 5.00 kg block is on top of a 2.00 kg block. (a) If the coefficient of static friction between the two blocks is 0.400 and the coefficient of static friction between the bottom block and the floor is 0.

> (a) If a spacecraft moves in a straight line between Earth and the Sun, at what point would the force of gravity on the spacecraft due to the Sun be as large as that due to Earth? (b) If the spacecraft is close to, but not at, this equilibrium point, do

> A student's head is bent over her physics book. The head weighs 50.0 N and is supported by the muscle force Fm exerted by the neck extensor muscles and by the contact force Fc exerted at the atlantooccipital joint. Given that the magnitude of Fm is 60.0

> A large wrecking ball of mass m is resting against a wall. It hangs from the end of a cable that is attached at its upper end to a crane that is just touching the wall. The cable makes an angle of θ with the wall. Ignoring friction between t

> Two canal workers pull a barge along the narrow waterway at a constant speed. One worker pulls with a force of 105 N at an angle of 28° with respect to the forward motion of the barge, and the other worker, on the opposite tow path, pulls at an angle of

> A tire swing hangs at a constant 12° angle to the vertical when a stiff breeze is blowing. In terms of the tire's weight W, (a) what is the magnitude of the horizontal force exerted on the tire by the wind? (b) What is the tension in the rope supporting

> By what percentage does the weight of an object change when it is moved from the equator at sea level, where the effective value of g is 9.784 N/kg, to the North Pole where g = 9.832 N/kg?

> The tallest spot on Earth is Mt. Everest, which is 8850 m above sea level. If the radius of Earth to sea level is 6370 km, how much does the gravitational field strength change between the sea level value at that location (9.826 N/kg) and the top of Mt.

> Spring scale A is attached to the ceiling. A 10.0 kg object is suspended from the scale. A second spring scale, B, is hanging from a hook at the bottom of the 10.0 kg object and a 4.0 kg object hangs from the second spring scale. (a) What are the readin

> A 50.0 kg crate is suspended between the floor and the ceiling using two spring scales, one attached to the ceiling and one to the floor. If the lower scale reads 120 N, what is the reading of the upper scale? Ignore the weights of the scales.

> What is the distinction between a vector and a scalar quantity? Give two examples of each.

> In the sport of curling, a player slides a 20.0 kg granite stone down a 38 m long ice rink. Draw FBDs for the stone (a) while it sits at rest on the ice; (b) while it slides down the rink; (c) during a head-on collision with an opponent's stone that was

> Four identical spring scales, A, B, C, and D are used to hang a 220.0 N sack of potatoes. (a) Assume that the scales have negligible weights and that all four scales show the same reading. What is the reading of each scale? (b) Suppose that each scale

> A box full of books rests on a wooden floor. The normal force the floor exerts on the box is 250 N. (a) You push horizontally on the box with a force of 120 N, but it refuses to budge. What can you say about the coefficient of static friction between the