Question: You want to hang a 15 N
You want to hang a 15 N picture as in the figure (a) using some very fine twine that will break with more than 12 N of tension. Can you do this? What if you have it as illustrated in Figure (b)?
> Repeat Problem 81 if the monthly rate of increase in sales is found to be approximated by S′(t) = 20 - 20e-0.05t 0 ≤ t ≤ 24 Data from Problem 81: (A) What will be the total sales S1t2 t months after the beginning of the national campaign if we assume
> In 2016, U.S. consumption of renewable energy was 9.97 quadrillion Btu (or 9.97 * 1015 Btu). Since the 1950s, consumption has been growing at a rate (in quadrillion Btu per year) given by ′(t) = 0.002t + 0.03 where t is years after 1950. Find (t) and
> The weekly marginal revenue from the sale of x pairs of tennis shoes is given by where R(x) is revenue in dollars. Find the revenue function. Find the revenue from the sale of 1,000 pairs of shoes.
> Show that the indefinite integral of the difference of two functions is the difference of the indefinite integrals.
> The marginal price at a supply level of x bottles of laundry detergent per week is given by Find the price–supply equation if the distributor of the detergent is willing to supply 75 bottles a week at a price of $5.00 per bottle. How m
> Assuming that x [Hint: Use the chain rule after noting that ln |x| = ln ( -x) for x 6 0.]
> Find the family of all antiderivatives of each derivative.
> find the limiting matrix for the indicated standard form. Find the long-run probability of going from each nonabsorbing state to each absorbing state and the average number of trials needed to go from each nonabsorbing state to an absorbing state.
> Use differentiation to justify the formula
> Find the family of all antiderivatives of each derivative.
> find the derivative or indefinite integral as indicated.
> Find the family of all antiderivatives of each derivative.
> find the derivative or indefinite integral as indicated.
> Find each indefinite integral and check the result by differentiating.
> find each indefinite integral
> Find each indefinite integral and check the result by differentiating.
> find each indefinite integral
> Find each indefinite integral and check the result by differentiating.
> find a standard form for the absorbing Markov chain with the indicated transition matrix.
> identify the absorbing states for each transition diagram, and determine whether or not the diagram represents an absorbing Markov chain.
> 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 //
> 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
> 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.
> Rank vectors /
> 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 w
> 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 th
> The coefficient of static friction between a block and a horizontal floor is 0.40, while the coefficient of kinetic friction is 0.15. The mass of the block is 5.0 kg. A horizontal force is applied to the block and slowly increased. (a) What is the value
> A toy freight train consists of an engine and three identical cars. The train is moving to the right at constant speed along a straight, level track. Three spring scales are used to connect the cars as follows: spring scale A is located between the engin
> 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 /
> 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
> 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
> 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?
> 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
> 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?
> 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?
> 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 supportin
> Tamar wants to cut down a dead poplar tree with her chain saw, but she does not want it to fall onto the nearby gazebo. Yoojin, a physicist, suggests they tie a rope taut from the poplar to an oak tree and then pull sideways on the rope as shown in the f
> While trying to decide where to hang a framed picture, you press it against the wall to keep it from falling. The picture weighs 5.0 N, and you press against the flat frame with a force of 6.0 N at an angle of 40° from the vertical. (a) What
> The coefficient of static friction between block A and a horizontal floor is 0.45, and the coefficient of static friction between block B and the floor is 0.30. The mass of each block is 2.0 kg, and they are connected together by a cord. / (b) What is t
> When you hold up a 50 N object in your hand, with your forearm horizontal and your palm up, the upward force exerted by your biceps is much larger than 50 N—perhaps as much as 5000 N. How can that be? What other forces are acting on you
> You grab a book and give it a quick push across the top of a horizontal table. After a short push, the book slides across the table, and because of friction, comes to a stop. (a) Draw an FBD of the book while you are pushing it. (b) Draw an FBD of the
> A box containing a new TV weighs 350 N. Phineas is pushing horizontally on it with a force of 150 N, but it doesn't budge. (a) Identify all the forces acting on the crate. Describe each as: (type of force) exerted on the crate by (object). (b) Identify
> A bike is hanging from a hook in a garage. Consider the following forces: (1) the force of Earth pulling down on the bike, (2) the force of the bike pulling up on Earth, and (3) the force of the hook pulling up on the bike. (a) Which two forces are e
> 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 h
> An ideal pulley is hung from the ceiling by a rope. A block of mass M is suspended by another rope that passes over the pulley and is attached to the wall. The rope fastened to the wall makes a right angle with the wall. Ignore the masses of the rope and
> A 45 N lithograph is supported by two wires. One wire makes a 25° angle with the vertical and the other makes a 15° angle with the vertical. Find the tension in each wire.
> A 2.0 kg ball tied to a string fixed to the ceiling is pulled to one side by a force //
> A crow perches on a clothesline midway between two poles. Each end of the rope makes an angle of θ below the horizontal where it connects to the pole. If the weight of the crow is W, what is the tension in the rope? Ignore the weight of the
> The drawing shows a wire attached to two back teeth and stretched across a front tooth. The /
> A 200.0 N sign is suspended from a horizontal strut of negligible weight. The force exerted on the strut by the wall is horizontal. Draw an FBD to show the forces acting on the strut. Find the tension T in the diagonal cable supporting the strut.
> Two boxes with different masses are tied together on a frictionless ramp surface. What is the tension in each of the cords?
> Two springs are connected in series so that spring scale A hangs from a hook on the ceiling and a second spring scale, B, hangs from the hook at the bottom of scale A. Apples weighing 120 N hang from the hook at the bottom of scale B. What are the readin
> A spring scale hangs from a cord that is attached to a hook in the ceiling. A 10 kg object hangs from a second cord connected to the bottom of the scale. The weights of the cords and the scale are negligible. (a) What is the reading of the scale? (b) T
> You are pulling a suitcase through the airport at a constant speed by exerting a force of 25.0 N at angle 30.0° from the vertical. What is the force of friction acting on the suitcase?
> 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.
