You and your friend Peter are putting new shingles on a

The three ropes in Figure EX6.2 are tied to a small, very light ring. Two of these ropes are anchored to walls at right angles with the tensions shown in the figure. What are the magnitude and direction of the tension \(\vec{T}_{3}\) in the third rope? Equation Transcription: Text Transcription: ^vec T_3

The machine in FIGURE CP6.73 has an \(800 \mathrm{~g}\) steel shuttle that is pulled along a square steel rail by an elastic cord. The shuttle is released when the elastic cord has \(20 \mathrm{~N}\) tension at a \(45^{\circ}\) angle. What is the initial acceleration of the shuttle? Equation Transcription: Text Transcription: 800 g 20 N 45^circ

FIGURE CP6.74 shows an accelerometer, a device for measuring the horizontal acceleration of cars and airplanes. A ball is free to roll on a parabolic track described by the equation \(y=x^{2}\), where both \(x\) and \(y\) are in meters. A scale along the bottom is used to measure the ball's horizontal position \(x\). a. Find an expression that allows you to use a measured position \(x\) (in \(\mathrm{m}\) ) to compute the acceleration \(a_{x}\) (in \(\mathrm{m} / \mathrm{s}^{2}\) ). (For example, \(a_{x}=3 x\) is a possible expression.) b. What is the acceleration if \(x=20 \mathrm{~cm}\) ? Equation Transcription: Text Transcription: y=x^2 x y x x(in m) a_x(in m/s^2) a_x=3x x= 20 cm

An object with cross section \(A\) is shot horizontally across frictionless ice. Its initial velocity is \(v_{0 x}\) at \(t_{0}=0 \mathrm{~s}\). Air resistance is not negligible. a. Show that the velocity at time \(t\) is given by the expression \(v_{x}=\frac{v_{0 x}}{1+C \rho A v_{0 x} t / 2 m}\) b. A 1.6-m-wide, 1.4-m-high, 1500 kg car with a drag coefficient of 0.35 hits a very slick patch of ice while going 20 m/s. If friction is neglected, how long will it take until the car’s speed drops to 10 m/s? To 5 m/s? c. Assess whether or not it is reasonable to neglect kinetic friction. Equation Transcription: Text Transcription: A t_0=0 v_x=v_0x/1+C rho A v_0x t/2m

An object moving in a liquid experiences a linear drag force: \(\vec{D}=(b v\), direction opposite the motion ), where \(b\) is a constant called the drag coefficient. For a sphere of radius \(R\), the drag constant can be computed as \(b=6 \pi \eta R\), where \(\eta\) is the viscosity of the liquid. a. Find an algebraic expression for \(v_{x}(t)\), the \(x\)-component of velocity as a function of time, for a spherical particle of radius \(R\) and mass \(m\) that is shot horizontally with initial speed \(v_{0}\) through a liquid of viscosity \(\eta\). b. Water at \(20^{\circ} \mathrm{C}\) has viscosity \(\eta=1.0 \times 10^{-3} \mathrm{~N} \mathrm{~s} / \mathrm{m}^{2}\). Suppose a 4.0-cm-diameter, 33 g ball is shot horizontally into a tank of \(20^{\circ} \mathrm{C}\) water. How long will it take for the horizontal speed to decrease to \(50 \%\) of its initial value? Equation Transcription: Text Transcription: ^vec D=(bv, direction opposite the motion) b b=6 pi eta R eta v_x(t) x-component R m 20^circC eta=1.0 x 10^-3Ns/m^2 20^circC 50%

An object moving in a liquid experiences a linear drag force: \(\vec{D}=(b v\), direction opposite the motion ), where \(b\) is a constant called the drag coefficient. For a sphere of radius \(R\), the drag constant can be computed as \(b=6 \pi \eta R\), where \(\eta\) is the viscosity of the liquid. a. Use what you've learned in calculus to prove that \(a_{x}=v_{x} \frac{d v_{x}}{d x}\) b. Find an algebraic expression for \(v_{x}(x)\), the \(x\)-component of velocity as a function of distance traveled, for a spherical particle of radius \(R\) and mass \(m\) that is shot horizontally with initial speed \(v_{0}\) through a liquid of viscosity \(\eta\). c. Water at \(20^{\circ} \mathrm{C}\) has viscosity \(\eta=1.0 \times 10^{-3} \mathrm{Ns} / \mathrm{m}^{2}\). Suppose a 1.0-cm-diameter,1.0 g marble is shot horizontally into a tank of \(20^{\circ} \mathrm{C}\) water at \(10 \mathrm{~cm} / \mathrm{s}\). How far will it travel before stopping? Equation Transcription: ,direction opposite the motion) Text Transcription: ^vec D=(bv,direction opposite the motion) b R b=6 pi eta R eta a_x=v_x dv_x/dx v_x(x) x-components R m v_0 eta 20^circ C eta=1.0 x 10^-3 N s/m^2 20^circ C

Problem 3E A 20 kg loudspeaker is suspended 2.0 m below the ceiling by two 3.0-m-long cables that angle outward at equal angles. What is the tension in the cables?

Problem 3CQ Kat, Matt, and Nat are arguing about why a physics book on a table doesn’t fall. According to Kat, “Gravity pulls down on it, but the table is in the way so it can’t fall.” “Nonsense,” says Matt. “There are all kinds of forces acting on the book, but the upward forces overcome the downward forces to prevent it from falling.” “But what about Newton’s first law?” counters Nat. “It’s not moving, so there can’t be any forces acting on it.” None of the statements is exactly correct. Who comes closest, and how would you change his or her statement to make it correct?

Problem 4CQ If you know all of the forces acting on a moving object, can you tell the direction the object is moving? If yes, explain how. If no, give an example.

Problem 4E A football coach sits on a sled while two of his players build their strength by dragging the sled across the field with ropes. The friction force on the sled is 1000 N and the angle between the two ropes is 20°. How hard must each player pull to drag the coach at a steady 2.0 m/s?

Problem 5E A construction worker with a weight of 850 N stands on a roof that is sloped at 20°. What is the magnitude of the normal force of the roof on the worker?

Problem 6CQ An elevator, hanging from a single cable, moves downward and is slowing. Friction and ah resistance are negligible. Is the tension in the cable greater than, less than, or equal to the gravitational force on the elevator? Explain. Include a free-body diagram as part of your explanation.

Problem 5CQ An elevator, hanging from a single cable, moves upward at constant speed. Friction and air resistance are negligible. Is the tension in the cable greater than, less than, or equal to the gravitational force on the elevator? Explain. Include a free-body diagram as part of your explanation.

Problem 7CQ Are the following statements true or false? Explain. a. The mass of an object depends on its location. ________________ b. The weight of an object depends on its location. ________________ c. Mass and weight describe the same thing in different units.

In each of the two free-body diagrams in FIGURE EX6.6, the forces are acting on a \(2.0 \mathrm{~kg}\) object. For each diagram, find the values of \(a_{x}\) and \(a_{y}\), the \(x\) - and \(y\)-components of the acceleration. Equation Transcription: Text Transcription: 2.0 kg a_x a_y x- and y-components

In each of the two free-body diagrams in FIGURE EX6.7, the forces are acting on a \(2.0 \mathrm{~kg}\) object. For each diagram, find the values of \(a_{x}\) and \(a_{y}\), the \(x\) - and \(y\)-components of the acceleration. Equation Transcription: Text Transcription: 2.0 kg a_x a_y x- and y-components

The four balls in Figure Q6.9 have been thrown straight up. They have the same size, but different masses. Air resistance is negligible. Rank in order, from largest to smallest, the magnitude of the net force acting on each ball. Some may be equal. Give your answer in the form \(a>b=c>d\) and explain your ranking. Equation Transcription: Text Transcription: a>b=c>d

Problem 8CQ An astronaut takes his bathroom scale to the moon and then stands on it. Is the reading of the scale his true weight? Explain.

Problem 10CQ Suppose you attempt to pour out 100 g of salt, using a pan balance for measurements, while in a rocket accelerating upward. Will the quantity of salt be too much, too little, or the correct amount? Explain.

FIGURE EX6.9 shows the force acting on a \(2.0 \mathrm{~kg}\) object as it moves along the \(x\)-axis. The object is at rest at the origin at \(t=0 \mathrm{~s}\). What are its acceleration and velocity at \(t=6 \mathrm{~s}\)? Equation Transcription: Text Transcription: 2.0 kg x-axis t=0 s t=6 s

A horizontal rope is tied to \(50 \mathrm{~kg}\) box on frictionless ice. What is the tension in the rope if: a. The box is at rest? b. The box moves at a steady \(5.0 \mathrm{~m} / \mathrm{s}\)? c. The box has \(v_{x}=5.0 \mathrm{~m} / \mathrm{s}\) and \(a_{x}=5.0 \mathrm{~m} / \mathrm{s}^{2}\)? Equation Transcription: Text Transcription: 50 kg 5.0 m/s v_x=5.0 m/s a_x=5.0 m/s^2

FIGURE EX6.8 shows the velocity graph of a \(2.0 \mathrm{~kg}\) object as it moves along the \(x\)-axis. What is the net force acting on this object at \(t=1 \mathrm{~s}\) ? At \(4 \mathrm{~s}\) ? At \(7 \mathrm{~s}\) ? Equation Transcription: Text Transcription: 2.0 kg x-axis t=1 s 4 s 7 s

Problem 11E A 50 kg box hangs from a rope. What is the tension in the rope if: a. The box is at rest? ________________ b. The box moves up at a steady 5.0 m/s? ________________ c. The box has vy = 5.0 m/s and is speeding up at 5.0 m/s2? ________________ d. The box has vy =5.0 m/s and is slowing down at 5.0 m/s2?

Problem 11CQ A box with a passenger inside is launched straight up into the air by a giant rubber band. Before launch, the passenger stood on a scale and weighed 750 N. Once the box has left the rubber band but is still moving upward, is the passenger’s weight more than 750 N, 750 N, less than 750 N but not zero, or zero? Explain.

1. The block in Figure EX6.12 floats on a cushion of air. It is pushed to the right with a force that remains constant as the block moves from 0 to 1. The block A. Speeds up from 0 to 1. B. Speeds up at first, then has constant speed. C. Moves with constant speed from 0 to 1. 2. From 1 to 2, the size of the force steadily decreases until it reaches half of its initial value. The block A. Continues to speed up from 1 to 2. B. Moves with constant speed from 1 to 2. C. Slows down.

Problem 12CQ An astronaut orbiting the earth is handed two balls that have identical outward appearances. However, one is hollow while the other is filled with lead. How can the astronaut determine which is which? Cutting or altering the balls is not allowed.

A hand presses down on the book in FIGURE Q6.13. Is the normal force of the table on the book larger than, smaller than, or equal to \(m g\) ? Equation Transcription: Text Transcription: mg

Problem 14CQ Suppose you push a hockey puck of mass m across frictionless ice for a time ?t, starting from rest, giving the puck speed v after traveling distance d. If you repeat the experiment with a puck of mass 2m, a. How long will you have to push for the puck to reach the same speed v? ________________ b. How long will you have to push for the puck to travel the same distance d?

A woman has a mass of \(55 \mathrm{~kg}\). a. What is her weight while standing on earth? b. What are her mass and her weight on Mars, where \(g=3.76 \mathrm{~m} / \mathrm{s}^{2}\) ? Equation Transcription: Text Transcription: 55 kg g=3.76 m/s^2

Problem 14E It takes the elevator in a skyscraper 4.0 s to reach its cruising speed of 10 m/s. A 60 kg passenger gets aboard on the ground floor. What is the passenger’s apparent weight a. Before the elevator starts moving? b. While the elevator is speeding up? c. After the elevator reaches its cruising speed?

Problem 15CQ A block pushed along the floor with velocity v0x slides a distance d after the pushing force is removed. a. If the mass of the block is doubled but its initial velocity is not changed, what distance does the block slide before stopping? ________________ b. If the initial velocity is doubled to 2v0x but the mass is not changed, what distance does the block slide before stopping?

Problem 16CQ Can the friction force on an object ever point in the direction of the object’s motion? If yes, give an example. If no, why not?

Problem 16E What thrust does a 200 g model rocket need in order to have a vertical acceleration of 10 m/s a. On earth? ________________ b. On the moon, where g =1.62 m/s2?

Problem 17CQ A crate of fragile dishes is in the back of a pickup truck. The truck accelerates north from a stop sign, and the crate moves without slipping. Does the friction force on the crate point north or south? Or is the friction force zero? Explain.

FIGURE EX. 15 shows the velocity graph of a \(75 \mathrm{~kg}\) passenger in an elevator. What is the passenger's weight at \(t=1 \mathrm{~s}\) ? At \(5 \mathrm{~s}\) ? At \(9 \mathrm{~s}\) ? Equation Transcription: Text Transcription: 75 kg t=1 s 5 s 9 s

Five balls move through the air as shown in FIGURE Q6.18. All five have the same size and shape. Air resistance is not negligible. Rank in order, from largest to smallest, the magnitudes of the accelerations \(a_{\mathrm{a}}\) to \(a_{\mathrm{c}}\). Some may be equal. Give your answer in the form \(\mathrm{a}>\mathrm{b}=\mathrm{c}>\mathrm{d}>\mathrm{e}\) and explain your ranking. Equation Transcription: Text Transcription: a_a a_e a>b=c>d

Problem 17E Bonnie and Clyde are sliding a 300 kg bank safe across the floor to their getaway car. The safe slides with a constant speed if Clyde pushes from behind with 385 N of force while Bonnie pulls forward on a rope with 350 N of force. What is the safe’s coefficient of kinetic friction on the bank floor?

A stubborn, \(120 \mathrm{~kg}\) mule sits down and refuses to move. To drag the mule to the barn, the exasperated farmer ties a rope around the mule and pulls with his maximum force of \(800 \mathrm{~N}\). The coefficients of friction between the mule and the ground are \(\mu_{\mathrm{s}}=0.8\) and \(\mu_{\mathrm{k}}=0.5\). Is the farmer able to move the mule? Equation Transcription: Text Transcription: 120 kg 800 N mu_s=0.8 mu_k=0.5

A \(10 \mathrm{~kg}\) crate is placed on a horizontal conveyor belt. The materials are such that \(\mu_{\mathrm{s}}=0.5\) and \(\mu_{\mathrm{k}}=0.3\). a. Draw a free-body diagram showing all the forces on the crate if the conveyer belt runs at constant speed. b. Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up. c. What is the maximum acceleration the belt can have without the crate slipping?

Problem 20E Bob is pulling a 30 kg filing cabinet with a force of 200 N, but the filing cabinet refuses to move. The coefficient of static friction between the filing cabinet and the floor is 0.80. What is the magnitude of the friction force on the filing cabinet?

Problem 21E A 4000 kg truck is parked on a 15° slope. How big is the friction force on the truck? The coefficient of static friction between the tires and the road is 0.90.

Problem 22E A 1500 kg car skids to a halt on a wet road where ?k = 0.50. How fast was the car traveling if it leaves 65-m-long skid marks?

Problem 24E A 75 kg skydiver can be modeled as a rectangular “box” with dimensions 20 cm × 40 cm ×1.8 m. What is his terminal speed if he falls feet first?

Problem 25E A 6.5-cm-diameter tennis ball has a terminal speed of 26 m/s. What is the ball’s mass?

The \(1000 \mathrm{~kg}\) steel beam in FIGURE P6.28 is supported by two ropes. What is the tension in each? Equation Transcription: Text Transcription: 1000 kg

A \(5.0 \mathrm{~kg}\) object initially at rest at the origin is subjected to the time-varying force shown in FIGURE P6.26. What is the object's velocity at \(t=6 \mathrm{~s}\)? Equation Transcription: Text Transcription: 5.0 kg t=6 s

A \(2.0 \mathrm{~kg}\) object initially at rest at the origin is subjected to the time-varying force shown in Figure P6.27. What is the object's velocity at \(t=4\)s? Equation Transcription: Text Transcription: 2.0 kg t=4 s

In an electricity experiment, a \(1.0 \mathrm{~g}\) plastic ball is suspended on a \(60-\mathrm{cm}\)-long string and given an electric charge. A charged rod brought near the ball exerts a horizontal electrical force \(\vec{F}_{\text {elec }}\) on it, causing the ball to swing out to a \(20^{\circ}\) angle and remain there. a. What is the magnitude of \(\vec{F}_{\text {elec }}\)? b. What is the tension in the string? Equation Transcription: Text Transcription: 1.0 g 60 cm ^vec F_elec 20^circ ^vec F_elec

Problem 30P ||| A 500 kg piano is being lowered into position by a crane while two people steady it with ropes pulling to the sides. Bob’s rope pulls to the left, 15° below horizontal, with 500 N of tension. Ellen’s rope pulls toward the right, 25° below horizontal. a. What tension must Ellen maintain in her rope to keep the piano descending vertically at constant speed? b. What is the tension in the vertical main cable supporting the piano?

Problem 23E A 50,000 kg locomotive is traveling at 10 m/s when its engine and brakes both fail. How far will the locomotive roll before it comes to a stop? Assume the track is level.

Henry gets into an elevator on the 50 th floor of a building and it begins moving at \(t=0 \mathrm{~s}\). FIGURE P6.31 shows his weight over the next \(12 \mathrm{~s}\). a. Is the elevator's initial direction up or down? Explain how you can tell. b. What is Henry's mass? c. How far has Henry traveled at \(t=12 \mathrm{~s}\)? Equation Transcription: Text Transcription: t=0 s 12 s t=12 s

Zach, whose mass is 80 kg, is in an elevator descending at 10 m/s. The elevator takes 3.0 s to brake to a stop at the first floor. a. What is Zach’s weight before the elevator starts braking? b. What is Zach’s weight while the elevator is braking?

II An accident victim with a broken leg is being placed in traction. The patient wears a special boot with a pulley attached to the sole. The foot and boot together have a mass of \(4.0 \mathrm{~kg}\), and the doctor has decided to hang a \(6.0 \mathrm{~kg}\) mass from the rope. The boot is held suspended by the ropes, as shown in FIGURE P6.33, and does not touch the bed. a. Determine the amount of tension in the rope by using Newton's laws to analyze the hanging mass. b. The net traction force needs to pull straight out on the leg. What is the proper angle \(\theta\) for the upper rope? c. What is the net traction force pulling on the leg? Equation Transcription: Text Transcription: 4.0 kg 6.0 kg theta

Problem 35P The position of a 2.0 kg mass is given by x = (2t3 ? 3t2) m, where t is in seconds. What is the net horizontal force on the mass at (a) t =0 s and (b) t = 1 s?

Problem 34P Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a “crumple zone” in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about 1 m as the front of the car crumples. An occupant restrained by seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton’s first law!) until hitting the dashboard or windshield. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about 5 mm. a. A 60 kg person is in a head-on collision. The car’s speed at impact is 15 m/s. Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys. ________________ b. Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag. ________________ c. How do these two forces compare to the person’s weight?

Problem 37P Compressed air is used to fire a 50 g ball vertically upward from a 1.0-m-tall tube. The air exerts an upward force of 2.0 N on the ball as long as it is in the tube. How high does the ball go above the top of the tube?

Problem 36P The piston of a machine exerts a constant force on a ball as it moves horizontally through a distance of 15 cm. You use a motion detector to measure the speed of five different balls as they come off the piston; the data are shown below. Use theory to find two quantities that, when graphed, should give a straight line. Then use the graph to find the size of the piston’s force. Mass (g) Speed (m/s) 200 9.4 400 6.3 600 5.2 800 4.9 1000 4.0

a. A rocket of mass \(m\) is launched straight up with thrust \(\vec{F}_{\text {thrust }}\). Find an expression for the rocket's speed at height \(h\) if air resistance is neglected. b. The motor of a \(350 \mathrm{~g}\) model rocket generates \(9.5 \mathrm{~N}\) thrust. If air resistance can be neglected, what will be the rocket's speed as it reaches a height of 85 \mathrm{~m}\)? ________________ Equation Transcription: Text Transcription: m vec{F}_thrust h g N m

Problem 41P a. An object of mass m is at rest at the top of a smooth slope of height h and length L. The coefficient of kinetic friction between the object and the surface, ?k,is small enough that the object will slide down the slope if given a very small push to get it started. Find an expression for the object’s speed at the bottom of the slope. ________________ b. Sam, whose mass is 75 kg, stands at the top of a 12-m-high, 100-m-long snow-covered slope. His skis have a coefficient of kinetic friction on snow of 0.07. If he uses his poles to get started, then glides down, what is his speed at the bottom?

Problem 39P A rifle with a barrel length of 60 cm fires a 10 g bullet with a horizontal speed of 400 m/s. The bullet strikes a block of wood and penetrates to a depth of 12 cm. a. What resistive force (assumed to be constant) does the wood exert on the bullet? ________________ b. How long does it take the bullet to come to rest? ________________ c. Draw a veloity-versus-time graph for the bullet in the wood.

Problem 42P Sam, whose mass is 75 kg, takes off across level snow on his jet-powered skis. The skis have a thrust of 200 N and a coefficient of kinetic friction on snow of 0.10. Unfortunately, the skis run out of fuel after only 10 s. a. What is Sam’s top speed? ________________ b. How far has Sam traveled when he finally coasts to a stop?

A \(20,000 \mathrm{~kg}\) rocket has a rocket motor that generates \(3.0 \times 10^{5} \mathrm{~N}\) of thrust. a. What is the rocket's initial upward acceleration? b. At an altitude of \(5000 \mathrm{~m}\) the rocket's acceleration has increased to \(6.0 \mathrm{~m} / \mathrm{s}^{2}\). What mass of fuel has it burned? ________________ Equation Transcription: Text Transcription: kg 3.0 X 10^{5} N m 6.0 m/s^2

Problem 44P A baggage handler drops your 10 kg suitcase onto a conveyor belt running at 2.0 m/s. The materials are such that ?s = 0.50 and ?k = 0.30. How far is your suitcase dragged before it is riding smoothly on the belt?

Problem 43P Sam, whose mass is 75 kg, takes off down a 50-m-high, 10° slope on his jet-powered skis. The skis have a thrust of 200 N. Sam’s speed at the bottom is 40 m/s. What is the coefficient of kinetic friction of his skis on snow?

Problem 45P You and your friend Peter are putting new shingles on a roof pitched at 25°. You’re sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.0 m away, asks you for the box of nails. Rather than carry the 2.5 kg box of nails down to Peter, you decide to give the box a push and have it slide down to him. If the coefficient of kinetic friction between the box and the roof is 0.55, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

Problem 48P A 2.0 kg wood block is launched up a wooden ramp that is inclined at a 30° angle. The block’s initial speed is 10 m/s. a. What vertical height does the block reach above its starting point? ________________ b. What speed does it have when it slides back down to its starting point?

Problem 47P An Airbus A320 jetliner has a takeoff mass of 75,000 kg. It reaches its takeoff speed of 82 m/s (180 mph) in 35 s. What is the thrust of the engines? You can neglect air resistance but not rolling friction.

Problem 50P a. A large box of mass M is pulled across a horizontal, frictionless surface by a horizontal rope with tension T. A small box of mass m sits on top of the large box. The coefficients of static and kinetic friction between the two boxes are ?s and ?k,respectively. Find an expression for the maximum tension Tmax for which the small box rides on top of the large box without slipping. ________________ b. A horizontal rope pulls a 10 kg wood sled across friction-less snow. A 5.0 kg wood box rides on the sled. What is the largest tension force for which the box doesn’t slip?

Problem 46P It’s moving day, and you need to push a 100 kg box up a 20° ramp into the truck. The coefficients of friction for the box on the ramp are ?s = 0.90 and ?k = 0.60. Your largest pushing force is 1000 N. Can you get the box into the truck without assistance if you get a running start at the ramp? If you stop on the ramp, will you be able to get the box moving again?

Problem 51P a. A large box of mass M is moving on a horizontal surface at speed v0. A small box of mass msits on top of the large box. The coefficients of static and kinetic friction between the two boxes are ?s and ?k,respectively. Find an expression for the shortest distance dmin in which the large box can stop without the small box slipping. ________________ b. A pickup truck with a steel bed is carrying a steel file cabinet. If the truck’s speed is 15 m/s, what is the shortest distance in which it can stop without the file cabinet sliding?

Problem 49P It’s a snowy day and you’re pulling a friend along a level road on a sled. You’ve both been taking physics, so she asks what you think the coefficient of friction between the sled and the snow is. You’ve been walking at a steady 1.5 m/s, and the rope pulls up on the sled at a 30° angle. You estimate that the mass of the sled, with your friend on it, is 60 kg and that you’re pulling with a force of 75 N. What answer will you give?

The \(2.0 \mathrm{~kg}\) wood box in FIGURE P6.54 slides down a vertical wood wall while you push on it at a \(45^{\circ}\) angle. What magnitude of force should you apply to cause the box to slide down at a constant speed. ________________ Equation Transcription: Text Transcription: kg 45 degrees celsius

Problem 52P Your assignment in lab is to measure the coefficient of kinetic friction between a 350 g block and a smooth metal table. To do so, you decide to launch the block at various speeds and measure how far it slides; your data are listed in the table. Use a graph to determine the value of ?k. Speed (m/s) Distance (cm) 0.5 5 1.0 24 1.5 41 2.0 83 2.5 130

Problem 53P You’re driving along at 25 m/s with your aunt’s valuable antiques in the back of your pickup truck when suddenly you see a giant hole in the road 55 m ahead of you. Fortunately, your foot is right beside the brake and your reaction time is zero! Will the antiques be as fortunate? a. Can you stop the truck before it falls into the hole? ________________ b. If your answer to part a is yes, can you stop without the antiques sliding and being damaged? Their coefficients of friction are ?s = 0.60 and ?k = 0.30. Hint: You’re not trying to stop in the shortest possible distance. What’s your best strategy for avoiding damage to the antiques?

A 1.0 \(kg\) wood block is pressed against a vertical wood wall by the 12 \(N\) force shown in FIGURE P6.55 If the block is initially at rest, will it move upward, move downward, or stay at rest? ________________ Equation Transcription: Text Transcription: kg N

A person with compromised pinch strength in his fingers can exert a force of only 6.0 \(N\) to either side of a pinch-held object, such as the book shown in FIGURE P6.56. What is the heaviest book he can hold vertically before it slips out of his fingers? The coefficient of static friction between his fingers and the book cover is . ________________ Equation Transcription: Text Transcription: N

A ball is shot from a compressed-air gun at twice its terminal speed. a. What is the ball’s initial acceleration, as a multiple of g, if it is shot straight up? b. What is the ball’s initial acceleration, as a multiple of g, if it is shot straight down?

Problem 57P What is the terminal speed for an 80 kg skier going down a 40° snow-covered slope on wooden skis? Assume that the skier is 1.8 m tall and 0.40 m wide.

If An artist friend of yours needs help hanging a 500 lb sculpture from the ceiling. For artistic reasons, she wants to use just two ropes. One will be \(30^{\circ}\)from vertical, the other \(60^{\circ}\). She needs you to determine the smallest diameter rope that can safely support this expensive piece of art. On a visit to the hardware store you find that rope is sold in increments of \(\frac{1}{8}\)-inch diameter and that the safety rating is 4000 pounds per square inch of cross section. What diameter rope should you buy? ________________ Equation Transcription: Text Transcription: 30^circ 60^circ frac{1}{8}

Problem 61P Astronauts in space “weigh” themselves by oscillating on a spring. Suppose the position of an oscillating 75 kg astronaut is given by x =(0.30 m) sin ((? rad/s) · t), where t is in s. What force does the spring exert on the astronaut at (a) t = 1.0 s and (b) 1.5 s? Note that the angle of the sine function is in radians.

Problem 62P A particle of mass m moving along the A’-axis experiences the net force Fx ? ct, where c is a constant. The particle has velocity v0x at t = 0. Find an algebraic expression for the particle’s velocity vx at a later time t.

Problem 60P You’ve entered a “slow ski race” where the winner is the skier who takes the longest time to go down a 15° slope without ever stopping. You need to choose the best wax to apply to your skis. Red wax has a coefficient of kinetic friction 0.25, yellow is 0.20, green is 0.15, and blue is 0.10. Having just finished taking physics, you realize that a wax too slippery will cause you to accelerate down the slope and lose the race. But a wax that’s too sticky will cause you to stop and be disqualified. You know that a strong headwind will apply a 50 N horizontal force against you as you ski, and you know that your mass is 82 kg. Which wax do you choose?

Problems 67 and 68 show a free-body diagram. For each: a. Write a realistic dynamics problem for which this is the correct free-body diagram. Your problem should ask a question that can be answered with a value of position or velocity (such as “How far?” or “How fast?”), and should give sufficient information to allow a solution. b. Solve your problem!

Very small objects, such as dust particles, experience a linear drag force, \(\vec{D}=\)( \(b v\), direction opposite the motion), where \(b\) is a constant. That is, the quadratic model of drag of Equation 6.16 fails for very small particles. For a sphere of radius \(R\), the drag constant can be shown to be \(b=6 \pi \eta R\), where \(\eta\) is the viscosity of the gas. a. Find an expression for the terminal speed \(v_{\text {tem }}\) of a spherical particle of radius \(R\) and mass \(m\) falling through a gas of viscosity \(\eta\). b. Suppose a gust of wind has carried a 50- \(\mu\) m-diameter dust particle to a height of \(300 \mathrm{~m}\). If the wind suddenly stops, how long will it take the dust particle to settle back to the ground? Dust has a density of \(2700 \mathrm{~kg} / \mathrm{m}^{3}\), the viscosity of \(25^{\circ} \mathrm{C}\) air is \(2.0 \times 10^{-5} \mathrm{Ns} / \mathrm{m}^{2}\), and you can assume that the falling dust particle reaches terminal speed almost instantly. ________________ Equation Transcription: Text Transcription: vec{D}= ( b v b R b=6 pi eta R eta v_{\text {tem }} R m eta mu 300 m 2700 kg/}^3 25^circ C 2.0 X 10^{-5} Ns/m^2

Problem 63P At t = 0, an object of mass m is at rest at x = 0 on a horizontal. frictionless surface. A horizontal force Fx = F0(1 ? t/T), which decreases from F0 at t = 0 to zero at t = T, is exerted on the object. Find an expression for the object’s (a) velocity and (b) position at time T.

Problems 67 and 68 show a free-body diagram. For each: a. Write a realistic dynamics problem for which this is the correct free-body diagram. Your problem should ask a question that can be answered with a value of position or velocity (such as “How far?” or “How fast?”), and should give sufficient information to allow a solution. b. Solve your problem!

Problem 64P At t =0, an object of mass m is at rest at x = 0 on a horizontal, frictionless surface. Starting at t = 0, a horizontal force Fx = F0e?t/T is exerted on the object. a. Find and graph an expression for the object’s velocity at an arbitrary lateer time t. ________________ b. What is the object’s velocity after a very long time has elapsed?

Large objects have inertia and tend to keep movingNewton's first law. Life is very different for small microorganisms that swim through water. For them, drag forces are so large that they instantly stop, without coasting, if they cease their swimming motion. To swim at constant speed, they must exert a constant propulsion force by rotating corkscrew-like flagella or beating hair-like cilia. The quadratic model of drag of Equation 6.16 fails for very small particles. Instead, a small object moving in a liquid experiences a linear drag force, \(\vec{D}=(b v\), direction opposite the motion), where \(b\) is a constant. For a sphere of radius \(R\), the drag constant can be shown to be \(b=6 \pi \eta R\), where \(\eta\) is the viscosity of the liquid. Water at \(20^{\circ} \mathrm{C}\) has viscosity \(1.0 \times 10^{-3} \mathrm{~N} \mathrm{~s} / \mathrm{m}^{2}\). a. A paramecium is about \(100 \mu \mathrm{m}\) long. If it's modeled as a sphere, how much propulsion force must it exert to swim at a typical speed of \(1.0 \mathrm{~mm} / \mathrm{s}\)? How about the propulsion force of a \(2.0-\mu \mathrm{m}\)-diameter \(E\). coli bacterium swimming at \(30 \mu \mathrm{m} / \mathrm{s}\) ? b. The propulsion forces are very small, but so are the organisms. To judge whether the propulsion force is large or small relative to the organism, compute the acceleration that the propulsion force could give each organism if there were no drag. The density of both organisms is the same as that of water, \(1000 \mathrm{~kg} / \mathrm{m}^{3}\). ________________ Equation Transcription: Text Transcription: vec{D}=(b v b R b = 6 pi eta R eta 20^circ C 1.0 X 10^{-3} Ns/m^2 100 mu m 1.0 mm/ s 2.0-mu m E 30 mu m/s 1000 kg / m^3

Problem 70P In Problem you are given the dynamics equations that are used to solve a problem. For the of this, you are to a. Write a realistic problem for which these are the correct equations. ________________ b. Draw the free-body diagram and the pictorial representation for your problem. ________________ c. Finish the solution of the problem. T ? 0.20n ? (20 kg)(9.80 m/s2) sin20° = (20 kg)(2.0 m/s2) n ? (20 kg)(9.80 m/s2) cos 20° = 0

Problem 69P In Problem you are given the dynamics equations that are used to solve a problem. For the of this, you are to a. Write a realistic problem for which these are the correct equations. ________________ b. Draw the free-body diagram and the pictorial representation for your problem. ________________ c. Finish the solution of the problem. ? 0.80n = (1500 kg)ax n ? (1500kg)(9.80 m/s2) = 0

Problem 71P In Problem you are given the dynamics equations that are used to solve a problem. For the of this, you are to a. Write a realistic problem for which these are the correct equations. ________________ b. Draw the free-body diagram and the pictorial representation for your problem. ________________ c. Finish the solution of the problem. (100 N) cos 30° ? fk = (20 kg)ax n + (100 N) sin 30° ? (20 kg)(9.80 m/s2) = 0 fk = 0.20n

A block of mass \(m\) is at rest at the origin at \(t=0 .\) It is pushed with constant force \(F_{0}\) from \(x=0\) to \(x=L\) across a horizontal surface whose coefficient of kinetic friction is \(\mu_{\mathrm{k}}=\mu_{0}(1-x / L)\). That is, the coefficient of friction decreases from \(\mu_{0}\) at \(x=0\) to zero at \(x=L\). a. Use what you've learned in calculus to prove that \(a_{x}=v_{x} \frac{d v_{x}}{d x}\) b. Find an expression for the block's speed as it reaches position \(L\). ________________ Equation Transcription: Text Transcription: m t = 0 F_0 x = 0 x = L mu_k = mu_{0}(1-x / L) mu_{0}t x = 0 x = L a_{x} =v_{x} frac{d v_{x}}{d x} L

Problem 1CQ Are the objects described here in static equilibrium, dynamic equilibrium, or not in equilibrium at all? Explain. a. A 200 pound barbell is held over your head. ________________ b. A girder is lifted at constant speed by a crane. ________________ c. A girder is being lowered into place. It is slowing down. ________________ d. A jet plane has reached its cruising speed and altitude. ________________ e. A box in the back of a truck doesn’t slide as the truck stops.

The three ropes in Figure EX6.1 are tied to a small, very light ring. Two of the ropes are anchored to walls at right angles, and the third rope pulls as shown. What are \(T_{1}\) and \(T_{2}\), the magnitudes of the tension forces in the first two ropes? Equation Transcription: Text Transcription: T_1 T_2

Problem 2CQ A ball tossed straight up has v = 0 at its highest point. Is it in equilibrium? Explain.