Solution: If you know all of the forces acting on a moving

How are Newtons laws used to solve problems?

How are dynamics problems solved?

How are equilibrium problems solved?

What are mass and weight?

How do we model friction and drag?

How do we solve problems?

Your kneecap (patella) is attached by a tendon to your quadriceps muscle. This tendon pulls at a 10 angle relative to the femur, the bone of your upper leg. The patella is also attached to your lower leg (tibia) by a tendon that pulls parallel to the leg. To balance these forces, the end of your femur pushes outward on the patella. Bending your knee increases the tension in the tendons, and both have a tension of 60 N when the knee is bent to make a 70 angle between the upper and lower leg. What force does the femur exert on the kneecap in this position?

A Martian lander is approaching the surface. It is slowing its descent by firing its rocket motor. Which is the correct free-body diagram?

A car with a weight of 15,000 N is being towed up a 20 slope at constant velocity. Friction is negligible. The tow rope is rated at 6000 N maximum tension. Will it break?

An elevator that has descended from the 50th floor is coming to a halt at the 1st floor. As it does, your weight is a. More than mg. b. Less than mg. c. Equal to mg. d. Zero.

A 1500 kg car is pulled by a tow truck. The tension in the tow rope is 2500 N, and a 200 N friction force opposes the motion. If the car starts from rest, what is its speed after 5.0 seconds?

Rank in order, from largest to smallest, the sizes of the friction forces f u a to f u e in these 5 different situations. The box and the floor are made of the same materials in all situations. No push At rest (a) fa u Push On the verge of slipping (b) fb u Push Speeding up (c) fc a u u (d) Push Constant speed fd u Push Slowing down (e)

A 500 g model rocket with a weight of 4.90 N is launched straight up. The small rocket motor burns for 5.00 s and has a steady thrust of 20.0 N. What maximum altitude does the rocket reach?

The terminal speed of a Styrofoam ball is 15 m/s. Suppose a Styrofoam ball is shot straight down from a high tower with an initial speed of 30 m/s. Which velocity graph is correct? 0 t vy (m/s) -30 (a) 0 t -30 vy (m/s) (b) 0 t -30 vy (m/s) (c) 0 t -30 vy (m/s) (d) 0 t -30 vy (m/s) (e)

Carol pushes a 25 kg wood box across a wood floor at a steady speed of 2.0 m/s. How much force does Carol exert on the box? If she stops pushing, how far will the box slide before coming to rest?

A 50 kg steel file cabinet is in the back of a dump truck. The trucks bed, also made of steel, is slowly tilted. What is the size of the static friction force on the cabinet when the bed is tilted 20? At what angle will the file cabinet begin to slide?

The profile of a typical 1500 kg passenger car, as seen from the front, is 1.6 m wide and 1.4 m high. Aerodynamic body shaping gives a drag coefficient of 0.35. At what speed does the magnitude of the drag equal the magnitude of the rolling friction?

A 1500 kg car is traveling at a speed of 30 m/s when the driver slams on the brakes and skids to a halt. Determine the stopping distance if the car is traveling up a 10 slope, down a 10 slope, or on a level road.

Your instructor has set up a lecture demonstration in which a 250 g cart can roll along a level, 2.00-m-long track while its velocity is measured with a motion detector. First, the instructor simply gives the cart a push and measures its velocity as it rolls down the track. The data below show that the cart slows slightly before reaching the end of the track. Then, as FIGURE 6.23 shows, the instructor attaches a string to the cart and uses a falling weight to pull the cart. She then asks you to determine the tension in the string. For extra credit, find the coefficient of rolling friction

A 100 kg box of dimensions 50 cm * 50 cm * 50 cm is in the back of a flatbed truck. The coefficients of friction between the box and the bed of the truck are ms = 0.40 and mk = 0.20. What is the maximum acceleration the truck can have without the box slipping?

Force Fx = c sin1pt/T2, where c and T are constants, is applied to an object of mass m that moves on a horizontal, frictionless surface. The object is at rest at the origin at t = 0. a. Find an expression for the objects velocity. Graph your result for 0 t T. b. What is the maximum velocity of a 500 g object if c = 2.5 N and T = 1.0 s?

Are the objects described here in equilibrium while at rest, in equilibrium while in motion, 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 doesnt slide as the truck stops

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

Kat, Matt, and Nat are arguing about why a physics book on a table doesnt fall. According to Kat, Gravity pulls down on it, but the table is in the way so it cant fall. Nonsense, says Matt. An upward force simply overcomes the downward force to prevent it from falling. But what about Newtons first law? counters Nat. Its not moving, so there cant 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?

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

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

An elevator, hanging from a single cable, moves downward and is slowing. 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.

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

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

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 7 b 7 c = d and explain your ranking. 3 m/s c 4 m/s b 5 m/s a 3 m/s 200 g 300 g 300 g 400 g d

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.

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 Q6.12. Is the normal force of the table on the book larger than, smaller than, or equal to mg?

Boxes A and B in FIGURE Q6.13 both remain at rest. Is the friction force on A larger than, smaller than, or equal to the friction force on B? Explain.

Suppose you push a hockey puck of mass m across frictionless ice for 1.0 s, starting from rest, giving the puck speed v after traveling distance d. If you repeat the experiment with a puck of mass 2m, pushing with the same force, 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 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?

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

Five balls move through the air as shown in FIGURE Q6.17. 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 aa to ae. Some may be equal. Give your answer in the form a 7 b = c 7 d 7 e and explain your ranking. a 50 g Just released vy = 0 b 100 g Just released vy = 0 c 50 g d 100 g e 50 g vy = 20 m/s vy = -20 m/s vy = -20 m/

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.

The three ropes in FIGURE EX6.1 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 T u 3 in the third rope?

The three ropes in FIGURE EX6.2 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 T1 and T2, the magnitudes of the tension forces in the first two ropes?

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, the players have equal pulls, 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?

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?

A 65 kg gymnast wedges himself between two closely spaced vertical walls by pressing his hands and feet against the walls. What is the magnitude of the friction force on each hand and foot? Assume they are all equal

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?

60-cm-long string and given an electric charge. A charged rod brought near the ball exerts a horizontal electrical force F u elec on it, causing the ball to swing out to a 20 angle and remain there. a. What is the magnitude of F u elec? b. What is the tension in the string?

The forces in FIGURE EX6.8 act on a 2.0 kg object. What are the values of ax and ay, the x- and y-components of the objects acceleration?

The forces in FIGURE EX6.9 act on a 2.0 kg object. What are the values of ax and ay, the x- and y-components of the objects acceleration?

FIGURE EX6.10 shows the velocity graph of a 2.0 kg object as it moves along the x-axis. What is the net force acting on this object at t = 1 s? At 4 s? At 7 s?

FIGURE EX6.11 shows the force acting on a 2.0 kg object as it moves along the x-axis. The object is at rest at the origin at t = 0 s. What are its acceleration and velocity at t = 6 s?

A horizontal rope is tied to a 50 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 m/s? c. The box has vx = 5.0 m/s and ax = 5.0 m/s2 ?

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 ?

A 2.0 * 107 kg train applies its brakes with the intent of slowing down at a 1.2 m/s2 rate. What magnitude force must its brakes provide?

A 8.0 * 104 kg spaceship is at rest in deep space. Its thrusters provide a force of 1200 kN. The spaceship fires its thrusters for 20 s, then coasts for 12 km. How long does it take the spaceship to coast this distance?

The position of a 2.0 kg mass is given by x = 12t 3 - 3t 2 2 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?

A woman has a mass of 55 kg. a. What is her weight while standing on earth? b. What are her mass and her weight on Mars, where g = 3.76 m/s2 ?

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 passengers weight a. Before the elevator starts moving? b. While the elevator is speeding up? c. After the elevator reaches its cruising speed?

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 Zachs weight before the elevator starts braking? b. What is Zachs weight while the elevator is braking?

FIGURE EX6.20 shows the velocity graph of a 75 kg passenger in an elevator. What is the passengers weight at t = 1 s? At 5 s? At 9 s?

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

A 20,000 kg rocket has a rocket motor that generates 3.0 * 105 N of thrust. Assume no air resistance. a. What is the rockets initial upward acceleration? b. At an altitude of 5000 m the rockets acceleration has increased to 6.0 m/s2 . What mass of fuel has it burned?

The earth is 1.50 * 1011 m from the sun. The earths mass is 5.98 * 1024 kg, while the mass of the sun is 1.99 * 1030 kg. What is earths acceleration toward the sun?

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 safes coefficient of kinetic friction on the bank floor?

A stubborn, 120 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 N. The coefficients of friction between the mule and the ground are ms = 0.8 and mk = 0.5. Is the farmer able to move the mule?

A 10 kg crate is placed on a horizontal conveyor belt. The materials are such that ms = 0.5 and mk = 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?

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?

A rubber-wheeled 50 kg cart rolls down a 15 concrete incline. What is the carts acceleration if rolling friction is (a) neglected and (b) included?

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.

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

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.

You and your friend Peter are putting new shingles on a roof pitched at 25. Youre 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?

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

A medium-sized jet has a 3.8-m-diameter fuselage and a loaded mass of 85,000 kg. The drag on an airplane is primarily due to the cylindrical fuselage, and aerodynamic shaping gives it a drag coefficient of 0.37. How much thrust must the jet's engines provide to cruise at 230 m/s at an altitude where the air density is 1.0 \(kg/m^3\)?

A 75 kg skydiver can be modeled as a rectangular box with dimensions 20 cm * 40 cm * 180 cm. What is his terminal speed if he falls feet first? Use 0.8 for the drag coefficient

A 6.5-cm-diameter ball has a terminal speed of 26 m/s. What is the balls mass?

A 2.0 kg object initially at rest at the origin is subjected to the time-varying force shown in FIGURE P6.37. What is the objects velocity at t = 4 s?

A 5.0 kg object initially at rest at the origin is subjected to the time-varying force shown in FIGURE P6.38. What is the objects velocity at t = 6 s?

The 1000 kg steel beam in FIGURE P6.39 is supported by two ropes. What is the tension in each?

Henry, whose mass is 95 kg, stands on a bathroom scale in an elevator. The scale reads 830 N for the first 3.0 s after the elevator starts moving, then 930 N for the next 3.0 s. What is the elevators velocity 6.0 s after starting?

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 kg, and the doctor has decided to hang a 6.0 kg mass from the rope. The boot is held suspended by the ropes, as shown in FIGURE P6.41, and does not touch the bed. a. Determine the amount of tension in the rope by using Newtons laws to analyze the hanging mass. b. The net traction force needs to pull straight out on the leg. What is the proper angle u for the upper rope? c. What is the net traction force pulling on the leg? Hint: If the pulleys are frictionless, which we will assume, the tension in the rope is constant from one end to the othe

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 (Newtons 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 cars 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

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 in the table. Use theory to find two quantities that, when graphed, should give a straight line. Then use the graph to find the size of the pistons force

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?

a. A rocket of mass m is launched straight up with thrust F u thrust. Find an expression for the rockets speed at height h if air resistance is neglected. b. The motor of a 350 g model rocket generates 9.5 N thrust. If air resistance can be neglected, what will be the rockets speed as it reaches a height of 85 m?

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?

A truck with a heavy load has a total mass of 7500 kg. It is climbing a 15 incline at a steady 15 m/s when, unfortunately, the poorly secured load falls off! Immediately after losing the load, the truck begins to accelerate at 1.5 m/s2 . What was the mass of the load? Ignore rolling friction

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, mk, is small enough that the object will slide down the slope after being given a very small push to get it started. Find an expression for the objects speed at the bottom of the slope

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 Sams top speed? b. How far has Sam traveled when he finally coasts to a stop?

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

A 2.0 kg wood block is launched up a wooden ramp that is inclined at a 30 angle. The blocks 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?

Its a snowy day and youre pulling a friend along a level road on a sled. Youve both been taking physics, so she asks what you think the coefficient of friction between the sled and the snow is. Youve 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 youre pulling with a force of 75 N. What answer will you give?

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 ms and mk, respectively. Find an expression for the maximum tension Tmax for which the small box rides on top of the large box without slipping

A large box of mass M is moving on a horizontal surface at speed v0. 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 ms and mk, respectively. Find an expression for the shortest distance dmin in which the large box can stop without the small box slipping

Youre driving along at 25 m/s with your aunts 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! 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 ms = 0.60 and mk = 0.30. Hint: Youre not trying to stop in the shortest possible distance. Whats your best strategy for avoiding damage to the antiques

The 2.0 kg wood box in FIGURE P6.56 slides down a vertical wood wall while you push on it at a 45 angle. What magnitude of force should you apply to cause the box to slide down at a constant speed?

A 1.0 kg wood block is pressed against a vertical wood wall by the 12 N force shown in FIGURE P6.57. If the block is initially at rest, will it move upward, move downward, or stay at rest?

A person with compromised pinch strength in his fingers can exert a force of only 6.0 N to either side of a pinchheld object, such as the book shown in FIGURE P6.58. 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 0.80.

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

Starting from rest, a 2500 kg helicopter accelerates straight up at a constant 2.0 m/s2 . What is the helicopters height at the moment its blades are providing an upward force of 26 kN? The helicopter can be modeled as a 2.6-m-diameter sphere.

Astronauts in space weigh themselves by oscillating on a spring. Suppose the position of an oscillating 75 kg astronaut is given by x = 10.30 m2 sin1(p rad/s) * t2, 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

A particle of mass m moving along the x-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 particles velocity vx at a later time t.

At t = 0, an object of mass m is at rest at x = 0 on a horizontal, frictionless surface. A horizontal force Fx = F011 - t/T2, which decreases from F0 at t = 0 to zero at t = T, is exerted on the object. Find an expression for the objects (a) velocity and (b) position at time T

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 objects velocity at an arbitrary later time t. b. What is the objects velocity after a very long time has elapsed?

Large objects have inertia and tend to keep movingNewtons 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 6.15 fails for very small particles. Instead, a small object moving in a liquid experiences a linear drag force, F u drag = (bv, direction opposite the motion), where b is a constant. For a sphere of radius R, the drag constant can be shown to be b = 6phR, where h is the viscosity of the liquid. Water at 20C has viscosity 1.0 * 10-3 N s/m2 . a. A paramecium is about 100 mm long. If its modeled as a sphere, how much propulsion force must it exert to swim at a typical speed of 1.0 mm/s? How about the propulsion force of a 2.0@mm@diameter E. coli bacterium swimming at 30 mm/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 kg/m3

A 60 kg skater is gliding across frictionless ice at 4.0 m/s. Air resistance is not negligible. You can model the skater as a 170-cm-tall, 36-cm-diameter cylinder. What is the skaters speed 2.0 s later?

Very small objects, such as dust particles, experience a linear drag force, F u drag = (bv, direction opposite the motion), where b is a constant. That is, the quadratic model of drag of Equation 6.15 fails for very small particles. For a sphere of radius R, the drag constant can be shown to be b = 6phR, where h is the viscosity of the gas. a. Find an expression for the terminal speed vterm of a spherical particle of radius R and mass m falling through a gas of viscosity h. b. Suppose a gust of wind has carried a 50@mm@diameter dust particle to a height of 300 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 kg/m3 , the viscosity of 25C air is 2.0 * 10-5 N s/m2 , and you can assume that the falling dust particle reaches terminal speed almost instantly

Problems 68 and 69 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!

Problems 68 and 69 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!

In Problems 70 through 72 you are given the dynamics equations that are used to solve a problem. For each of these, 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 = 11500 kg2ax n - 11500 kg219.80 m/s2 2 = 0

In Problems 70 through 72 you are given the dynamics equations that are used to solve a problem. For each of these, 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 - 120 kg219.80 m/s2 2 sin 20 = 120 kg212.0 m/s2 2 n - 120 kg219.80 m/s2 2 cos 20 = 0

In Problems 70 through 72 you are given the dynamics equations that are used to solve a problem. For each of these, 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.1100 N2 cos 30 - fk = 120 kg2ax n + 1100 N2 sin 30 - 120 kg219.80 m/s2 2 = 0 fk = 0.20n

A block of mass m is at rest at the origin at t = 0. It is pushed with constant force F0 from x = 0 to x = L across a horizontal surface whose coefficient of kinetic friction is mk = m011 - x/L2. That is, the coefficient of friction decreases from m0 at x = 0 to zero at x = L. a. Use what youve learned in calculus to prove that ax = vx dvx dx b. Find an expression for the blocks speed as it reaches position L

A spring-loaded toy gun exerts a variable force on a plastic ball as the spring expands. Consider a horizontal spring and a ball of mass m whose position when barely touching a fully expanded spring is x = 0. The ball is pushed to the left, compressing the spring. Youll learn in Chapter 9 that the spring force on the ball, when the ball is at position x (which is negative), can be written as 1FSp2x = -kx, where k is called the spring constant. The minus sign is needed to make the x-component of the force positive. Suppose the ball is initially pushed to x0 = -L, then released and shot to the right. a. Use what youve learned in calculus to prove that ax = vx dvx dx b. Find an expression, in terms of m, k, and L, for the speed of the ball as it comes off the spring at x = 0

FIGURE CP6.75 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 = x2 , where both x and y are in meters. A scale along the bottom is used to measure the balls horizontal position x. a. Find an expression that allows you to use a measured position x (in m) to compute the acceleration ax (in m/s2 ). (For example, ax = 3x is a possible expression.) b. What is the acceleration if x = 20 cm?

An object moving in a liquid experiences a linear drag force: F u drag = (bv, 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 = 6phR, where h is the viscosity of the liquid. a. Find an algebraic expression for vx1t2, 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 v0 through a liquid of viscosity h. b. Water at 20C has viscosity h = 1.0 * 10-3 N s/m2 . Suppose a 4.0-cm-diameter, 33 g ball is shot horizontally into a tank of 20C water. How long will it take for the horizontal speed to decrease to 50% of its initial value?

An object moving in a liquid experiences a linear drag force: F u drag = (bv, 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 = 6phR, where h is the viscosity of the liquid. a. Use what youve learned in calculus to prove that ax = vx dvx dx b. Find an algebraic expression for vx1x2, 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 v0 through a liquid of viscosity h. c. Water at 20C has viscosity h = 1.0 * 10-3 N s/m2 . Suppose a 1.0-cm-diameter, 1.0 g marble is shot horizontally into a tank of 20C water at 10 cm/s. How far will it travel before stopping?

An object with cross section A is shot horizontally across frictionless ice. Its initial velocity is v0x at t0 = 0 s. Air resistance is not negligible. a. Show that the velocity at time t is given by the expression vx = v0x 1 + CrAv0x t/2m 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 cars speed drops to 10 m/s? To 5 m/s? c. Assess whether or not it is reasonable to neglect kinetic friction