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Physics for Scientists and Engineers A Strategic Approach with Modern Physics 4th edition Randall D. Knight - Solutions
FIGURE EX5.14 shows the acceleration of objects of different mass that experience the same force. What is the magnitude of the force?Figure Ex 5.14
FIGURE EX5.13 shows an acceleration-versus-force graph for a 500 g object. What acceleration values go in the blanks on the vertical scale?Figure Ex 5.13
FIGURE EX5.12 shows an acceleration-versus-force graph for a 200 g object. What force values go in the blanks on the horizontal scale?Figure Ex 5.12
You’ll learn in Chapter 25 that the potential energy of two electric charges is inversely proportional to the distance between them. Two charges 30 nm apart have 1.0 J of potential energy. What is their potential energy if they are 20 nm apart?
For an object starting from rest and accelerating with constant acceleration, distance traveled is proportional to the square of the time. If an object travels 2.0 furlongs in the first 2.0 s, how far will it travel in the first 4.0 s?
FIGURE EX5.9 shows an acceleration-versus-force graph for three objects pulled by rubber bands. The mass of object 2 is 0.20 kg. What are the masses of objects 1 and 3? Explain your reasoning.Figure Ex 5.9
FIGURE EX5.8 shows acceleration-versus-force graphs for two objects pulled by rubber bands. What is the mass ratio m1 / m2?Figure Ex 5.8
Two rubber bands pulling on an object cause it to accelerate at 1.2 m/s2.a. What will be the object’s acceleration if it is pulled by four rubber bands?b. What will be the acceleration of two of these objects glued together if they are pulled by two rubber bands?
Two rubber bands cause an object to accelerate with acceleration a. How many rubber bands are needed to cause an object with half the mass to accelerate three times as quickly?
An arrow has just been shot from a bow and is now traveling horizontally. Air resistance is not negligible. Identify the forces on the arrow?
A jet plane is speeding down the runway during takeoff. Air resistance is not negligible. Identify the forces on the jet?
A baseball player is sliding into second base. Identify the forces on the baseball player?
A chandelier hangs from a chain in the middle of a dining room. Identify the forces on the chandelier?
A car is parked on a steep hill. Identify the forces on the car?
Which of the following are inertial reference frames? Explain.a. A car driving at steady speed on a straight and level road.b. A car driving at steady speed up a 10° incline.c. A car speeding up after leaving a stop sign.d. A car driving at steady speed around a curve.
Which, if either, of the basketballs in FIGURE Q5.16 are in equilibrium? Explain.Figure Q5.16
FIGURE Q5.15 shows a hollow tube forming three-quarters of a circle. It is lying flat on a table. A ball is shot through the tube at high speed. As the ball emerges from the other end, does it follow path A, path B, or path C? Explain.Figure Q5.15
Suppose you press your physics book against a wall hard enough to keep it from moving. Does the friction force on the book point(a) Into the wall,(b) Out of the wall,(c) Up,(d) Down, or(e) Is there no friction force? Explain.
Is it possible for the friction force on an object to be in the direction of motion? If so, give an example. If not, why not?
Newton’s second law saysSo isa force? Explain.
Is the statement “An object always moves in the direction of the net force acting on it” true or false? Explain.
If a force is exerted on an object, is it possible for that object to be moving with constant velocity? Explain.
If an object is at rest, can you conclude that there are no forces acting on it? Explain.
An object experiencing a constant force accelerates at 8 m/s2.What will the acceleration of this object be ifa. The force is halved? Explain.b. The mass is halved?c. The force is halved and the mass is halved?
An object experiencing a constant force accelerates at 10 m/s2.What will the acceleration of this object be ifa. The force is doubled? Explain.b. The mass is doubled?c. The force is doubled and the mass is doubled?
A constant force applied to A causes A to accelerate at 5 m/s2.The same force applied to B causes an acceleration of 3 m/s2.Applied to C, it causes an acceleration of 8 m/s2.(a) Which object has the largest mass? Explain.(b) Which object has the smallest mass?(c) What is the ratio mA / mB of the
You toss a ball straight up in the air. Immediately after you let go of it, what force or forces are acting on the ball? For each force you name,(a) State whether it is a contact force or a long-range force and(b) Identify the agent of the force?
In FIGURE Q5.4, block B is falling and dragging block A across a table. How many force vectors would be shown on a free-body diagram of block A? Name them.Figure Q5.4
A brick is falling from the roof of a three-story building. How many force vectors would be shown on a free-body diagram? Name them.
A compressed spring is pushing a block across a rough horizontal table. How many force vectors would be shown on a free-body diagram? Name them.
An elevator suspended by a cable is descending at constant velocity. How many force vectors would be shown on a free-body diagram? Name them.
A child in danger of drowning in a river is being carried downstream by a current that flows uniformly with a speed of 2.0 m/s. The child is 200 m from the shore and 1500 m upstream of the boat dock from which the rescue team sets out. If their boat speed is 8.0 m/s with respect to the water, at
A cannon on a train car fires a projectile to the right with speed v0, relative to the train, from a barrel elevated at angle q. The cannon fires just as the train, which had been cruising to the right along a level track with speed vtrain, begins to accelerate with acceleration a, which can be
An archer standing on a 15o slope shoots an arrow 20 above the horizontal, as shown in FIGURE CP4.82. How far down the slope does the arrow hit if it is shot with a speed of 50 m/s from 1.75 m above the ground?Figure CP4.82
In one contest at the county fair, seen in FIGURE CP4.81, a spring-loaded plunger launches a ball at a speed of 3.0 m/s from one corner of a smooth, flat board that is tilted up at a 20° angle. To win, you must make the ball hit a small target at the adjacent corner, 2.50 m away. At what angle u
You are given the equations that are used to solve a problem. For each of these, you are toa. Write a realistic problem for which these are the correct equations. Be sure that the answer your problem requests is consistent with the equations given.b. Finish the solution of the problem, including a
A long string is wrapped around a 6.0-cm-diameter cylinder, initially at rest, that is free to rotate on an axle. The string is then pulled with a constant acceleration of 1.5 m/s2 until 1.0 m of string has been unwound. If the string unwinds without slipping, what is the cylinder’s angular
A car starts from rest on a curve with a radius of 120 m and accelerates tangentially at 1.0 m/s2. Through what angle will the car have traveled when the magnitude of its total acceleration is 2.0 m/s2?
A painted tooth on a spinning gear has angular acceleration a = 120 - t2 rad / s2, where t is in s. Its initial angular velocity, at t = 0 s, is 300 rpm. What is the tooth’s angular velocity in rpm at t = 20 s?
A 6.0-cm-diameter gear rotates with angular velocity v = (2.0 + 1 / 2 t2) rad / s, where t is in seconds. At t = 4.0 s, what are:a. The gear’s angular acceleration?b. The tangential acceleration of a tooth on the gear?
A Ferris wheel of radius R speeds up with angular acceleration a starting from rest. Find an expression for the(a) Velocity and(b) Centripetal acceleration of a rider after the Ferris wheel has rotated through angle Δθ?
The angular velocity of a process control motor is ω = (20 – 1 / 2 t2) 22rad/s, where t is in seconds.a. At what time does the motor reverse direction?b. Through what angle does the motor turn between t = 0 s and the instant at which it reverses direction?
Your 64-cm-diameter car tire is rotating at 3.5 rev/s when suddenly you press down hard on the accelerator. After traveling 200 m, the tire’s rotation has increased to 6.0 rev/s. What was the tire’s angular acceleration? Give your answer in rad / s2.
A turbine is spinning at 3800 rpm. Friction in the bearings is so low that it takes 10 min to coast to a stop. How many revolutions does the turbine make while stopping?
Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The radius of the earth is 6.37 × 106 m, and the altitude of a geosynchronous orbit is 3.58 × 107 m (»22,000 miles2).
A high-speed drill rotating ccw at 2400 rpm comes to a halt in 2.5 s.a. What is the magnitude of the drill’s angular acceleration?b. How many revolutions does it make as it stops?
A computer hard disk 8.0 cm in diameter is initially at rest. A small dot is painted on the edge of the disk. The disk accelerates at 600 rad / s2 for 12 s, then coasts at a steady angular velocity for another ½ s.a. What is the speed of the dot at t = 1.0 s?b. Through how many revolutions has the
Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 30 s to speed up from rest to its top speed of 1 rotation every 1.3 s. The astronaut is strapped into a seat 6.0 m from the axis.a. What is the astronaut’s tangential acceleration during the first 30
A typical laboratory centrifuge rotates at 4000 rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations.a. What is the acceleration at the end of a test tube that is 10 cm from the axis of rotation?b. For comparison, what is the magnitude of the
A circular track has several concentric rings where people can run at their leisure. Phil runs on the outermost track with radius rP while Annie runs on an inner track with radius rA = 0.80rP. The runners start side by side, along a radial line, and run at the same speed in a counterclockwise
You’ve been assigned the task of using a shaft encoder—a device that measures the angle of a shaft or axle and provides a signal to a computer—to analyze the rotation of an engine crankshaft under certain conditions. The table lists the crankshaft’s angles over a 0.6 s interval.Time (s)
While driving north at 25 m/s during a rainstorm you notice that the rain makes an angle of 38° with the vertical. While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. From these observations, determine the speed and
Ships A and B leave port together. For the next two hours, ship A travels at 20 mph in a direction 30° west of north while ship B travels 20° east of north at 25 mph.a. What is the distance between the two ships two hours after they depart?b. What is the speed of ship A as seen by ship B?
You are asked to consult for the city’s research hospital, where a group of doctors is investigating the bombardment of cancer tumors with high-energy ions. As FIGURE P4.60 shows, ions are fired directly toward the center of the tumor at speeds of 5.0 × 106 m/s. To cover the entire tumor area,
You’re 6.0 m from one wall of the house seen in FIGURE P4.55. You want to toss a ball to your friend who is 6.0 m from the opposite wall. The throw and catch each occur 1.0 m above the ground.a. What minimum speed will allow the ball to clear the roof?b. At what angle should you toss the
A particle moving in the xy-plane has velocityat t = 0. It undergoes accelerationwhere b and c are constants. Find an expression for the particle’s velocity at a later time t?
A spaceship maneuvering near Planet Zeta is located atrelative to the planet, and traveling atIt turns on its thruster engine and accelerates withfor 35 min. What is the spaceship’s position when the engine shuts off? Give your answer as a position vector measured in km?
A physics student on Planet Exidor throws a ball, and it follows the parabolic trajectory shown in FIGURE EX4.12. The ball’s position is shown at 1 s intervals until t = 3 s. At t = 1 s, the ball’s velocity isa. Determine the ball’s velocity at t = 0 s, 2 s, and 3 s.b. What is the value of g
A particle moving in the xy-plane has velocitywhere t is in s. What is the particle’s acceleration vector at t = 4 s?
A particle’s trajectory is described by x = (1/2t3 – 2t2)m and y = (1/2 t2 – 2t) m, where t is in s.a. What are the particle’s position and speed at t = 0 s and t = 4 s?b. What is the particle’s direction of motion, measured as an angle from the x-axis, at t = 0 s and t = 4 s?
A rocket-powered hockey puck moves on a horizontal friction less table. FIGURE EX4.7 shows graphs of vx and vy, the x- and y-components of the puck’s velocity. The puck starts at the origin. What is the magnitude of the puck’s acceleration at t = 5 s?Figure Ex 4.7
A rocket-powered hockey puck moves on a horizontal friction less table. FIGURE EX4.6 shows graphs of vx and vy, the x- and y-components of the puck’s velocity. The puck starts at the origin.a. In which direction is the puck moving at t = 2 s? Give your answer as an angle from the x-axis.b. How
Answer Problems 1 through 3 by choosing one of the eight labeled acceleration vectors or selecting option I:1. At this instant, the particle has steady speed and is curving to the right. What is the direction of its acceleration?Figure Ex 4.32. At this instant, the particle is speeding up and
Show a partial motion diagram. For each:a. Complete the motion diagram by adding acceleration vectors.b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Don’t forget to include enough information to make the problem complete and to state clearly what is to be
FIGURE Q4.15 shows a pendulum at one end point of its arc.a. At this point, is v positive, negative, or zero? Explain.b. At this point, is a positive, negative, or zero? Explain.Figure Q4.15
FIGURE Q4.14 shows four rotating wheels. For each, determine the signs (+ or –) of v and a.Figure Q4.14(a)(b)(c)(d)
A projectile is launched at an angle of 30°.a. Is there any point on the trajectory whereare parallel to each other? If so, where?b. Is there any point whereare perpendicular to each other? If so, where?
Tarzan swings through the jungle by hanging from a vine.a. Immediately after stepping off a branch to swing over to another tree, is Tarzan’s acceleration au zero or not zero? If not zero, which way does it point? Explain.b. Answer the same question at the lowest point in Tarzan’s swing?
a. At this instant, is the particle in FIGURE Q4.2 speeding up, slowing down, or traveling at constant speed?b. Is this particle curving upward, curving downward, or traveling straight?Figure Q4.2
a. At this instant, is the particle in FIGURE Q4.1 speeding up, slowing down, or traveling at constant speed?b. Is this particle curving to the right, curving to the left, or traveling straight?Figure Q4.1
a. At this instant, is the particle in FIGURE Q4.2 speeding up, slowing down, or traveling at constant speed?b. Is this particle curving upward, curving downward, or traveling straight?Figure Q4.2
a. At this instant, is the particle in FIGURE Q4.1 speeding up, slowing down, or traveling at constant speed?b. Is this particle curving to the right, curving to the left, or traveling straight?Figure Q4.1
FIGURE P3.45 shows four electric charges located at the corners of a rectangle. Like charges, you will recall, repel each other while opposite charges attract. Charge B exerts a repulsive force (directly away from B) on charge A of 3.0 N. Charge C exerts an attractive force (directly toward C) on
Four forces are exerted on the object shown in FIGURE P3.44. (Forces are measured in newtons, abbreviated N.) The net force on the object isWhat are(a)and(b)Give your answers in component form.Figure P3.44
FIGURE P3.43 shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. How hard and in what direction must you pull on the third rope to keep the knot from moving?Figure P3.43
The bacterium E. coli is a single-cell organism that lives in the gut of healthy animals, including humans. When grown in a uniform medium in the laboratory, these bacteria swim along zig-zag paths at a constant speed of 20 μm/s. FIGURE P3.41 shows the trajectory of an E. coli as it moves from
The treasure map in FIGURE P3.40 gives the following directions to the buried treasure: “Start at the old oak tree, walk due north for 500 paces, then due east for 100 paces. Dig.” But when you arrive, you find an angry dragon just north of the tree. To avoid the dragon, you set off along the
Ruth sets out to visit her friend Ward, who lives 50 mi north and 100 mi east of her. She starts by driving east, but after 30 mi she comes to a detour that takes her 15 mi south before going east again. She then drives east for 8 mi and runs out of gas, so Ward flies there in his small plane to
While vacationing in the mountains you do some hiking. In the morning, your displacement isAfter lunch, your displacement isa. At the end of the hike, how much higher or lower are you compared to your starting point?b. What is the magnitude of your net displacement for the day?
Find a vector that points in the same direction as the vectorand whose magnitude is 1?
FIGURE P3.26 shows vectorsWrite your answer in component form.Figure P3.26
FIGURE P3.25 shows vectorsFind vectorSuch thatWrite your answer in component form.Figure P3.25
a. What is the angle f between vectorsin FIGURE P3.24?b. Use geometry and trigonometry to determine the magnitude and direction ofc. Use components to determine the magnitude and direction ofFigure P3-24
The position of a particle as a function of time is given bywhere t is in seconds.a. What is the particle’s distance from the origin at t = 0, 2, and 5 s?b. Find an expression for the particle’s velocityas a function of time.c. What is the particle’s speed at t = 0, 2, and 5 s?
Let A = (3.0 m, 20° south of east),anda. Draw and labelwith their tails at the origin. Use a coordinate system with the x-axis to the east.b. Writein component form, using unit vectors.c. Find the magnitude and the direction of
The magnetic field inside an instrument isT whererepresents the magnetic field vector and T stands for tesla, the unit of the magnetic field. What are the magnitude and direction of the magnetic field?
For the three vectors shown in FIGURE EX3.20,What is vectora. Write in component form.b. Writeas a magnitude and a direction.Figure Ex 3.20
What are the x- and y-components of the velocity vector shown in FIGURE EX3.19?Figure Ex 3.19
Let B = (5.0 m, 30° counterclockwise from vertical). Find the x- and y-components of in each of the two coordinate systems shown in FIGURE EX3.18.Figure Ex 3.18(a)(b)
Find the magnitude ofa. b. c.
a. Write vector F in component form.b. Draw a coordinate system and on it show vectorsc. What are the magnitude and direction of vectorLet
a. Write vector E in component form.b. Draw a coordinate system and on it show vectorsc. What are the magnitude and direction of vectorLet
a. Write vector D in component form.b. Draw a coordinate system and on it show vectorsc. What are the magnitude and direction of vectorLet
a. Write vector C in component form.b. Draw a coordinate system and on it show vectorsLet
a. Write vector C in component form.b. Draw a coordinate system and on it show vectorsc. What are the magnitude and direction of vectorLet
Draw each of the following vectors, label an angle that specifies the vector’s direction, and then find the vector’s magnitude and direction.a. b. c. d.
Draw each of the following vectors, label an angle that specifies the vector’s direction, then find its magnitude and direction.a. b.c. d.
Find the x- and y-components of each vector.Let15° above the negative x-axis) and30° to the right of the negative y-axis2?
Draw each of the following vectors. Then find its x- and y-components.a.= (7.5 m/s, 30° clockwise from the positive y-axis)b.= (1.5 m/s2, 30° above the negative x-axis)c.= (50.0 N, 36.9° counterclockwise from the positive y-axis).
Draw each of the following vectors. Then find its x- and y-components.a. = (3.5 m/s2, negative x-direction)b.= (440 m/s, 30° below the positive x-axis)c.= (12 m, 40° above the positive x-axis).
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