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mathematics
calculus early transcendentals 9th

Physics For Scientists And Engineers A Strategic Approach With Modern Physics 3rd Edition Randall D. Knight - Solutions

A 750 g, 50-cm-long metal rod is free to rotate about a frictionless axle at one end. While at rest, the rod is given a short but sharp 1000 N hammer blow at the center of the rod, aimed in a direction that causes the rod to rotate on the axle. The blow lasts a mere 2.0 ms. What is the rod’s
a. Figure P 11.40a shows the force Fx exerted on a particle that moves along the x-axis. Draw a graph of the particle’s potential energy as a function of position x. Let U be zero at x = 0 m.b. FIGURE P 11.40b shows the potential energy U of a particle that moves along the x-axis. Draw a graph of
Jimmy has caught two fish in Yellow Creek. He has tied the line holding the 3.0 kg steelhead trout to the tail of the 1.5 kg carp. To show the fish to a friend, he lifts upward on the carp with a force of 60 N.a. Draw separate free-body diagrams for the trout and the carp. Label all forces, then
0.10 mol of gas undergoes the process 1 → 2 shown in Figure P 16.59.a. What are temperatures T1 and T2 (in °C)?b. What type of process is this?c. The gas undergoes an isothermal compression from point 2 until the volume is restored to the value it had at point 1. What is the final pressure of
A gas cylinder with a tight-fitting, movable piston contains 200 cm3 of air at 1.0 atm. It floats on the surface of a swimming pool filled with 15°C water. The cylinder is then pulled slowly underwater to a depth of 3.0 m. What is the volume of gas at this depth?
An element in its solid phase forms a cubic crystal lattice (see Problem 33) with mass density 7950 kg/m3. The smallest spacing between two adjacent atoms is 0.227 nm. What is the element’s atomic mass number?Data From Problem# 33:The atomic mass number of copper is A = 64. Assume that
A 10-cm-diameter cylinder of neon gas is 30 cm long and at 30°C. The pressure gauge reads 120 psi. What is the mass density of the gas?
The lowest and highest natural temperatures ever recorded on earth are -127°F in Antarctica and 136°F in Libya. What are these temperatures in °C and in K?
What volume of water has the same mass as 100 cm3 of gold?
A cylindrical tank of diameter 2R contains water to a depth d. A small hole of diameter 2r is opened in the bottom of the tank. r << R, so the tank drains slowly. Find an expression for the time it takes to drain the tank completely.
A cylinder of density ρo , length l, and cross-section area A floats in a liquid of density ρf with its axis perpendicular to the surface. Length h of the cylinder is submerged when the cylinder floats at rest.a. Show that h = (ρo/ρf)l.b. Suppose the cylinder is distance y above its equilibrium
A cylindrical steel pressure vessel with volume 1.30 m3 is to be tested. The vessel is entirely filled with water, then a piston at one end of the cylinder is pushed in until the pressure inside the vessel has increased by 2000 kPa. Suddenly, a safety plug on the top bursts. How many liters of
Suppose the density of the earth’s atmosphere were a constant 1.3 kg/m3, independent of height, until reaching the top. How thick would the atmosphere be?
A gymnasium is 16 m high. By what percent is the air pressure at the floor greater than the air pressure at the ceiling?
What hanging mass will increase the length of a 1.0-mmdiameter aluminum wire by 1.0%?
Water flowing through a hose at 4.0 m/s fills a 600 L child’s wading pool in 8.0 min. What is the diameter in cm of the hose?
In Figure Q15.5, is pA larger than, smaller than, or equal to pB? Explain. A В
Containers A and B have equal volumes. Container A holds helium gas at 1.0 atm pressure and 0°C. Container B is completely filled with a liquid whose mass is 7000 times the mass of helium gas in container A. Identify the liquid in container B.
a. A mass m oscillating on a spring has period T. Suppose the mass changes very slightly from m to m + Δm, where Δm << m. Find an expression for ΔT, the small change in the period. Your expression should involve T, m, and Δm but not the spring constant.b. Suppose the period is 2.000 s and
An ice cube can slide around the inside of a vertical circular hoop of radius R. It undergoes small-amplitude oscillations if displaced slightly from the equilibrium position at the lowest point. Find an expression for the period of these small-amplitude oscillations.
A geologist needs to determine the local value of g. Unfortunately, his only tools are a meter stick, a saw, and a stopwatch. He starts by hanging the meter stick from one end and measuring its frequency as it swings. He then saws off 20 cm—using the centimeter markings—and measures the
Show that Equation 14.51 for the angular frequency of a physical pendulum gives Equation 14.48 when applied to a simple pendulum of a mass on a string.
While grocery shopping, you put several apples in the spring scale in the produce department. The scale reads 20 N, and you use your ruler (which you always carry with you) to discover that the pan goes down 9.0 cm when the apples are added. If you tap the bottom of the apple-filled pan to make it
A spring with spring constant k is suspended vertically from a support and a mass m is attached. The mass is held at the point where the spring is not stretched. Then the mass is released and begins to oscillate. The lowest point in the oscillation is 20 cm below the point where the mass was
A block on a spring is pulled to the right and released at t = 0 s. It passes x = 3.00 cm at t = 0.685 s, and it passes x = -3.00 cm at t = 0.886 s.a. What is the angular frequency?b. What is the amplitude?
A 1.0 kg block oscillates on a spring with spring constant 20 N/m. At t = 0 s the block is 20 cm to the right of the equilibrium position and moving to the left at a speed of 100 cm/s. Determine The period
The two graphs in Figure P14.32 are for two different vertical mass spring systems. If both systems have the same mass, what is the ratio kA/kB of their spring constants? A В -t (s) /12
Sketch a position graph from t = 0 s to t = 10 s of a damped oscillator having a frequency of 1.0 Hz and a time constant of 4.0 s.
What is the period of a 1.0-m-long pendulum on(a) The earth(b) Venus?
Your job with NASA is to monitor satellite orbits. One day, during a routine survey, you find that a 400 kg satellite in a 1000-kmhigh circular orbit is going to collide with a smaller 100 kg satellite traveling in the same orbit but in the opposite direction. Knowing the construction of the two
A projectile is fired from the earth in the direction of the earth’s motion around the sun. What minimum speed must the projectile have relative to the earth to escape the solar system? Ignore the earth’s rotation.
In 1996, the Solar and Heliospheric Observatory (SOHO) was “parked” in an orbit slightly inside the earth’s orbit, as shown in Figure CP13.63. The satellite’s period in this orbit is exactly one year, so it remains fixed relative to the earth. At this point, called a Lagrange point, the
A spaceship is in a circular orbit of radius r0 about a planet of mass M. A brief but intense firing of its engine in the forward direction decreases the spaceship’s speed by 50%. This causes the spaceship to move into an elliptical orbit.a. What is the spaceship’s new speed, just after the
Mercury moves in a fairly elliptical orbit around the sun. Mercury’s speed is 38.8 km/s when it is at its most distant point, 6.99 × 1010 m from the sun. How far is Mercury from the sun at ts closest point, where its speed is 59.0 km/s?
Three stars, each with the mass and radius of our sun, form an equilateral triangle 5.0 × 109 m on a side. If all three are simultaneously released from rest, what are their speeds as they crash together in the center?
A projectile is fired straight away from the moon from a base on the far side of the moon, away from the earth. What is the projectile’s escape speed from the earth-moon system?
Suppose that on earth you can jump straight up a distance of 50 cm. Can you escape from a 4.0-km-diameter asteroid with a mass of 1.0 × 1014 kg?
A 1.0 kg object is released from rest 500 km (≈ 300 miles) above the earth.a. What is its impact speed as it hits the ground? Ignore air resistance.b. What would the impact speed be if the earth were flat?c. By what percentage is the flat-earth calculation in error?
Planet X orbits the star Omega with a “year” that is 200 earth days long. Planet Y circles Omega at four times the distance of Planet X. How long is a year on Planet Y?
Use information about the earth and its orbit to determine the mass of the sun.
What is the escape speed from Jupiter?
What is the free-fall acceleration at the surface of Jupiter?
a. What is the free-fall acceleration at the surface of the sun?b. What is the sun’s free-fall acceleration at the distance of the earth?
A 1.0-m-diameter lead sphere has a mass of 5900 kg. A dust particle rests on the surface. What is the ratio of the gravitational force of the sphere on the dust particle to the gravitational force of the earth on the dust particle?
What is the angle θ between vectors A(vector) and B(vector) in each part of Exercise 2?Data From Exercise# 2:Evaluate the dot product A(vector) ∙ B(vector) ifa. A(vector) = 4î - 2ĵ and B(vector) = -2î - 3ĵ.b. A(vector) = -4î + 2ĵ and B(vector) = 2î + 4ĵ.
Figure P 12.75 shows a hoop of mass M and radius R rotating about an axle at the edge of the hoop. The hoop starts at its highest position and is given a very small push to start it rotating. At its lowest position, what are(a) The angular velocity(b) The speed of the lowest point on the hoop?
A 60-cm-long, 500 g bar rotates in a horizontal plane on an axle that passes through the center of the bar. Compressed air is fed in through the axle, passes through a small hole down the length of the bar, and escapes as air jets from holes at the ends of the bar. The jets are perpendicular to the
A 60-cm-diameter wheel is rolling along at 20 m/s. What is the speed of a point at the forward edge of the wheel?
A 70 kg man’s arm, including the hand, can be modeled as a 75-cm-long uniform rod with a mass of 3.5 kg. When the man raises both his arms, from hanging down to straight up, by how much does he raise his center of mass?
Consider the vector C(vector) = 3î.a. What is a vector D(vector) such that C(vector) × D(vector) = 0(vector)?b. What is a vector E(vector) such that C(vector) × E(vector) = 6k̂?c. What is a vector F(vector) such that C(vector) × F(vector) = -3ĵ?
Vector A(vector) = 3î + ĵ and vector B(vector) = 3î – 2ĵ + 2k̂. What is the cross product A(vector) × B(vector)?
a. What is î × (î × ĵ)?b. What is (î × ĵ) × k̂?
a. What is (î × ĵ) × î?b. What is î × (ĵ × î)?
Evaluate the cross products A(vector) × B(vector) and C(vector) × D(vector).(a)(b) B 135° 4 6
Is the object in Figure EX12.29 in equilibrium? Explain. 100 N 2.0 m 1.0 m 40 N Massless 60 N
How much torque must the pin exert to keep the rod in Figure EX 12.28 from rotating? 80 cm 2.0 kg Pin 500 g
The equation mgy for gravitational potential energy is valid only for objects near the surface of a planet. Consider two very large objects of mass m1 and m2, such as stars or planets, whose centers are separated by the large distance r. These two large objects exert gravitational forces on each
A 10.2 kg weather rocket generates a thrust of 200 N. The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 500 N/m, is anchored to the ground.a. Initially, before the engine is ignited, the rocket sits at rest on top of the
The force required to tow a water skier at speed v is proportional to the speed. That is, Ftow = Av, where A is a proportionality constant. If a speed of 2.5 mph requires 2 hp, how much power is required to tow a water skier at 7.5 mph?
A 5.0 kg cat leaps from the floor to the top of a 95-cm-high table. If the cat pushes against the floor for 0.20 s to accomplish this feat, what was her average power output during the pushoff period?
A particle of mass m starts from x0 = 0 m with v0 > 0 m/s. The particle experiences the variable force Fx = F0sin(cx) as it moves to the right along the x-axis, where F0 and c are constants.a. What are the units of F0 ?b. What are the units of c ?c. At what position xmax does the force first
Show that Hooke’s law for an ideal spring is a conservative force. To do so, first calculate the work done by the spring as it expands from A to B. Then calculate the work done by the spring as it expands from A to point C, which is beyond B, then returns from C to B.
A 5.0 kg box slides down a 5.0-m-high frictionless hill, starting from rest, across a 2.0-m-wide horizontal surface, then hits a horizontal spring with spring constant 500 N/m. The other end of the spring is anchored against a wall. The ground under the spring is frictionless, but the 2.0-m-wide
You’ve taken a summer job at a water park. In one stunt, a water skier is going to glide up the 2.0-m-high frictionless ramp shown in Figure P11.53, then sail over a 5.0-m-wide tank filled with hungry sharks. You will be driving the boat that pulls her to the ramp. She’ll drop the tow rope at
Bob can throw a 500 g rock with a speed of 30 m/s. He moves his hand forward 1.0 m while doing so.a. How much work does Bob do on the rock?b. How much force, assumed to be constant, does Bob apply to the rock?c. What is Bob’s maximum power output as he throws the rock?
Figure P 11.41 is the velocity-versus-time graph of a 500 g particle that starts at x = 0 m and moves along the x-axis. Draw graphs of the following by calculating and plotting numerical values at t = 0, 1, 2, 3, and 4 s. Then sketch lines or curves of the appropriate shape between the points. Make
A 10 g particle has the potential energy shown in Figure P 11.39.a. Draw a force-versus-position graph from x = 0 cm to x = 8 cm.b. How much work does the force do as the particle moves from x = 2 cm to x = 6 cm?c. What speed does the particle need at x = 2 cm to arrive at x = 6 cm with a speed of
a. Estimate the height in meters of the two flights of stairs that go from the first to the third floor of a building.b. Estimate how long it takes you to run up these two flights of stairs.c. Estimate your power output in both watts and horsepower while running up the stairs.
A 2.0 hp electric motor on a water well pumps water from 10 m below the surface. The density of water is 1.0 kg per liter. How many liters of water does the motor pump in 1 h?
A cable with 20.0 N of tension pulls straight up on a 1.02 kg block that is initially at rest. What is the block’s speed after being lifted 2.00 m? Solve this problem using work and energy.
A 20 kg child slides down a 3.0-m-high playground slide. She starts from rest, and her speed at the bottom is 2.0 m/s.a. Describe the energy transfers and transformations occurring during the slide.b. What is the change in the combined thermal energy of the slide and the seat of her pants?
The mass of a carbon atom is 2.0 × 10-26kg.a. What is the kinetic energy of a carbon atom moving with a speed of 500 m/s?b. Two carbon atoms are joined by a spring-like carbon-carbon bond. The potential energy stored in the bond has the value you calculated in part a if the bond is stretched 0.050
The motor of a crane uses power P to lift a steel beam. By what factor must the motor’s power increase to lift the beam twice as high in half the time?
Give a specific example of a situation in whicha. Wext → K with ΔU = 0 and ΔEth = 0.b. Wext → Eth with ΔK = 0 and ΔU = 0.
What energy transformations occur as a skier glides down a gentle slope at constant speed?
A car traveling at 60 mph slams on its brakes and skids to a halt. What happened to the kinetic energy the car had just before stopping?
How much work is done by the force F(vector) = (-4.0î – 6.0ĵ)N on a particle that moves through displacement(a) Δr(vector) = – 3.0îm(b) Δr(vector) = (3.0î – 2.0ĵ)m?
How much work is done by the force F(vector) = (–3.0î + 6.0ĵ)N on a particle that moves through displacement(a) Δr(vector) = 2.0îm(b) Δr(vector) = 2.0ĵm?
You drop a ball from a high balcony and it falls freely. Does the ball’s kinetic energy increase by equal amounts in equal time intervals, or by equal amounts in equal distances? Explain.
What is the angle θ between vectors A(vector) and B(vector) in each part of Exercise 1?Data from Exercise 1Evaluate the dot product A(vector) ∙ B(vector) ifa. A(vector) = 3î + 4ĵ and B(vector) = 2î - 6ĵ.b. A(vector) = 3î – 2ĵ and B(vector) = 6î + 4ĵ.
The kinetic energy of a system decreases while its potential energy and thermal energy are unchanged. Does the environment do work on the system, or does the system do work on the environment? Explain.
Evaluate the dot product A(vector) · B(vector) ifa. A(vector) = 4î – 2ĵ and B(vector) = –2î - 3ĵ.b. A(vector) = –4î + 2ĵ and B(vector) = 2î + 4ĵ.
Evaluate the dot product A(vector) · B(vector) ifa. A(vector) = 3î + 4ĵ and B(vector) = 2î – 6ĵ.b. A(vector) = 3î – 2ĵ and B(vector) = 6î + 4ĵ.
A 100 g steel ball and a 200 g steel ball each hang from 1.0-m-long strings. At rest, the balls hang side by side, barely touching. The 100 g ball is pulled to the left until the angle between its string and vertical is 45°. The 200 g ball is pulled to a 45° angle on the right. The balls are
A 2.0 kg cart has a spring with k = 5000 N/m attached to its front, parallel to the ground. This cart rolls at 4.0 m/s toward a stationary 1.0 kg cart.a. What is the maximum compression of the spring during the collision?b. What is the speed of each cart after the collision?
A massless pan hangs from a spring that is suspended from the ceiling. When empty, the pan is 50 cm below the ceiling. If a 100 g clay ball is placed gently on the pan, the pan hangs 60 cm below the ceiling. Suppose the clay ball is dropped from the ceiling onto an empty pan. What is the pan’s
A 50 g air-track glider is repelled by a post fixed at one end of the track. It is hypothesized that the glider’s potential energy is U = c/x, where x is the distance from the post and c is an unknown constant. To test this hypothesis, you launch the glider with the same speed at various
A new event has been proposed for the Winter Olympics. As seen in Figure P 10.54, an athlete will sprint 100 m, starting from rest, then leap onto a 20 kg bobsled. The person and bobsled will then slide down a 50-m-long ice-covered ramp, sloped at 20°, and into a spring with a carefully calibrated
A vertical spring with k = 490 N/m is standing on the ground. You are holding a 5.0 kg block just above the spring, not quite touching it.a. How far does the spring compress if you let go of the block suddenly?b. How far does the spring compress if you slowly lower the block to the point where you
a. A block of mass m can slide up and down a frictionless slope tilted at angle θ. The block is pressed against a spring at the bottom of the slope, compressing the spring (with spring constant k) by Δx, then released. Find an expression for the block’s maximum height h above its starting
You’re driving at 35 km/h when the road suddenly descends 15 m into a valley. You take your foot off the accelerator and coast down the hill. Just as you reach the bottom you see the policeman hiding behind the speed limit sign that reads; 70 km/h.< Are you going to get a speeding ticket?
Ball 1, with a mass of 100 g and traveling at 10 m/s, collides head-on with ball 2, which has a mass of 300 g and is initially at rest. What is the final velocity of each ball if the collision is(a) Perfectly elastic?(b) Perfectly inelastic?
The desperate contestants on a TV survival show are very hungry. The only food they can see is some fruit hanging on a branch high in a tree. Fortunately, they have a spring they can use to launch a rock. The spring constant is 1000 N/m, and they can compress the spring a maximum of 30 cm. All the
A spring hanging from the ceiling has equilibrium length L0. Hanging mass m from the spring stretches its length to L1. Find an expression for the spring’s length L3 when mass 3m hangs from it.
You need to make a spring scale for measuring mass. You want each 1.0 cm length along the scale to correspond to a mass difference of 100 g. What should be the value of the spring constant?
The three balls in Figure Q 10.7, which have equal masses, are fired with equal speeds at the angles shown. Rank in order, from largest to smallest, their speeds va, vb, and vc as they cross the dashed horizontal line. Explain. (All three are fired with sufficient speed to reach the line.) 45°
A boy reaches out of a window and tosses a ball straight up with a speed of 10 m/s. The ball is 20 m above the ground as he releases it. Use energy to finda. The ball’s maximum height above the ground.b. The ball’s speed as it passes the window on its way down.c. The speed of impact on the
You are given the equation used to solve a problem. For each of these, you are toa. Write a realistic problem for which this is the correct equation.b. Finish the solution of the problem, including a pictorial representation.(50 g)(vfx)1 + (100 g)(7.5 m/s) = (150 g)(1.0 m/s)
You are a world-famous physicist-lawyer defending a client who has been charged with murder. It is alleged that your client, Mr. Smith, shot the victim, Mr. Wesson. The detective who investigated the scene of the crime found a second bullet, from a shot that missed Mr. Wesson, that had embedded
You are the ground-control commander of a 2000 kg scientific rocket that is approaching Mars at a speed of 25,000 km/h. It needs to quickly slow to 15,000 km/h to begin a controlled descent to the surface. If the rocket enters the Martian atmosphere too fast it will burn up, and if it enters too

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