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physics
physics scientists and engineers
Questions and Answers of
Physics Scientists and Engineers
What is the difference between the driving frequency and the natural frequency of an oscillator?
An object in simple harmonic motion has amplitude 8.0 cm and frequency 0.50 Hz. At t = 0 s it has its most negative position.Write the function x(t) that describes the object’s position.
a. Describe the difference between τ and T. Don’t just name them; say what is different about the physical concepts they represent.b. Describe the difference between τ and t1/2.
An object in simple harmonic motion has amplitude 4.0 cm and frequency 4.0 Hz, and at t = 0 s it passes through the equilibrium point moving to the right. Write the function x(t) that describes the
Suppose the damping constant b of an oscillator increases.a. Is the medium more resistive or less resistive?b. Do the oscillations damp out more quickly or less quickly?c. Is the time constant t
An object in simple harmonic motion has an amplitude of 8.0 cm, a frequency of 0.25 Hz, and a phase constant of -π/2 rad. Draw a position graph showing two cycles of the motion.
FIGURE Q15.9 shows the potential-energy diagram and the total energy line of a particle oscillating on a spring.a. What is the springs equilibrium length?b. Where are the turning points
An object in simple harmonic motion has an amplitude of 4.0 cm, a frequency of 2.0 Hz, and a phase constant of 2π/3 rad.Draw a position graph showing two cycles of the motion.
The solid disk and circular hoop in FIGURE Q15.8 have the same radius and the same mass. Each can swing back and forth as a pendulum from a pivot at the top edge. Which, if either, has the larger
FIGURE EX15.8 is the velocity-versus-time graph of a particle in simple harmonic motion. a. What is the amplitude of the oscillation?b. What is the phase constant?c. What is the position at t = 0 s?
A block oscillating on a spring has a maximum speed of 20 cm/s.What will the block’s maximum speed be if the total energy is doubled? Explain.
FIGURE EX15.7 is the position-versus-time graph of a particle in simple harmonic motion. a. What is the phase constant?b. What is the velocity at t = 0 s?c. What is vmax? х (ст) 10- 5- 2 (s) 4 1 3
A block oscillating on a spring has an amplitude of 20 cm. What will the amplitude be if the total energy is doubled? Explain.
What are the(a) Amplitude,(b) Frequency,(c) Phase constantof the oscillation shown in FIGURE EX15.6? x (ст) 10- - (s) 2 3. -5- -10- FIGURE EX15.6
What are the(a) Amplitude,(b) Frequency,(c) Phase constant of the oscillation shown in FIGURE EX15.5? x (cm) 20- 10 -t (s) -10 -20- FIGURE EX15.5 4. 2.
FIGURE Q15.4 shows a position-versus-time graph for a particle in SHM.a. What is the phase constant Ï0? Explain.b. What is the phase of the particle at each of the three numbered points on
An object in SHM oscillates with a period of 4.0 s and an amplitude of 10 cm. How long does the object take to move from x = 0.0 cm to x = 6.0 cm?
FIGURE Q15.3 shows a positionversus- time graph for a particle in SHM. What are (a) The amplitude A,(b) The angular frequency v,(c) The phase constant Ï0? х (ст) 10 -t (s) 4 -10-
When a guitar string plays the note “A,” the string vibrates at 440 Hz. What is the period of the vibration?
A pendulum on Planet X, where the value of g is unknown, oscillates with a period T = 2 s. What is the period of this pendulum if:a. Its mass is doubled? Explain. Note that you do not know the value
An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t = 0 s. It then oscillates with a period of 2.0 s and a maximum speed of 40 cm/s.a. What is
A block oscillating on a spring has period T = 2 s. What is the period if:a. The block’s mass is doubled? Explain. Note that you do not know the value of either m or k, so do not assume any
An air-track glider attached to a spring oscillates between the 10 cm mark and the 60 cm mark on the track. The glider completes 10 oscillations in 33 s. What are the(a) Period,(b) Frequency,(c)
A 2.0-m-diameter vertical cylinder, open at the top, is filled with ethyl alcohol to the 2.5 m mark. A worker pulls a plug from a hole 55 cm from the bottom, causing the fluid level to begin dropping
Water from a vertical pipe emerges as a 10-cm-diameter cylinder and falls straight down 7.5 m into a bucket. The water exits the pipe with a speed of 2.0 m/s. What is the diameter of the column of
Water flowing out of a 16-mm-diameter faucet fills a 2.0 L bottle in 10 s. At what distance below the faucet has the water stream narrowed to 10 mm diameter?
The 1.0-m-tall cylinder in FIGURE P14.61 contains air at a pressure of 1 atm. A very thin, frictionless piston of negligible mass is placed at the top of the cylinder, to prevent any air from
Water flows from the pipe shown in FIGURE P14.60 with a speed of 4.0 m/s.a. What is the water pressure as it exits into the air?b. What is the height h of the standing column of water? Open 5.0 cm?
A tree loses water to the air by the process of transpiration at the rate of 110 g/h. This water is replaced by the upward flow of sap through vessels in the trunk. If the trunk contains 2000
a. A liquid of density r flows at speed v0 through a horizontal pipe that expands smoothly from diameter d0 to a larger diameter d1. The pressure in the narrower section is p0. Find an expression for
A nuclear power plant draws 3.0 × 106 L/min of cooling water from the ocean. If the water is drawn in through two parallel, 3.0-m-diameter pipes, what is the water speed in each pipe?
A 355 mL soda can is 6.2 cm in diameter and has a mass of 20 g. Such a soda can half full of water is floating upright in water.What length of the can is above the water level?
A plastic “boat” with a 25 cm2 square cross section floats in a liquid. One by one, you place 50 g masses inside the boat and measure how far the boat extends below the surface. Your data are as
A spring with spring constant 35 N/m is attached to the ceiling, and a 5.0-cm-diameter, 1.0 kg metal cylinder is attached to its lower end. The cylinder is held so that the spring is
One day when you come into physics lab you find several plastic hemispheres floating like boats in a tank of fresh water. Each lab group is challenged to determine the heaviest rock that can be
A 30-cm-tall, 4.0-cm-diameter plastic tube has a sealed bottom. 250 g of lead pellets are poured into the bottom of the tube, whose mass is 30 g, then the tube is lowered into a liquid.The tube
A less-dense liquid of density ρ1 floats on top of a more-dense liquid of density ρ2. A uniform cylinder of length l and density ρ, with ρ1 < ρ < ρ2, floats at the interface with its long
A cylinder with cross-section area A floats with its long axis vertical in a liquid of density ρ.a. Pressing down on the cylinder pushes it deeper into the liquid.Find an expression for the force
The average density of the body of a fish is 1080 kg/m3. To keep from sinking, a fish increases its volume by inflating an internal air bladder, known as a swim bladder, with air. By what percent
It’s possible to use the ideal-gas law to show that the density of the earth’s atmosphere decreases exponentially with height. That is, ρ = ρ0 exp(-z/z0), where z is the height above sea level,
An aquarium of length L, width (front to back) W, and depth D is filled to the top with liquid of density ρ.a. Find an expression for the force of the liquid on the bottom of the aquarium.b. Find an
Glycerin is poured into an open U-shaped tube until the height in both sides is 20 cm. Ethyl alcohol is then poured into one arm until the height of the alcohol column is 20 cm. The two liquids do
Geologists place tiltmeters on the sides of volcanoes to measure the displacement of the surface as magma moves inside the volcano. Although most tiltmeters today are electronic, the traditional
A U-shaped tube, open to the air on both ends, contains mercury.Water is poured into the left arm until the water column is 10.0 cm deep. How far upward from its initial position does the mercury in
A 55 kg cheerleader uses an oil-filled hydraulic lift to hold four 110 kg football players at a height of 1.0 m. If her piston is 16 cm in diameter, what is the diameter of the football players’
a. The 70 kg student in FIGURE P14.42 balances a 1200 kg elephant on a hydraulic lift. What is the diameter of the piston the student is standing on?b. When a second student joins the first, the
A friend asks you how much pressure is in your car tires. You know that the tire manufacturer recommends 30 psi, but it’s been a while since you’ve checked. You can’t find a tire gauge in the
Postural hypotension is the occurrence of low systolic blood pressure when a person stands up too quickly from a reclining position. A brain blood pressure lower than 90 mm of Hg can cause fainting
The two 60-cm-diameter cylinders in FIGURE P14.39, closed at one end, open at the other, are joined to form a single cylinder, then the air inside is removed.a. How much force does the atmosphere
A 5.0-m-diameter solid aluminum sphere is launched into space.By how much does its diameter increase? Give your answer in μm.
A large 10,000 L aquarium is supported by four wood posts (Douglas fir) at the corners. Each post has a square 4.0 cm × 4.0 cm cross section and is 80 cm tall. By how much is each post compressed by
a. What is the pressure at a depth of 5000 m in the ocean?b. What is the fractional volume change ΔV/V of seawater at this pressure?c. What is the density of seawater at this pressure?
A 3.0-m-tall, 50-cm-diameter concrete column supports a 200,000 kg load. By how much is the column compressed?
An 80-cm-long, 1.0-mm-diameter steel guitar string must be tightened to a tension of 2000 N by turning the tuning screws. By how much is the string stretched?
A 70 kg mountain climber dangling in a crevasse stretches a 50-m-long, 1.0-cm-diameter rope by 8.0 cm. What is Young’s modulus for the rope?
A 2.0 mL syringe has an inner diameter of 6.0 mm, a needle inner diameter of 0.25 mm, and a plunger pad diameter (where you place your finger) of 1.2 cm. A nurse uses the syringe to inject medicine
What does the top pressure gauge read in FIGURE EX14.30? 200 kPa 3.0 m/s 10 m Oil 2.0 m/s FIGURE EX14.30
A bucket is filled with water to a height of 23 cm, then a plug is removed from a 4.0-mm-diameter hole in the bottom of the bucket. As the water begins to pour out of the hole, how fast is it moving?
A 1.0-cm-diameter pipe widens to 2.0 cm, then narrows to 5.0 mm. Liquid flows through the first segment at a speed of 4.0 m/s.a. What is the speed in the second and third segments?b. What is the
Water flows through a 2.5-cm-diameter hose at 3.0 m/s.How long, in minutes, will it take to fill a 600 L child’s wading pool?
You and your friends are playing in the swimming pool with a 60-cm-diameter beach ball. How much force would be needed to push the ball completely under water?
Styrofoam has a density of 150 kg/m3. What is the maximum mass that can hang without sinking from a 50-cm-diameter Styrofoam sphere in water? Assume the volume of the mass is negligible compared to
You need to determine the density of a ceramic statue. If you suspend it from a spring scale, the scale reads 28.4 N.If you then lower the statue into a tub of water, so that it is completely
A 10-cm-diameter, 20-cm-tall steel cylinder (ρsteel = 7900 kg/m3) floats in mercury. The axis of the cylinder is perpendicular to the surface. What length of steel is above the surface?
What is the tension of the string in FIGURE EX14.21? 100 cm³ of aluminum, density PAI = 2700 kg/m³ Ethyl alcohol FIGURE EX14.21
A 5.0 kg rock whose density is 4800 kg/m3 is suspended by a string such that half of the rock’s volume is under water. What is the tension in the string?
Rank in order, from largest to smallest, the pressures at d, e, and f in FIGURE Q14.2. Explain. f d a b
FIGURE CP13.72 shows a particle of mass m at distance x from the center of a very thin cylinder of mass M and length L. The particle is outside the cylinder, so x > L/2.a. Calculate the
Lets look in more detail at how a satellite is moved from one circular orbit to another. FIGURE CP13.71 shows two circular orbits, of radii r1and r2, and an elliptical orbit that connects
A moon lander is orbiting the moon at an altitude of 1000 km. By what percentage must it decrease its speed so as to just graze the moon’s surface one-half period later?
While visiting Planet Physics, you toss a rock straight up at 11 m/s and catch it 2.5 s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet’s radius every
A satellite in a circular orbit of radius r has period T. A satellite in a nearby orbit with radius r + Δr, where Δr << r, has the very slightly different period T + ΔT.a. Show that ΔT/T =
Two Jupiter-size planets are released from rest 1.0 × 1011 m apart. What are their speeds as they crash together?
a. Write a realistic problem for which this is the correct equation(s).b. Draw a pictorial representation.c. Finish the solution of the problem. {(100 kg)v? (6.67 × 10-1" Nm²/kg²)(7.36 × 10²²
a. Write a realistic problem for which this is the correct equation(s).b. Draw a pictorial representation.c. Finish the solution of the problem.
a. Write a realistic problem for which this is the correct equation(s).b. Draw a pictorial representation.c. Finish the solution of the problem.
A 55,000 kg space capsule is in a 28,000-km-diameter circular orbit around the moon. A brief but intense firing of its engine in the forward direction suddenly decreases its speed by 50%. This causes
Comets move around the sun in very elliptical orbits. At its closet approach, in 1986, Comet Halley was 8.79 × 107 km from the sun and moving with a speed of 54.6 km/s. What was the comet’s speed
Three stars, each with the mass of our sun, form an equilateral triangle with sides 1.0 × 1012 m long. (This triangle would just about fit within the orbit of Jupiter.) The triangle has to rotate,
The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0 × 108 m/s. Astronomers have determined that
Large stars can explode as they finish burning their nuclear fuel, causing a supernova. The explosion blows away the outer layers of the star. According to Newton’s third law, the forces that push
Figure 13.17 showed a graph of log T versus log r for the planetary data given in Table 13.2. Such a graph is called a log-log graph.The scales in Figure 13.17 are logarithmic, not linear, meaning
FIGURE P13.57 shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radius r, but are always at opposite ends of a diameter. Find an exact expression for the
A satellite orbiting the earth is directly over a point on the equator at 12:00 midnight every two days. It is not over that point at any time in between.What is the radius of the satellite’s orbit?
In 2014, the European Space Agency placed a satellite in orbit around comet 67P/Churyumov-Gerasimenko and then landed a probe on the surface. The actual orbit was elliptical, but we’ll approximate
NASA would like to place a satellite in orbit around the moon such that the satellite always remains in the same position over the lunar surface. What is the satellite’s altitude?
How much energy would be required to move the earth into a circular orbit with a radius 1.0 km larger than its current radius?
The 75,000 kg space shuttle used to fly in a 250-km-high circular orbit. It needed to reach a 610-km-high circular orbit to service the Hubble Space Telescope. How much energy was required to boost
A 4000 kg lunar lander is in orbit 50 km above the surface of the moon. It needs to move out to a 300-km-high orbit in order to link up with the mother ship that will take the astronauts home.How
The two stars in a binary star system have masses 2.0 × 1030 kg and 6.0 × 1030 kg. They are separated by 2.0 × 1012 m. What area. The system’s rotation period, in years?b. The speed of each star?
A starship is circling a distant planet of radius R. The astronauts find that the free-fall acceleration at their altitude is half the value at the planet’s surface. How far above the surface are
Two spherical asteroids have the same radius R. Asteroid 1 has mass M and asteroid 2 has mass 2M. The two asteroids are released from rest with distance 10R between their centers. What is the speed
A rogue band of colonists on the moon declares war and prepares to use a catapult to launch large boulders at the earth.Assume that the boulders are launched from the point on the moon nearest the
Suppose that on earth you can jump straight up a distance of 45 cm. Asteroids are made of material with mass density 2800 kg/m3.What is the maximum diameter of a spherical asteroid from which you
An astronaut circling the earth at an altitude of 400 km is horrified to discover that a cloud of space debris is moving in the exact same orbit as his spacecraft, but in the opposite direction. The
The unexplored planet Alpha Centauri III has a radius of 7.0 × 106 m. A visiting astronaut drops a rock, from rest, into a 100 m deep crevasse. She records that it takes 6.0 s for the rock to reach
A projectile is shot straight up from the earth’s surface at a speed of 10,000 km/h. How high does it go?
An object of mass m is dropped from height h above a planet of mass M and radius R. Find an expression for the object’s speed as it hits the ground.
A rogue black hole with a mass 12 times the mass of the sun drifts into the solar system on a collision course with earth. How far is the black hole from the center of the earth when objects on the
Two 100 kg lead spheres are suspended from 100-m-long massless cables. The tops of the cables have been carefully anchored exactly 1 m apart. By how much is the distance between the centers of the
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