Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 36, Problem 28P
To determine
Show that the particle moving with velocity
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(ii) Two Rockets, each 10000 cm long when they are measured at rest, move toward each other with speeds of 0.9c with respect to the earth (where c is the speed of light).
(a) How long is each Rocket as measured by the observer on the earth?
(b) Using velocity addition formula how fast is traveling each rocket as calculated by an observer on one of the rockets?
(c) How long is one rocket when measured by an observer on one of the rockets?
(e) Explain why can we write the following equation for large r
d F., 2µE
dr2
F = 0
(21)
Before we solve for F we to utilize the fact if E > 0 then the particles
will behave as if they are free (free meaning independent) (there will be
too much energy for the particles to stay together if E > 0); however we
want to interpret a situation where the particles interact with each other,
hence we are only interested in E 0, then we can
write E = -E' (ensuring E is negative because E' is positive) Now we
will rewrite equation (21) as
dF 2µE'
-F
(22)
%3D
dr2
Note that 4, E' and h are all positive constants.
3.19 Particle A, at rest, decays into particles Band C (A → B + C).
(a) Find the energy of the outgoing particles, in terms of the various masses.
Chapter 36 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 36.4 - Examine the experiment of Fig. 366 from O1s...Ch. 36.5 - What is the muons mean lifetime (Example 361) if...Ch. 36.5 - A certain atomic clock keeps perfect time on...Ch. 36.6 - Prob. 1DECh. 36.8 - Use Eqs. 367 to calculate the speed of rocket 2 in...Ch. 36.8 - A rocket is headed away from Earth at a speed of...Ch. 36.11 - A proton is traveling in an accelerator with a...Ch. 36.11 - For 1% accuracy, does an electron with K = 100 eV...Ch. 36 - You are in a windowless car in an exceptionally...Ch. 36 - You might have had the experience of being at a...
Ch. 36 - Prob. 3QCh. 36 - Does the Earth really go around the Sun? Or is it...Ch. 36 - If you were on a spaceship traveling at 0.5c away...Ch. 36 - The time dilation effect is sometimes expressed as...Ch. 36 - Does time dilation mean that time actually passes...Ch. 36 - Prob. 8QCh. 36 - If you were traveling away from Earth at speed...Ch. 36 - Do time dilation and length contraction occur at...Ch. 36 - Suppose the speed of light were infinite. What...Ch. 36 - Discuss how our everyday lives would be different...Ch. 36 - Explain how the length contraction and time...Ch. 36 - The drawing at the start of this Chapter shows the...Ch. 36 - Prob. 15QCh. 36 - Can a particle of nonzero mass attain the speed of...Ch. 36 - Prob. 17QCh. 36 - If mass is a form of energy, does this mean that a...Ch. 36 - Prob. 19QCh. 36 - Is our intuitive notion that velocities simply...Ch. 36 - (I) A spaceship passes you at a speed of 0.850c....Ch. 36 - Prob. 2PCh. 36 - (II) According to the special theory of...Ch. 36 - (II) If you were to travel to a star 135...Ch. 36 - (II) What is the speed of a pion if its average...Ch. 36 - (II) In an Earth reference frame, a star is 56...Ch. 36 - (II) Suppose you decide to travel to a star 65...Ch. 36 - (II) At what speed v will the length of a 1.00-m...Ch. 36 - (II) Escape velocity from the Earth is 11.2 km/s....Ch. 36 - (II) A friend speeds by you in her spacecraft at a...Ch. 36 - (II) At what speed do the relativistic formulas...Ch. 36 - (II) A certain star is 18.6 light-years away. How...Ch. 36 - (II) Suppose a news report stated that starship...Ch. 36 - (II) An unstable particle produced in an...Ch. 36 - (II) When it is stationary, the half-life of a...Ch. 36 - (II) In its own reference frame, a box has the...Ch. 36 - (II) When at rest, a spaceship has the form of an...Ch. 36 - (II) How fast must a pion be moving on average to...Ch. 36 - (I) An observer on Earth sees an alien vessel...Ch. 36 - (I) Suppose in Fig. 3611 that the origins of S and...Ch. 36 - (I) Repeat Problem 20 using the Lorentz...Ch. 36 - (II) In Problem 21, suppose that the person moves...Ch. 36 - (II) Two spaceships leave Earth in opposite...Ch. 36 - (II) Reference frame S moves at speed v = 0.92c in...Ch. 36 - (II) A spaceship leaves Earth traveling at 0.61c....Ch. 36 - (II) Your spaceship, traveling at 0.90c, needs to...Ch. 36 - (II) A spaceship traveling at 0.76c away from...Ch. 36 - Prob. 28PCh. 36 - (II) A stick of length 0, at rest in reference...Ch. 36 - (III) In the old West, a marshal riding on a train...Ch. 36 - (III) Two lightbulbs, A and B, are placed at rest...Ch. 36 - (III) An observer in reference frame S notes that...Ch. 36 - (III) A farm boy studying physics believes that he...Ch. 36 - (I) What is the momentum of a proton traveling at...Ch. 36 - Prob. 35PCh. 36 - (II) A particle of mass m travels at a speed v =...Ch. 36 - (II) An unstable particle is at rest and suddenly...Ch. 36 - Prob. 38PCh. 36 - Prob. 39PCh. 36 - Prob. 40PCh. 36 - (I) The total annual energy consumption in the...Ch. 36 - Prob. 42PCh. 36 - Prob. 43PCh. 36 - Prob. 44PCh. 36 - (II) How much energy can be obtained front...Ch. 36 - (II) To accelerate a particle of mass m from rest...Ch. 36 - Prob. 47PCh. 36 - Prob. 48PCh. 36 - Prob. 49PCh. 36 - Prob. 50PCh. 36 - (II) What is the speed of a proton accelerated by...Ch. 36 - (II) Two identical particles of mass m approach...Ch. 36 - (II) What is the speed of an electron just before...Ch. 36 - Prob. 55PCh. 36 - Prob. 56PCh. 36 - (II) Suppose a spacecraft of mass 17,000 kg is...Ch. 36 - Prob. 58PCh. 36 - Prob. 59PCh. 36 - Prob. 60PCh. 36 - Prob. 61PCh. 36 - Prob. 62PCh. 36 - (III) (a) In reference frame S, a particle has...Ch. 36 - Prob. 64PCh. 36 - (II) A spaceship moving toward Earth at 0.70c...Ch. 36 - Prob. 66PCh. 36 - (III) A radar speed gun emits microwaves of...Ch. 36 - (III) A certain atom emits light of frequency f0...Ch. 36 - An atomic clock is taken to the North Pole, while...Ch. 36 - A spaceship in distress sends out two escape pods...Ch. 36 - An airplane travels 1300 km/h around the Earth in...Ch. 36 - The nearest star to Earth is Proxima Centauri, 4.3...Ch. 36 - Prob. 73GPCh. 36 - A healthy astronauts heart rate is 60 beats/min....Ch. 36 - A spacecraft (reference frame S) moves past Earth...Ch. 36 - Rocket A passes Earth at a speed of 0.65c. At the...Ch. 36 - (a) What is the speed v of an electron whose...Ch. 36 - As a rough rule, anything traveling faster than...Ch. 36 - Prob. 79GPCh. 36 - Prob. 80GPCh. 36 - Prob. 81GPCh. 36 - A free neutron can decay into a proton, an...Ch. 36 - The Sun radiates energy at a rate of about 4 1026...Ch. 36 - An unknown particle is measured to have a negative...Ch. 36 - How much energy would be required to break a...Ch. 36 - Prob. 86GPCh. 36 - Two protons, each having a speed of 0.985c in the...Ch. 36 - When two moles of hydrogen molecules (H2) and one...Ch. 36 - The fictional starship Enterprise obtains its...Ch. 36 - A spaceship and its occupants have a total mass of...Ch. 36 - In a nuclear reaction two identical particles are...Ch. 36 - A 32,000-kg spaceship is to travel to the vicinity...Ch. 36 - Suppose a 14,500-kg spaceship left Earth at a...Ch. 36 - A pi meson of mass m decays at rest into a muon...Ch. 36 - Astronomers measure the distance to a particular...Ch. 36 - A 1.88-kg mass oscillates on the end of a spring...Ch. 36 - Show that the spacetime interval, (c t)2 (x)2, is...Ch. 36 - Prob. 98GPCh. 36 - (II) For a 1.0-kg mass, make a plot of the kinetic...
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- A particle is moving at a speed less than c/2. If the speed of the particle is doubled, what happens to its momentum?arrow_forwardA spacecraft is launched from the surface of the Earth with a velocity of 0.600c at an angle of 50.0° above the horizontal, positive x-axis. Another spacecraft is moving past with a velocity of 0.700c in the negative x direction. Determine the magnitude and direction of the velocity of the first spacecraft as measured by the pilot of the second spacecraft.arrow_forwardAs seen from Earth, two spaceships A and B are approaching along perpendicular directions. If A is observed by an Earth observer to have velocity uy = 0.90c and B to have a velocity ux = +0.90c, find the speed of ship A as measured by the pilot of B.arrow_forward
- Calculate the momentum of a proton moving with a speed of (a) 0.010c, (b) 0.50c, (c) 0.90c. (d) Convert the answers of (a)(c) to MeV/c.arrow_forwardSuppose the primed and laboratory observers want to measure the length of a rod that rests on the ground horizontally in the space between the helicopter and the tower (Fig. 39.8B). To derive the length transformation L = L (Eq. 39.5), we had to assume that the positions of the two ends were determined simultaneously. What happens to the length transformation equation if both observers measure the end below the helicopter at one time t1 and the other end at a later time t2?arrow_forwardTwo spaceships approach each other, each moving with the same speed as measured by an observer on the Earth. If their relative speed is 0.70c, what is the speed of each spaceship?arrow_forward
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- Owen and Dina are at rest in frame S, which is moving at 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P9.63). Owen throws the ball to Dina at 0.800c (according to Owen), and their separation (measured in S) is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, (d) how fast is the ball moving, and (e) what time interval is required for the ball to reach Dina? Figure P9.63arrow_forwardYou measure the volume of a cube at rest to be V0. You then measure the volume of the same cube as it passes you in a direction parallel to one side of the cube. The speed of the cube is 0.980c, so 5. Is the volume you measure close to (a) V0/25, (b) V0/5, (c) V0, (d) 5V0, or (e) 25V0?arrow_forwardOwen and Dina are at rest in frame S. which is moving at 0.600c with respect to frame S. They play a game of catch while Ed. at rest in frame S, watches the action (Fig. P39.91). Owen throws the ball to Dina at 0.800c (according to Owen), and their separation (measured in S') is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, (d) how fast is the ball moving, and (e) what time interval is required for the ball to reach Dina?arrow_forward
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