
(a)
The length measured in the rest frame of the particle, if the length of the field between goal lines in the earth frame is
(a)

Answer to Problem 15P
The length measured in the rest frame of the particle is
Explanation of Solution
Since the length of the field between the goal lines in the rest frame of earth is
Write the expression for the length of field between the goal lines as measured in the rest frame of particle.
Here,
Write the expression for the Lorentz factor.
Here,
Substitute
Conclusion:
Substitute
Therefore, the length measured in the rest frame of the particle is
(b)
The time the particle takes to go from one goal line to the other according to Earth observers.
(b)

Answer to Problem 15P
The time the particle takes to go from one goal line to the other according to Earth observers is
Explanation of Solution
The speed of the particle is constant with respect to earth. Thus, the time can be found using the equation
Write the expression for the time taken by the particle to move from one goal line to another relative to earth observer.
Substitute
Conclusion:
Substitute
Therefore, the time the particle takes to go from one goal line to the other with respect to Earth observers is
(c)
The time the particle takes to go from one goal line to the other in the rest frame of the particle.
(c)

Answer to Problem 15P
The time the particle takes to go from one goal line to the other in the rest frame of the particle is
Explanation of Solution
In rest frame of the particle, the distance travelled is
Write the expression for the time required to travel between goal lines in the rest frame of the particle.
Here,
Conclusion:
Substitute
Substitute
Therefore, the time the particle takes to go from one goal line to the other with respect to rest frame of the particle is
Want to see more full solutions like this?
Chapter 26 Solutions
Physics
- Jack Sparrow and his crew snuck up on their enemies by submerging an upturned wooden rowboat and breathing in an air pocket in the upside-down boat's cavity. What stupidly large force would be needed to hold such a boat underwater? The total volume of the wood is 0.0686 m3 and the density of the boat is 380. kg/m3. It will hold 5.28 m3 of air which has a density of 1.20 kg/m3. The density of water is 1000. kg/m3.arrow_forwardA high-speed lifting mechanism supports an 881 kg object with a steel cable that is 22.0 m long and 4.00 cm^2 in cross-sectional area. Young's modulus for steel is 20.0 ⋅10^10 Pa. The elongation of the cable is 2.377x10^-3 m. By what amount does the cable increase in length if the object is accelerated upwards at a rate of 3.11 m/s2?arrow_forwardLet us assume you are lifting out a 179 lb sheep. The density of the air around the balloon is 1.23 kg/m3 and the density of the air inside the balloon is 0.946 kg/m3. If the sheep accelerates upwards at 4.84 m/s2, what is the volume of the balloon? 1 kg = 2.20 lbsarrow_forward
- Air streams past a small airplane's wings such that speed is 50 m/s over the top surface and 30m/s past the bottom. If the plane has a wing of 9m^2. Ignoring the small height difference find 1.The pressure difference between the top and bottom of the plane's wings. 2. What would be the gravitational pull on the plane assuming the plane is moving horizontally. .arrow_forwardDraw a right-handed 3D Cartesian coordinate system (= x, y and z axes). Show a vector A with tail in the origin and sticking out in the positive x, y and z directions. Show the angles between A and the positive x, y and z axes, and call these angles α₁, α₂ and α3 Prove that Ax Acos α₁ Ay = Acos α₂ A₂- Acos α3arrow_forwardsolve for Voarrow_forward
- Draw a third quadrant vector C. (remember that boldface characters represent vector quantities). Show the standard angle 0 for this vector (= angle that C makes with the positive x- axis). Also show the angle that C makes with the negative y-axis: call the latter angle 8. Finally, show the smallest angles that C makes with the positive x-axis and the positive y-axis: call these angles p1 and p2, repectively. a) Prove the following formulas for the components of C involving the standard angle (hint: start with the formulas for the components based on the angle & and then use (look up if necessary) co-function identities linking cosine and sine of 8 to sine and cosine of 0 since 8 = 3π/2-8 (this will switch cosine and sine around and eliminate - signs as well)) - C=Ccose C₁=Csine b) Prove the following formulas for the components of C: C=Ccosp1 C=Ccosp2arrow_forwardNotation matters when working with vectors! In particular, it is important to distinguish between the vector itself (A) and its magnitude (A). Illustrate in four separate sketches that each of the following statements is possible: a) both R = A + B and R=A+B are correct b) R = A + B is correct, but R=A+B is incorrect c) R = A + B is incorrect, but R=A+B is correct d) both R = A + B and R=A+B are incorrectarrow_forwardYou know from your math courses that an infinitesimal segment of a circular arc can be considered as a straight line segment. Imagine that you cover a full circle in, say, the clockwise direction, with infinitesimal displacement vectors dr. Then evaluate fdr and fdr (the circle symbol on the integral just reminds us that we have to go around the full circle).arrow_forward
- When 1.00 g of water at 100˚C changes from the liquid to the gas phase at atmospheric pressure, its change in volume is: 1.67 x 10^-3 How much heat is added to vaporize the water? How much work is done by the water against the atmosphere in expansion? What is the change in the internal energy of the water?arrow_forward1 m3 of pure water is heated from 10˚C to 120˚C at a constant pressure of 1 atm. The volume of the water is contained, but allowed to expand as needed remaining at 1 atm. Calculate the change in enthalpy of the water. You are provided with the following information at the conditions of 1 atm: The density of pure water between 10˚C and 100˚C: 1000kh/m^3 The heat capacity of water: 4.18 kj/kgK Enthalpy required to convert liquid water to gas (enthalpy of vaporization): 2260 kj/kg The heat capacity of steam: 1.7kj/kgk Is the reaction endothermic or exothermic? Why?arrow_forwardWhen a dilute gas expands quasi-statically from 0.50 to 4.0 L, it does 250 J of work. Assuming that the gas temperature remains constant at 300 K. What is the change in the internal energy of the gas? How much heat is absorbed by the gas in this process?arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON





