In a lab frame of reference, an observer finds Newton’s second law is valid in the form
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Modern Physics
- According to special relativity, a particle of rest mass m0 accelerated in one dimension by a force F obeys the equation of motion dp/dt = F. Here p = m0v/(1 –v2/c2)1/2 is the relativistic momentum, which reduces to m0v for v2/c2 << 1. (a) For the case of constant F and initial conditions x(0) = 0 = v(0), find x(t) and v(t). (b) Sketch your result for v(t). (c) Suppose that F/m0 = 10 m/s2 ( ≈ g on Earth). How much time is required for the particle to reach half the speed of light and of 99% the speed of light?arrow_forwardAssertion (A): Any choice of an inertial frame is not acceptable in Newtonian Dynamics. Reason (R): The laws of motion are not equally valid in all such frames. (a) Both A and R are true, and R is the correct explanation of A (b) Both A and R are true, but R is not the correct explanation of A. (c) Both A and R are false. (d) A is false but R is true.arrow_forwardPlease answer this NEATLY, COMPLETELY, and CORRECTLY for an UPVOTE. A particle moves along the x-axis with an initial velocity of 30.55 fps (NOTE: fps means ft/s or feet per second, NOT “frame” per second) at the origin. For the first 5 seconds, it has no acceleration, and afterwards it is acted on by an opposing force which gives it a decreasing velocity until the particle stops at t = 10 s. a. Draw the a–t and s–t graphs for the motion. b. Calculate the velocity of the particle at t = 8 sc. Find the distance traveled by the particle at t = 10 s. The parabola at 5 s ≤ t ≤ 10 s has its vertex at ? = 10 s.arrow_forward
- Please answer this NEATLY, COMPLETELY, and CORRECTLY for an UPVOTE. A particle moves along the x-axis with an initial velocity of 30.55 fps (NOTE: fps means ft/s or feet per second, NOT “frame” per second) at the origin. For the first 5 seconds, it has no acceleration, and afterwards it is acted on by an opposing force which gives it adecreasing velocity until the particle stops at t = 10 s.a. Draw the a–t and s–t graphs for the motion.b. Calculate the velocity of the particle at t = 8 sc. Find the distance traveled by the particle at t = 10 s.The parabola at 5 s ≤ t ≤ 10 s has its vertex at t = 10 s.arrow_forwardThe coordinate axes of the reference frame S' remain parallel to those of S, as S' moves away from S at a constant velocity vs = (7.0î + 8.oĵ + 6.0k) m/s. (Express your answers in vector form. Use V the following as necessary: t. Assume all positions are in meters, velocities are in m/s, accelerations are in m/s2, and t is in seconds. Do not include units in your answers.) (a) If at time t = 0 the origins coincide, what is the position of the origin O' in the S frame as a function of time? O'(t) = (b) How is particle position for r(t) and r'(t), as measured in S and S', respectively, related? r(t) = r'(t) + (c) What is the relationship between particle velocities v(t) and v'(t)? v(t) = v'(t) + (d) How are accelerations a(t) and a'(t) related? a(t) = a'(t) +arrow_forwardThe velocity of a particle in reference frame A is (2.0i ^ + 3.0j ^ ) m/s. The velocity of reference frame A with respect to reference frame B is 4.0k ^ m/s, and the velocity of reference frame B with respect to C is 2.0j ^ m/s. What is the velocity of the particle in reference frame C?arrow_forward
- An accelerated frame is a non-inertial frame A. true B. falsearrow_forwardAn experimentalist in a laboratory finds that a particle has a helical path. The position of this particle in the laboratory frme is given by r(t)= R cos(wt)i + R sin(wt)j + vztk R,vz, and w are constants. A moving frame has velocity (Vm)L= vzk relative to the laboratory frame. In vector form: A)What is the path of the partical in the moving frame? B)what is the velocity of the particle as a function of time relative to the moving frame? C)What is the acceleration of the particle in each frame? D)How should the accelerartion in each frame be realted?Does your answer to part c make sense?arrow_forwardA 2.75 kg ball is dropped straight down on a concrete floor and bounces straight up. At an instant when the ball is in contact with the floor, its acceleration is 34.0 m·s−2 upward. At that instant, calculate the force on the ball that is exerted by the floor.arrow_forward
- Ex. 4: A body of mass 100 gm is suspended from a light spring which stretches it by 10 cm. Find the force constant of the spring.arrow_forwardAn interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 74.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 19.4 years as measured in a rest frame. Note that radio waves travel at the speed of light and fill the space between the probe and Earth at the time the battery fails. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (Ignore the delay between the time the battery fails and the time mission control stops receiving the signal.) yr (b) How far is the probe from Earth when its batteries fail as measured by mission control? (Ignore the delay between the time the battery fails and the time mission control stops receiving the signal.) ly (c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail? ly (d) For what total time…arrow_forwardThe homogeneous transformation is used the express a frame relative to an other frame. Select one: True Falsearrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning