By explicitly considering the trajectories of two particles moving in two dimensions with respect to two...
By explicitly considering the trajectories of two particles moving in two dimensions with respect to two different frames of reference, show that the relative velocity between the particles does not depend on the choice of reference frame.
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By explicitly considering the trajectories of two particles
moving in two dimensions with respect to two...
3) Two particles fly apart in opposite directions in a laboratory. Particle A travels to the left...
3) Two particles fly apart in opposite directions in a laboratory. Particle A travels to the left at speed 0.06c, and particle B travels to the right at speed 0.09c (both speeds are relative to the laboratory). We wish to calculate the relative velocity of particles A and B using the Galilean transformation. a) Using a figure, show which object in this scenario defines the Home frame and which object defines the Other frame. [Hint: Be careful - in the...
Choose all of the quantities that are different if you measure them in each of two...
Choose all of the quantities that are different if you measure them in each of two different inertial reference frames (inertial reference frames that are moving relative to one another) a) time intervals b) distance intervals c) spacetime intervals d) the relative velocity of the other frame
The trajectories of two particles moving in R3 are described by 10) = (a sin(e, sin(),...
The trajectories of two particles moving in R3 are described by 10) = (a sin(e, sin(), 5 coses) and r2(t) = (sin(2t), 2 sin?(t), 2 cos(t)) for tER. a) Show that one of these trajectories lies on a sphere S centered at the origin in R3, and that the other one is contained in a plane. In what follows, we denote by r(t) the position of the particle that lies in a sphere. b) Prove that r(t) is orthogonal to...
1. Consider two frames S and S' where S' is moving with velocity vector (0.9c,0,0) with...
1. Consider two frames S and S' where S' is moving with velocity vector (0.9c,0,0) with respect to S. At time t-t':0 the origins of the two frames coincide. At time t-2.2x10-6s a muon decays at coordinates (100,0.8, 1.0) meters in the frame S. (a) At what time and at what coordinates, does the muon decay in frame S'? (b) Starting with the coordinates derived in part (a) transform them back into frame S and verify that the original decay...
Time Dilation Time Dilation is a relativistic effect where time measured in two reference frames with...
Time Dilation Time Dilation is a relativistic effect where time measured in two reference frames with relative motion is different, even when the clocks in both reference frames are initially synchronized. Clocks are synchronized when the same time is measured when their inertial reference frames are at rest relative to one another (meaning there is no relative velocity). When t0, the clocks in the two reference frames are synchronized at the origin. The Proper Time (To) is the time difference...
5. (25 marks) Particles A and B are moving rectilinearly along the same line. At some point, they...
5. (25 marks) Particles A and B are moving rectilinearly along the same line. At some point, they collide with each other. Their masses and velocities before the collision are shown in the graph. Assume no external force or mass exchange. Determine: (1) The velocity of the center of mass (G) of the system consisting of A and B, and the velocities of A and B in the center-of-mass frame of reference before the collision. (2) The linear momentum and...
6. Four electrons are moving at the same velocity with respect to a magnetic field, but...
6. Four electrons are moving at the same velocity with respect to a magnetic field, but they are moving at different angles relative to the direction of the magnetic field. Upon which electron does the magnetic field exert the least force? (A)0° (B) 30° (C) 60° (D) 90
The drawing shows three particles that are moving with different velocities. Two of the particles have...
The drawing shows three particles that are moving with different velocities. Two of the particles have mass m, and the third has a mass 2m. The third particle has a velocity of V3 = +5.0 m/s. At the instant shown, the center of mass (cm) of the three particles is at the coordinate origin. What is the velocity Vem (magnitude and direction) of the center of mass? +4.0 m's -8.0 m/s cm vam = ? V3 Velocity of center of...
The figure shows six frames from the motion diagram of two moving cars. A and B...
The figure shows six frames from the motion diagram of two moving cars. A and B Choose an appropriate coordinate axis We'll use the same axis for both cars Draw both a position vs time graph and a velocity vs time graph Show both cars on each graph, labeling them A and B Also label the time frames on the time axis of both graphs Do the two cars ever have the same position at one instant of time? If...
Which of the following inertial reference frames are proper frames for the two events listed? Choose...
Which of the following inertial reference frames are proper frames for the two events listed? Choose all that apply. RED FRAME: Event A happened at a different place than event B. ORANGE FRAME: Event C happened at (-7 m, 3 m, 4 m) and event D happened at (-7 m, 3 m, 5 m). YELLOW FRAME: The distance between where event E occurred and where event F occurred was 0 m. GREEN FRAME: A rocket was traveling at a constant...
3) Two particles fly apart in opposite directions in a laboratory. Particle A travels to the left at speed 0.06c, and particle B travels to the right at speed 0.09c (both speeds are relative to the laboratory). We wish to calculate the relative velocity of particles A and B using the Galilean transformation. a) Using a figure, show which object in this scenario defines the Home frame and which object defines the Other frame. [Hint: Be careful - in the...
The trajectories of two particles moving in R3 are described by 10) = (a sin(e, sin(), 5 coses) and r2(t) = (sin(2t), 2 sin?(t), 2 cos(t)) for tER. a) Show that one of these trajectories lies on a sphere S centered at the origin in R3, and that the other one is contained in a plane. In what follows, we denote by r(t) the position of the particle that lies in a sphere. b) Prove that r(t) is orthogonal to...
1. Consider two frames S and S' where S' is moving with velocity vector (0.9c,0,0) with respect to S. At time t-t':0 the origins of the two frames coincide. At time t-2.2x10-6s a muon decays at coordinates (100,0.8, 1.0) meters in the frame S. (a) At what time and at what coordinates, does the muon decay in frame S'? (b) Starting with the coordinates derived in part (a) transform them back into frame S and verify that the original decay...
Time Dilation Time Dilation is a relativistic effect where time measured in two reference frames with relative motion is different, even when the clocks in both reference frames are initially synchronized. Clocks are synchronized when the same time is measured when their inertial reference frames are at rest relative to one another (meaning there is no relative velocity). When t0, the clocks in the two reference frames are synchronized at the origin. The Proper Time (To) is the time difference...
5. (25 marks) Particles A and B are moving rectilinearly along the same line. At some point, they collide with each other. Their masses and velocities before the collision are shown in the graph. Assume no external force or mass exchange. Determine: (1) The velocity of the center of mass (G) of the system consisting of A and B, and the velocities of A and B in the center-of-mass frame of reference before the collision. (2) The linear momentum and...
6. Four electrons are moving at the same velocity with respect to a magnetic field, but they are moving at different angles relative to the direction of the magnetic field. Upon which electron does the magnetic field exert the least force? (A)0° (B) 30° (C) 60° (D) 90
The drawing shows three particles that are moving with different velocities. Two of the particles have mass m, and the third has a mass 2m. The third particle has a velocity of V3 = +5.0 m/s. At the instant shown, the center of mass (cm) of the three particles is at the coordinate origin. What is the velocity Vem (magnitude and direction) of the center of mass? +4.0 m's -8.0 m/s cm vam = ? V3 Velocity of center of...
The figure shows six frames from the motion diagram of two moving cars. A and B Choose an appropriate coordinate axis We'll use the same axis for both cars Draw both a position vs time graph and a velocity vs time graph Show both cars on each graph, labeling them A and B Also label the time frames on the time axis of both graphs Do the two cars ever have the same position at one instant of time? If...
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