A point-like particle is moving along a straight line. Alice and Bob are two observers and...

   

Transcribed Image Text:

A point-like particle is moving along a straight line. Alice and Bob are two observers and they respectively measure the motion of the particle in two reference frames called "xAy" and "XBY" with the Cartesian coordinates in the figure (the origins A and B of the two reference frames overlap; the angle between x and X, as well as the angle between y and Y, is 0<2<90 degrees; the figure offers a possible visualization on how to determine the components of a generic vector r). Alice and Bob stand at the origins A and B. Along the x axis there is a point P at distance d from A. Alice observes that the point-like particle is moving with constant acceleration along the x axis with speed SÅ at A and speed så at P, with SA < SP. y! X X X 1) Determine the components of the velocities VA and vB measured by Alice (i.e. in Alice's Cartesian reference frame) 2) Determine the components of VA and vB measured by Bob (i.e. in Bob's Cartesian reference frame) 3) Determine the magnitude of the acceleration measured by Alice 4) Determine the magnitude of the acceleration measured by Bob 5) Determine the components of the acceleration measured by Alice, and those measured by Bob. 6) Alice (correctly) calculates the time required to the particle to go from A to P by using the data in her reference frame. What does she get? 7) Explain to Bob how to calculate the time required to the particle to go from A to P by means of his data. How much is the time resulting from this calculation? 8) Calculate the particle speed measured by Alice and the particle speed measured by Bob at a generic time fixing t=0 when the particle is on A. 9) You may remember that under a change of reference system: a scalar quantity does NOT change; the overall vector does NOT change; the vector components do change. Compare your answers to Q6 and Q7: do they confirm the previous statement? And now compare the particle speed measured by Alice and Bob: why is the speed also called "scalar velocity" in some textbooks? 10) Use your conclusions to Q9 to infer without any calculation the speed needed to move from A to P measured by the observer named Anti-Alice who is taking data using the reference frame X'Ay which is the same of Alice but with the x' axis oriented in the opposite direction of x. In addition, determine the components of the velocity in A measured by Alice and and Anti-Alice, and check whether such a velocity behaves as a scalar or a vector. 11) Use your answers to Q5 and Q6 to determine the acceleration and time measured by Alice in the case that sA =5 m/s, sP=10 m/s and d=12.5 m. A point-like particle is moving along a straight line. Alice and Bob are two observers and they respectively measure the motion of the particle in two reference frames called "xAy" and "XBY" with the Cartesian coordinates in the figure (the origins A and B of the two reference frames overlap; the angle between x and X, as well as the angle between y and Y, is 0<2<90 degrees; the figure offers a possible visualization on how to determine the components of a generic vector r). Alice and Bob stand at the origins A and B. Along the x axis there is a point P at distance d from A. Alice observes that the point-like particle is moving with constant acceleration along the x axis with speed SÅ at A and speed så at P, with SA < SP. y! X X X 1) Determine the components of the velocities VA and vB measured by Alice (i.e. in Alice's Cartesian reference frame) 2) Determine the components of VA and vB measured by Bob (i.e. in Bob's Cartesian reference frame) 3) Determine the magnitude of the acceleration measured by Alice 4) Determine the magnitude of the acceleration measured by Bob 5) Determine the components of the acceleration measured by Alice, and those measured by Bob. 6) Alice (correctly) calculates the time required to the particle to go from A to P by using the data in her reference frame. What does she get? 7) Explain to Bob how to calculate the time required to the particle to go from A to P by means of his data. How much is the time resulting from this calculation? 8) Calculate the particle speed measured by Alice and the particle speed measured by Bob at a generic time fixing t=0 when the particle is on A. 9) You may remember that under a change of reference system: a scalar quantity does NOT change; the overall vector does NOT change; the vector components do change. Compare your answers to Q6 and Q7: do they confirm the previous statement? And now compare the particle speed measured by Alice and Bob: why is the speed also called "scalar velocity" in some textbooks? 10) Use your conclusions to Q9 to infer without any calculation the speed needed to move from A to P measured by the observer named Anti-Alice who is taking data using the reference frame X'Ay which is the same of Alice but with the x' axis oriented in the opposite direction of x. In addition, determine the components of the velocity in A measured by Alice and and Anti-Alice, and check whether such a velocity behaves as a scalar or a vector. 11) Use your answers to Q5 and Q6 to determine the acceleration and time measured by Alice in the case that sA =5 m/s, sP=10 m/s and d=12.5 m.

Answer rating: 100% (QA)

9 Comparing Q 6 and Q 7 Alices and Bobs times are different ... View the full answer