Time Interval
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
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Exercise:
A Klingon spaceship travels at beaO of the speed of light with respect to the Earth. The Klingon crew measures a time erval of dtO between two events on Earth. abcliste abc Calculate the time between the two events for an observer on the Earth. abc Calculate the time erval they would measure between the same two events if they travelled at bebO of the speed of light. abcliste
Solution:
abcliste abc The time erval for the observers on the spaceship is the dilated time: Delta t gamma Deltatau It follow for the proper time as measured by an observer on Earth Deltatau fracDelta tgamma taF dt times sqrt-bea^ resulttaP abc The time ervals between the two events can be expressed as Delta t_ gamma_Deltatau fracDeltatausqrt-beta_^ where the index refers to the first and the index to the second situation. It follows for the ratio between the two time ervals fracDelta t_Delta t_ sqrtfrac-beta_^-beta_^ The time erval measured in the second sitution is Delta t_ dtbF dt times sqrtfrac-bea^-beb^ resultdtbP abcliste
A Klingon spaceship travels at beaO of the speed of light with respect to the Earth. The Klingon crew measures a time erval of dtO between two events on Earth. abcliste abc Calculate the time between the two events for an observer on the Earth. abc Calculate the time erval they would measure between the same two events if they travelled at bebO of the speed of light. abcliste
Solution:
abcliste abc The time erval for the observers on the spaceship is the dilated time: Delta t gamma Deltatau It follow for the proper time as measured by an observer on Earth Deltatau fracDelta tgamma taF dt times sqrt-bea^ resulttaP abc The time ervals between the two events can be expressed as Delta t_ gamma_Deltatau fracDeltatausqrt-beta_^ where the index refers to the first and the index to the second situation. It follows for the ratio between the two time ervals fracDelta t_Delta t_ sqrtfrac-beta_^-beta_^ The time erval measured in the second sitution is Delta t_ dtbF dt times sqrtfrac-bea^-beb^ resultdtbP abcliste
Meta Information
Exercise:
A Klingon spaceship travels at beaO of the speed of light with respect to the Earth. The Klingon crew measures a time erval of dtO between two events on Earth. abcliste abc Calculate the time between the two events for an observer on the Earth. abc Calculate the time erval they would measure between the same two events if they travelled at bebO of the speed of light. abcliste
Solution:
abcliste abc The time erval for the observers on the spaceship is the dilated time: Delta t gamma Deltatau It follow for the proper time as measured by an observer on Earth Deltatau fracDelta tgamma taF dt times sqrt-bea^ resulttaP abc The time ervals between the two events can be expressed as Delta t_ gamma_Deltatau fracDeltatausqrt-beta_^ where the index refers to the first and the index to the second situation. It follows for the ratio between the two time ervals fracDelta t_Delta t_ sqrtfrac-beta_^-beta_^ The time erval measured in the second sitution is Delta t_ dtbF dt times sqrtfrac-bea^-beb^ resultdtbP abcliste
A Klingon spaceship travels at beaO of the speed of light with respect to the Earth. The Klingon crew measures a time erval of dtO between two events on Earth. abcliste abc Calculate the time between the two events for an observer on the Earth. abc Calculate the time erval they would measure between the same two events if they travelled at bebO of the speed of light. abcliste
Solution:
abcliste abc The time erval for the observers on the spaceship is the dilated time: Delta t gamma Deltatau It follow for the proper time as measured by an observer on Earth Deltatau fracDelta tgamma taF dt times sqrt-bea^ resulttaP abc The time ervals between the two events can be expressed as Delta t_ gamma_Deltatau fracDeltatausqrt-beta_^ where the index refers to the first and the index to the second situation. It follows for the ratio between the two time ervals fracDelta t_Delta t_ sqrtfrac-beta_^-beta_^ The time erval measured in the second sitution is Delta t_ dtbF dt times sqrtfrac-bea^-beb^ resultdtbP abcliste
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