Use a space-time diagram to argue the following: (a) show that for two spacetime events separated by an arbitrary timelike intervals one can always (b) show that for two spacetime events separated by an arbitrary spacelike intervals one can always (c) in class, we argued that the straight line between two timelike separated spacetime points is the find a frame where they occur at the same place. find a frame where they occur simultaneously. longest space-time interval between them. is that true for spacelike separated points? explain. (you might want to consider the various paths between the origin and a simultaneous event in some frame).

Your pendulum clock which advances 1.0 s for every complete oscillation of the pendulum is running perfectly on earth at a site where the magnitude of the acceleration due to gravity is 9.80 m/s2. you send the clock to a location on the moon where the magnitude of the acceleration due to gravity is 1.65 m/s2.

When applying kirchhoff's rules, one of the essential steps is to mark each resistor with plus and minus signs to label how the electric potential changes from one end of the resistor to the other. the circuit in the drawing contains four resistors, each marked with the associated plus and minus signs. however, one resistor is marked incorrectly. which one is it?

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)