A pendulum is in a spacecraft to measure acceleration during lift off. Before the launch, its period
is 6.5 X 10-3 s. At a point during lift off, its period is 3.1
X 10-3 s. What is the acceleration at this point?

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

The force will determine the acceleration.

An electron and a proton have the same kinetic energy upon entering a region of constant magnetic field and their velocity vectors are perpendicular to the magnetic field. suppose the magnetic field is strong enough to allow the particles to circle in the field. note: you'll need to look up the masses for an electron and proton. 1) what is the ratio of the radii of their circular paths rp/re?