Two children push on opposite sides of a door during play. both push horizontally and perpendicular to the door. one child pushes with a force of 185 n at a distance of 0.500 m from the hinges, and the second pushes at a distance of 0.450 m. what force (in n) must the second exert to keep the door from moving? assume friction is negligible.

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 ?

In a vernier instrument the main scale is in 1/2 mm divisions .vernier is made by redividing 19 such divisions into 20 equal parts. calculate the least count of the instrument.

Henry, whose mass is 95 kg, stands on a bathroom scale in an elevator. the scale reads 830 n for the first 2.4 s after the elevator starts moving, then 930 n for the next 2.4 s. part a what is the elevator's speed 4.8 s after starting? express your answer with the appropriate units.