Ablow-back device for a diameter d = 0.22 (in) under p = 24000 [lb/in? ) pressure connects a breech block with a mass m = 1/2 (slug/32.2] to the origin, where x = 0, by a spring, which exerts a force of 3 (lb) when the breech block is moved back by 1.5 in), so that the spring constant is k=3/1.5 lb/in. friction is so small that the measuring instruments at hand do not detect any friction (3.1) find a formula for the force on the breech block in terms of pressure, diameter, and spring. (3.2) find an algebraic formula for the acceleration x(t) of the breech block at time t, for 0 0 when x(ti) = 0. (when is the breech block back at 0? )

An engineer designs a roller coaster so that a car travels horizontally for 152 ft, then climbs 137 ft at an angle of 34.0° above the horizontal. it then moves 137 ft at an angle of 48.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

Determine the maximum r-value of the polar equation r =3+3 cos 0

To understand the electric potential and electric field of a point charge in three dimensions consider a positive point charge q, located at the origin of three-dimensional space. throughout this problem, use k in place of 14? ? 0. part adue to symmetry, the electric field of a point charge at the origin must point from the origin.answer in one word.part bfind e(r), the magnitude of the electric field at distance r from the point charge q.express your answer in terms of r, k, and q. part cfind v(r), the electric potential at distance rfrom the point charge q.express your answer in terms of r, k, and q part dwhich of the following is the correct relationship between the magnitude of a radial electric field and its associated electric potential ? more than one answer may be correct for the particular case of a point charge at the origin, but you should choose the correct general relationship. a)e(r)=dv(r)drb)e(r)=v(r)rc)e(r)=? dv(r)drd)e(r)=? v(r)r