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upward shot in air assume we shoot a particle with mass m upward with initial velocity v0 air exerts a drag force -mkv
arc length element find the square of the element of arc length ds in cylindrical and spherical coordinate systems
cylindrical coordinate system and a helix a particle is moving on a helix of radius r and pitch a at a constant speed
a wounding cable figure 138 illustrates a turning cone and wounding cable that supports a hanging box if the cone is
natural coordinate system and important planes consider the space curvea find the equations of osculating perpendicular
moving on a given curve a particle is moving on a curve y f x such that the x-component of the velocity of the
frame dependent and frame independent a vector function of scalar variables is a frame-dependent quantity is a vector
angular momentum of a particle a particle p with mass m is moving such that its position vector has the components x
integrals of a spherical pendulum a spherical pendulum with mass m and length l is shown in figure 260 the angles and
second guldin theorem the volume of a solid generated by the revolution of a plane region about an axis lying in the
attraction of a spherical shell determine the gravitational potential of a spherical shell with inner radius r1 and
attraction of a sphere consider a uniform sphere with radius r and mass m as shown in figure 259 determine the
a moving load on a barge a load m 2000 kg is on the smooth deck of a barge of mass m 8000 kg the load is pulled with
double penduluma using a free-body diagram and the newton method determine the equations of motion of the double
conservative force check determine whether each of the following force fields f is conservative and determine the
impact of a particle in a circle a particle m is fired with initial velocity v0 from the intersection of a circle with
a particle in a cone a particle of mass m slides without friction inside an upside-down conical shell of semi vertical
moment of momentum determine the moment of momentum of m in figure 267 the mass m is attached to a mass less rod with
impact and motion figure 268 illustrates a carriage with mass m that has an oblique surface the carriage can move
projectile impact in figure 274 the particle b is released from rest at time t 0 the particle a is thrown after t 1s
motion in a fluid when a heavy body b of density rhob and volume v is immersed in a fluid of density rhof the weight w
cylindrical-spherical system relationship assume the position velocity and acceleration of a particle are given in a
covariant and contravariant componentsa express the scalar product of two vectors in terms of their covariant and
base vectors of cylindrical coordinate system consider the cylindrical coordinate systema determine the principal base
a homeowner paid 4000 for a solar water heater and received a tax credit of 30 the system saves 450 per year find a