contestada

Consider a particle of mass m acted on by a force F in an inertial frame.Prove that dK=F× ( d×r), where d×r is the change in position vector of a particle in a time d×t, and d×K is the corresponding change in the kinetic energy K=1÷2(mv²)

Respuesta :

onyebuchinnaji

From the change in the kinetic energy of the particle, the force that acted on the particle from an inertial frame is proved as F(dr) = dK.

Kinetic energy of the particle

The kinetic energy of the particle is given as;

K.E = ¹/₂mv²

dK/dv = mv

m = dK/vdv

Force on the particle

The force on the particle is given by Newton's second law of motion;

F = ma

a = dv/dt

F = m(dv/dt)

F = (dK/vdv) (dv/dt)

F = dK/vdt

F(vdt) = dK

v = dr/dt

F (dr/dt) x (dt) = dK

F(dr) = dK, proved

Learn more about kinetic energy here: https://brainly.com/question/25959744

Otras preguntas