Let the trajectory of the vehicle following the road be X ( t ) which is a curve in three-dimensional space.The work of the torque is calculated as dWTdt, displaystyle dWmathbf T cdot vec omega dt, where the T is the power over the instant.
Effort made in order to achieve or make something.Displaystyle Kfrac m2v2frac m2dot mathbf X cdot dot mathbf.
To be practicable and/or successful.Let the mass m move at the velocity v then the work of gravity on this mass as it moves from position r ( t 1) to r ( t 2) is given by W-int _mathbf r (t_1)mathbf r (t_2)frac GMmr3mathbf r cdot dmathbf.Work by a spring edit Forces in springs assembled in parallel Consider a spring that exerts a horizontal force F ( kx, 0, 0) that is proportional to its deflection in the x direction independent of how a body moves.
His lot would be years of back-breaking toil drudgery suggests dull and irksome labor.It is convenient to imagine this gravitational force concentrated at the center of mass of the object.Let the coordinates x i i 1,., n define these points in the moving rigid body's reference frame M, so that the trajectories traced in the fixed frame F are given by mathbf X _i(t)A(t)mathbf x _imathbf d (t)quad i1,ldots,n.
For convenience let the trajectory be along the X-axis, so X ( d, 0) and the velocity is V ( v, 0 then R V 0, and F V F x v, where F x is the component of F along the X-axis, so Fxvmvv.He's been out of work for months.This integral is computed along the trajectory X ( t ) of the particle and is therefore path dependent.