Question

rom mechanics we know the work done by a constant force, along a straight line is the DOT PRODUCT between the force and the vector pathengh The NET Force(assumed constant) acting on a mass, Mis The NET fForce movesthe mass from its intial position to the fial postion alongt he vector athlength given by 1. Find the WORK done by the constant force 2 Interupt this resutt physically in terms of speed of the object. Explain Find the UNIT VECTOR direction of the NET FORCE, of the VECTOR PATHLENGTH 4.Find the angle between the NET FORCE and the VECTOR PATHLENGTH 5 Find the direction angles of the NET FORCE and the direction angles of the VECTOR PATHLENGTH

Answer 1

The solution is given in the attached image.

Final answers are boxed.

F rightarrow = 6i + 8j N, delta S rightarrow = -4i + 3j m W = F rightarrow . delta S rightarrow = -24 + 24 = 0 So, physically no work is done on the particle So, its speed remains same. And the displacement is perpendicular to the force applied. F = ? delta S = ? F = F rightarrow / Vertical-bar F rightarrow Vertical-bar = 6i + 8j/ squareroot 36 + 64 = 6/10 i + 8/10 j and delta S rightarrow = delta S rightarrow / Vertical-bar delta S rightarrow Vertical-bar = -4i + 3j/ squareroot 16 + 9 = -4/5 i + 3/5 j theta = ? w_c know, F rightarrow . delta S rightarrow = Vertical-bar F rightarrow Vertical-bar Vertical-bar delta S rightarrow Vertical-bar cos theta rightdoublearrow cos theta times 10 times 5 = 0 cos theta = 0 theta = pi /2 theta_F = ? theta_delta S = ?