A block of mass 5kg riding on a horizontal frictionless xy-plane surface is subjected to three applied forces:→F1= 12√2N[ 45◦]→F2= (8,−6)N→F3= 14N[↑]. The normal force and the weight act perpendicular to the plane (along thez-axis) and cancel everywhere and always. At the instantt= 0sthe block is at rest at the origin,~r0= (0,0)m.
Employing energy methods we shall determine the speed of the block at the timet= 2s, when it reaches the point~r2= (8,8)m.
(a) (i) Determine the net force acting on the block.(ii) Is this force constant?YesNo(
b) Determine the [vector] displacement from~r0to~r2.
(c) Compute the work done by the net force acting through the vector displacement deter-mined in (b).(
d) (i) Compute the amount of work performed on the particle by each of the three applied forces acting separately.
(ii) Sum these to obtain the network.
(iii) Comment on the relation between your results for (d) (ii) and (c).
(e) (i) Compute the initial kinetic energy of the block.(ii) Determine the kinetic energy of the block when it reaches~r2. (iii) Compute the speed of the block when it is at~r2,i. e., at t= 2s.