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a force with k-positive constant acts on particle moving in xy plane. Starting frm origin the particle is taken along the positive x axis to the point(a,0) and then parallel yo y axis to the point(a,a).Displacement is -4i+2j-3k then total work done by the forces on the particle is???????

a force with k-positive constant acts on particle moving in xy plane. Starting frm origin the particle is taken along the positive x axis to the point(a,0) and then parallel yo y axis to the point(a,a).Displacement is -4i+2j-3k then total work done by the forces on the particle is???????

Grade:Upto college level

1 Answers

Aman Bansal
592 Points
7 years ago

Dear Student,

In this problem, you will use your prior knowledge to derive one ofthe most important relationships in mechanics: the work-energytheorem. We will start with a special case: a particle of massmmoving in the x direction at constant accelerationa.During a certain interval of time, the particle accelerates fromv_initial to v_final, undergoing displacement sgiven by s=x_{\rm final}-x_{\rm initial}.
part A.
Find the acceleration a of the particle.
Express the acceleration in terms ofv_initialv_final, and s.
part B
Find the net force F acting on the particle.
Express your answer in terms ofmand a.
part c
Find the net work Wdone on the particle by the external forces during the particle''smotion.
Express your answer in terms ofFand s.
part D
Substitute for Ffrom Part B in the expression for work from Part C. Then substitutefor afrom the relation in Part A. This will yield an expression for thenet work Wdone on the particle by the external forces during the particle''smotion in terms of mass and the initial and final velocities. Givean expression for the work Win terms of those quantities.
Express your answer in terms ofm,v_initial, and v_final.
part E
Find the net work Wdone on the particle by the external forces during the motion ofthe particle in terms of the initial and final kineticenergies.
Express your answer in terms ofK_initial and K_final.
part F
Evaluate the integral W=\int_{v_{\rm initial}}^{v_{\rm final}}m v\,dv.
Express your answer in terms ofm,v_initial, and v_final.
part G
A particle moving in the x directionis being acted upon by a net force F(x)=Cx^2, for some constant C.The particle moves from x_{\rm initial}=L to x_{\rm final}=3L. What is DeltaK, the change in kinetic energy of the particle during thattime?
Express your answer in terms ofCand L.

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