- #1
GKRM
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I was a bit confused about the work energy theorem. I perfectly understood it's applications for point sized particles but I'm a bit confused about its application on extended bodies both rigid and non rigid.
Case 1 {for rigid bodies} :-
Consider a rod of definite mass hinged at the top. It's initially vertical. Now you apply a horizontal force F to the lowest point in horizontal direction of constant magnitude. The magnitude is low enough so that the rod doesn't gain any significant kinetic energy. However it gains potential energy as it rotates. The hinge doesn't do any work because there is no displacement of the point of contact. The applied force F is always horizontal. So F.ds in vertical direction is always zero. My question is how does it gain potential energy then?
OR
Consider a square block kept on a rough horizontal surface (friction is sufficient enough to prevent slipping/sliding). You apply a horizontal force F on the topmost point ,constant in magnitude and direction. The magnitude is adjusted so that the block doesn't gain significant kinetic energy. Due to rotation about the axis passing through the line of contact of the ground and block, the potential energy of the block increases as it loses contact with the surface. How does it gain potential energy?
Case 2 {non-rigid body}:-
Consider 2 blocks each of mass M, connected by a massless spring. One of the blocks is in contact with a vertical wall. You now compress the spring and let the motion begin after you have left the other block. The normal force doesn't do any work because there is no displacement of the point of contact. So How does the system gain kinetic energy?
On the whole I want to understand what is actually meant by the elemental displacement term in the work energy equation. I assume that in case of a rigid body it's displacement of centre of mass and in case of non rigid body it's displacement of point of contact. Am I correct assuming this?
Case 1 {for rigid bodies} :-
Consider a rod of definite mass hinged at the top. It's initially vertical. Now you apply a horizontal force F to the lowest point in horizontal direction of constant magnitude. The magnitude is low enough so that the rod doesn't gain any significant kinetic energy. However it gains potential energy as it rotates. The hinge doesn't do any work because there is no displacement of the point of contact. The applied force F is always horizontal. So F.ds in vertical direction is always zero. My question is how does it gain potential energy then?
OR
Consider a square block kept on a rough horizontal surface (friction is sufficient enough to prevent slipping/sliding). You apply a horizontal force F on the topmost point ,constant in magnitude and direction. The magnitude is adjusted so that the block doesn't gain significant kinetic energy. Due to rotation about the axis passing through the line of contact of the ground and block, the potential energy of the block increases as it loses contact with the surface. How does it gain potential energy?
Case 2 {non-rigid body}:-
Consider 2 blocks each of mass M, connected by a massless spring. One of the blocks is in contact with a vertical wall. You now compress the spring and let the motion begin after you have left the other block. The normal force doesn't do any work because there is no displacement of the point of contact. So How does the system gain kinetic energy?
On the whole I want to understand what is actually meant by the elemental displacement term in the work energy equation. I assume that in case of a rigid body it's displacement of centre of mass and in case of non rigid body it's displacement of point of contact. Am I correct assuming this?