Normal force - Revision history

Vipul: /* Work and energy */

2011-12-04T01:35:27Z

Work and energy

← Older revision		Revision as of 01:35, 4 December 2011
Line 104:		Line 104:
	Normal force can do work if the normal force causes motion, e.g., with one body ''pushing'' the other body in some direction. It does ''not'' do work if the normal force is balanced by other forces perpendicular to the plane of contact that result in no net motion in that direction.		Normal force can do work if the normal force causes motion, e.g., with one body ''pushing'' the other body in some direction. It does ''not'' do work if the normal force is balanced by other forces perpendicular to the plane of contact that result in no net motion in that direction.

	For instance, if a person lifts a book by placing it on the palm of her hand and moving her palm upward, then the normal force between the palm and the book causes the book to be lifted. The overall work done by the normal force is obtained by using the expression <math>\int F \cdot ds</math> where <math>F</math> is the normal force. Part of this work is converted to [[potential energy]], since it combats the gravitational force acting on the book, namely <math>\int mg \cdot s = mgs</math> where <math>s</math> is the total height gained by the book. The rest of the work is converted into [[kinetic energy]], which is the energy that the book acquires because of its speed. This is given by <math>\int (F - mg) \cdot s</math>.		For instance, if a person lifts a book by placing it on the palm of her hand and moving her palm upward, then the normal force between the palm and the book causes the book to be lifted. The overall work done by the normal force is obtained by using the expression <math>\int F \cdot ds</math> where <math>F</math> is the normal force. Part of this work is converted to [[potential energy]], since it combats the gravitational force acting on the book, namely <math>\int mg \cdot ds = mgs</math> where <math>s</math> is the total height gained by the book. The rest of the work is converted into [[kinetic energy]], which is the energy that the book acquires because of its speed. This is given by <math>\int (F - mg) \cdot ds</math>.

	If a person pushes a block forward on a frictionless floor, the work done by the normal force is <math>\int F \cdot ds</math>, all of which is converted into the block's kinetic energy. If, however, the person pushes the block forward on a floor with friction, part of the work done, namely <math>\int \mu_k mg \cdot ds</math>, is dissipated in [[kinetic friction]], and the remaining is stored in the form of the block's kinetic energy.		If a person pushes a block forward on a frictionless floor, the work done by the normal force is <math>\int F \cdot ds</math>, all of which is converted into the block's kinetic energy. If, however, the person pushes the block forward on a floor with friction, part of the work done, namely <math>\int \mu_k mg \cdot ds</math>, is dissipated in [[kinetic friction]], and the remaining is stored in the form of the block's kinetic energy.

Vipul: /* Situational examples */

2010-10-31T01:16:45Z

Situational examples

← Older revision		Revision as of 01:16, 31 October 2010
Line 21:		Line 21:
	\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal: see [[sliding motion along a frictionless inclined plane]] and [[sliding motion along an inclined plane]] \|\| Upward/outward on the block, downward/inward on the surface \|\| The product <math>mg \cos \theta</math>, where <math>m</math> is the mass of the block, <math>g</math> is the acceleration due to gravity \|\| The normal force must balance the component of gravitational force that is trying to send the block into the inclined plane. \|\| [[File:Blockoninclineforcediagramnormalcomponents.png\|200px]]		\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal: see [[sliding motion along a frictionless inclined plane]] and [[sliding motion along an inclined plane]] \|\| Upward/outward on the block, downward/inward on the surface \|\| The product <math>mg \cos \theta</math>, where <math>m</math> is the mass of the block, <math>g</math> is the acceleration due to gravity \|\| The normal force must balance the component of gravitational force that is trying to send the block into the inclined plane. \|\| [[File:Blockoninclineforcediagramnormalcomponents.png\|200px]]
	\|-		\|-
	\| A person lifting a book placed on his horizontal palm \|\| Upward on the book, downward on the palm \|\| <math>m(g + a)</math> where <math>g</math> is the acceleration due to gravity and <math>a</math> is the upward acceleration. If the person is lifting the book with		\| A person lifting a book placed on his horizontal palm \|\| Upward on the book, downward on the palm \|\| <math>m(g + a)</math> where <math>g</math> is the acceleration due to gravity and <math>a</math> is the upward acceleration. If the person is lifting the book with constant speed, it is just <math>mg</math>. If the speed is reducing, the normal force is less than <math>mg</math>. \|\| Note that the normal force does ''not'' cancel <math>mg</math> but rather is determined so as to create the necessary acceleration. \|\|
	\|-		\|-
	\| Two blocks sliding down, adjacent to each other on an inclined plane. Assume that they do not get separated. \|\| The block farther down exerts a normal force up the inclined plane on the other block, and the block further up exerts a downward force on the lower blocks. \|\| {{fillin}}. Note that the normal force between the blocks is ''not'' set to ensure zero acceleration (hence, it does not balance out external forces in that direction), but it is set to ensure that the blocks accelerate equally, so that ''relative'' acceleration is still zero. \|\| Obtained by solving system of equations \|\| [[File:Adjacentblocksonincline.png\|200px]]		\| Two blocks sliding down, adjacent to each other on an inclined plane. Assume that they do not get separated. \|\| The block farther down exerts a normal force up the inclined plane on the other block, and the block further up exerts a downward force on the lower blocks. \|\| {{fillin}}. Note that the normal force between the blocks is ''not'' set to ensure zero acceleration (hence, it does not balance out external forces in that direction), but it is set to ensure that the blocks accelerate equally, so that ''relative'' acceleration is still zero. \|\| Obtained by solving system of equations \|\| [[File:Adjacentblocksonincline.png\|200px]]

Vipul: /* Situational examples */

2010-10-30T21:59:22Z

Situational examples

← Older revision		Revision as of 21:59, 30 October 2010
Line 20:		Line 20:
	\|-		\|-
	\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal: see [[sliding motion along a frictionless inclined plane]] and [[sliding motion along an inclined plane]] \|\| Upward/outward on the block, downward/inward on the surface \|\| The product <math>mg \cos \theta</math>, where <math>m</math> is the mass of the block, <math>g</math> is the acceleration due to gravity \|\| The normal force must balance the component of gravitational force that is trying to send the block into the inclined plane. \|\| [[File:Blockoninclineforcediagramnormalcomponents.png\|200px]]		\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal: see [[sliding motion along a frictionless inclined plane]] and [[sliding motion along an inclined plane]] \|\| Upward/outward on the block, downward/inward on the surface \|\| The product <math>mg \cos \theta</math>, where <math>m</math> is the mass of the block, <math>g</math> is the acceleration due to gravity \|\| The normal force must balance the component of gravitational force that is trying to send the block into the inclined plane. \|\| [[File:Blockoninclineforcediagramnormalcomponents.png\|200px]]
			\|-
			\| A person lifting a book placed on his horizontal palm \|\| Upward on the book, downward on the palm \|\| <math>m(g + a)</math> where <math>g</math> is the acceleration due to gravity and <math>a</math> is the upward acceleration. If the person is lifting the book with
	\|-		\|-
	\| Two blocks sliding down, adjacent to each other on an inclined plane. Assume that they do not get separated. \|\| The block farther down exerts a normal force up the inclined plane on the other block, and the block further up exerts a downward force on the lower blocks. \|\| {{fillin}}. Note that the normal force between the blocks is ''not'' set to ensure zero acceleration (hence, it does not balance out external forces in that direction), but it is set to ensure that the blocks accelerate equally, so that ''relative'' acceleration is still zero. \|\| Obtained by solving system of equations \|\| [[File:Adjacentblocksonincline.png\|200px]]		\| Two blocks sliding down, adjacent to each other on an inclined plane. Assume that they do not get separated. \|\| The block farther down exerts a normal force up the inclined plane on the other block, and the block further up exerts a downward force on the lower blocks. \|\| {{fillin}}. Note that the normal force between the blocks is ''not'' set to ensure zero acceleration (hence, it does not balance out external forces in that direction), but it is set to ensure that the blocks accelerate equally, so that ''relative'' acceleration is still zero. \|\| Obtained by solving system of equations \|\| [[File:Adjacentblocksonincline.png\|200px]]

Vipul: /* Confusion with Newton's third law */

2010-10-30T21:58:00Z

Confusion with Newton's third law

← Older revision		Revision as of 21:58, 30 October 2010
Line 41:		Line 41:
	\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal \|\| The upward/outward normal force exerted by the surface on the block forms an action-reaction pair with the component of gravitational force exerted on the block in the inward direction into the plane. \|\| The upward/outward normal force exerted by the surface on the block forms an action-reaction pair with an inward/downward normal force exerted by the block on the surface.		\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal \|\| The upward/outward normal force exerted by the surface on the block forms an action-reaction pair with the component of gravitational force exerted on the block in the inward direction into the plane. \|\| The upward/outward normal force exerted by the surface on the block forms an action-reaction pair with an inward/downward normal force exerted by the block on the surface.
	\|}		\|}

			{{quotation\|'''KEY POINT TO REMEMBER''': Two different forces acting on the same body ''cannot'' form an action-reaction pair. The two forces of an action-reaction pair must act on different bodies.}}

	==Units and dimensions==		==Units and dimensions==

Vipul: /* Normal force for a non-flat surface of contact */

2010-10-30T21:56:37Z

Normal force for a non-flat surface of contact

← Older revision		Revision as of 21:56, 30 October 2010
Line 78:		Line 78:
	===Normal force for a non-flat surface of contact===		===Normal force for a non-flat surface of contact===

	Consider a ball resting on a hemispherical surface of the same shape (so that there is a good fit). In this case, the surface of contact is not flat and there are different normal directions to different parts of the surface. The net direction of normal force in such situations is unclear. The normal force can be determined by the same integration as for a flat surface:		Consider a ball resting on/in a hemispherical surface of the same shape (so that there is a good fit). In this case, the surface of contact is not flat and there are different normal directions to different parts of the surface. The net direction of normal force in such situations is unclear. The normal force can be determined by the same integration as for a flat surface:

	<math>N =\int P d\overline{A}</math>		<math>N =\int P d\overline{A}</math>

Vipul: /* Situational examples */

2010-10-30T21:55:12Z

Situational examples

← Older revision		Revision as of 21:55, 30 October 2010
Line 19:		Line 19:
	\| A block placed on a fixed horizontal surface. \|\| Upward on the block, downward on the surface \|\| Equal to the [[weight]] of the block, which is the product of the mass and acceleration due to gravity\|\| The net vertical force on the block should be zero \|\| [[File:Blockonflatsurface.png\|200px]]		\| A block placed on a fixed horizontal surface. \|\| Upward on the block, downward on the surface \|\| Equal to the [[weight]] of the block, which is the product of the mass and acceleration due to gravity\|\| The net vertical force on the block should be zero \|\| [[File:Blockonflatsurface.png\|200px]]
	\|-		\|-
	\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal: see [[sliding motion along an inclined plane]] \|\| Upward/outward on the block, downward/inward on the surface \|\| The product <math>mg \cos \theta</math>, where <math>m</math> is the mass of the block, <math>g</math> is the acceleration due to gravity \|\| The normal force must balance the component of gravitational force that is trying to send the block into the inclined plane. \|\| [[File:Blockoninclineforcediagramnormalcomponents.png\|200px]]		\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal: see [[sliding motion along a frictionless inclined plane]] and [[sliding motion along an inclined plane]] \|\| Upward/outward on the block, downward/inward on the surface \|\| The product <math>mg \cos \theta</math>, where <math>m</math> is the mass of the block, <math>g</math> is the acceleration due to gravity \|\| The normal force must balance the component of gravitational force that is trying to send the block into the inclined plane. \|\| [[File:Blockoninclineforcediagramnormalcomponents.png\|200px]]
	\|-		\|-
	\| Two blocks sliding down, adjacent to each other on an inclined plane. Assume that they do not get separated. \|\| The block farther down exerts a normal force up the inclined plane on the other block, and the block further up exerts a downward force on the lower blocks. \|\| {{fillin}} \|\| Obtained by solving system of equations \|\| [[File:Adjacentblocksonincline.png\|200px]]		\| Two blocks sliding down, adjacent to each other on an inclined plane. Assume that they do not get separated. \|\| The block farther down exerts a normal force up the inclined plane on the other block, and the block further up exerts a downward force on the lower blocks. \|\| {{fillin}}. Note that the normal force between the blocks is ''not'' set to ensure zero acceleration (hence, it does not balance out external forces in that direction), but it is set to ensure that the blocks accelerate equally, so that ''relative'' acceleration is still zero. \|\| Obtained by solving system of equations \|\| [[File:Adjacentblocksonincline.png\|200px]]
			\|-
			\| A block on a circular incline, sliding down along the incline: see [[sliding motion along a frictionless circular incline]] and [[sliding motion along a circular incline]] \|\| Upward/outward on the block, downward/inward on the incline surface \|\| <math>mg \cos \theta - (mv^2/r)</math>, where <math>mg\cos \theta</math> is the component of gravitational force along the normal direction, and <math>mv^2/r</math> is the net centripetal force needed for the block to continue to stay on the circular incline. \|\| Newton's second law. Note that here, <math>N</math> does ''not'' balance external forces in the normal direction, because we want the net force in the normal direction to be, not zero, but the centripetal force.
	\|}		\|}

Vipul: /* Situational examples */

2010-10-30T21:50:36Z

Situational examples

← Older revision		Revision as of 21:50, 30 October 2010
Line 20:		Line 20:
	\|-		\|-
	\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal: see [[sliding motion along an inclined plane]] \|\| Upward/outward on the block, downward/inward on the surface \|\| The product <math>mg \cos \theta</math>, where <math>m</math> is the mass of the block, <math>g</math> is the acceleration due to gravity \|\| The normal force must balance the component of gravitational force that is trying to send the block into the inclined plane. \|\| [[File:Blockoninclineforcediagramnormalcomponents.png\|200px]]		\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal: see [[sliding motion along an inclined plane]] \|\| Upward/outward on the block, downward/inward on the surface \|\| The product <math>mg \cos \theta</math>, where <math>m</math> is the mass of the block, <math>g</math> is the acceleration due to gravity \|\| The normal force must balance the component of gravitational force that is trying to send the block into the inclined plane. \|\| [[File:Blockoninclineforcediagramnormalcomponents.png\|200px]]
			\|-
			\| Two blocks sliding down, adjacent to each other on an inclined plane. Assume that they do not get separated. \|\| The block farther down exerts a normal force up the inclined plane on the other block, and the block further up exerts a downward force on the lower blocks. \|\| {{fillin}} \|\| Obtained by solving system of equations \|\| [[File:Adjacentblocksonincline.png\|200px]]
	\|}		\|}

Vipul: /* Confusion with Newton's third law */

2010-10-30T21:46:43Z

Confusion with Newton's third law

← Older revision		Revision as of 21:46, 30 October 2010
Line 26:		Line 26:
	The normal force between two bodies exerted through a surface of contact depends on the other forces acting on these bodies that are creating a tendency for the bodies to move into each other. In fact, it adjusts itself in magnitude to ''precisely'' counteract the external forces along the normal direction. Hence, it is ''equal and opposite'' to these external forces and is sometimes called a ''reaction'' force.		The normal force between two bodies exerted through a surface of contact depends on the other forces acting on these bodies that are creating a tendency for the bodies to move into each other. In fact, it adjusts itself in magnitude to ''precisely'' counteract the external forces along the normal direction. Hence, it is ''equal and opposite'' to these external forces and is sometimes called a ''reaction'' force.

	However, the normal force is '''not''' a ''reaction'' to the external force in the sense of [[Newton's third law]], even though it is equal and opposite to the external force.		However, the normal force is '''not''' a ''reaction'' to the external force in the sense of [[Newton's third law]], even though it is (in many typical situations) equal and opposite to the external force.

	Rather, the normal forces that the two bodies exert on each other form an action-reaction pair. Here is an elaboration using the previous examples:		Rather, the normal forces that the two bodies exert on each other form an action-reaction pair. Here is an elaboration using the previous examples:

	{\| class="~~wikitable~~" border="1"		{\| class="sortable" border="1"
	! Example !! False interpretation of Newton's third law !! Correct interpretation of Newton's third law		! Example !! False interpretation of Newton's third law !! Correct interpretation of Newton's third law
	\|-		\|-

Vipul: /* Situational examples */

2010-09-18T00:05:30Z

Situational examples

← Older revision		Revision as of 00:05, 18 September 2010
Line 14:		Line 14:
	==Situational examples==		==Situational examples==

	{\| class="~~wikitable~~" border="1"		{\| class="sortable" border="1"
	! Example !! Direction of force on each body !! Magnitude of force !! Reason		! Example !! Direction of force on each body !! Magnitude of force !! Reason !! Picture
	\|-		\|-
	\| A block placed on a fixed horizontal surface \|\| Upward on the block, downward on the surface \|\| Equal to the [[weight]] of the block, which is the product of the mass and acceleration due to gravity\|\| The net vertical force on the block should be zero		\| A block placed on a fixed horizontal surface. \|\| Upward on the block, downward on the surface \|\| Equal to the [[weight]] of the block, which is the product of the mass and acceleration due to gravity\|\| The net vertical force on the block should be zero \|\| [[File:Blockonflatsurface.png\|200px]]
	\|-		\|-
	\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal \|\| Upward/outward on the block, downward/inward on the surface \|\| The product <math>mg \cos \theta</math>, where <math>m</math> is the mass of the block, <math>g</math> is the acceleration due to gravity \|\| The normal force must balance the component of gravitational force that is trying to send the block into the inclined plane.		\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal: see [[sliding motion along an inclined plane]] \|\| Upward/outward on the block, downward/inward on the surface \|\| The product <math>mg \cos \theta</math>, where <math>m</math> is the mass of the block, <math>g</math> is the acceleration due to gravity \|\| The normal force must balance the component of gravitational force that is trying to send the block into the inclined plane. \|\| [[File:Blockoninclineforcediagramnormalcomponents.png\|200px]]
	\|}		\|}

Vipul: /* Situational examples */

2010-05-11T18:41:47Z

Situational examples

← Older revision		Revision as of 18:41, 11 May 2010
Line 19:		Line 19:
	\| A block placed on a fixed horizontal surface \|\| Upward on the block, downward on the surface \|\| Equal to the [[weight]] of the block, which is the product of the mass and acceleration due to gravity\|\| The net vertical force on the block should be zero		\| A block placed on a fixed horizontal surface \|\| Upward on the block, downward on the surface \|\| Equal to the [[weight]] of the block, which is the product of the mass and acceleration due to gravity\|\| The net vertical force on the block should be zero
	\|-		\|-
	\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal \|\| Upward/outward on the block, downward/inward on the surface \|\| The product <math>mg \cos \theta</math>, where <math>m</math> is the mass of the block, <math>g</math> is the acceleration due to gravity \|\| The normal force must balance the component of gravitational force		\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal \|\| Upward/outward on the block, downward/inward on the surface \|\| The product <math>mg \cos \theta</math>, where <math>m</math> is the mass of the block, <math>g</math> is the acceleration due to gravity \|\| The normal force must balance the component of gravitational force that is trying to send the block into the inclined plane.
	\|}		\|}

			==Confusion with Newton's third law==

			The normal force between two bodies exerted through a surface of contact depends on the other forces acting on these bodies that are creating a tendency for the bodies to move into each other. In fact, it adjusts itself in magnitude to ''precisely'' counteract the external forces along the normal direction. Hence, it is ''equal and opposite'' to these external forces and is sometimes called a ''reaction'' force.

			However, the normal force is '''not''' a ''reaction'' to the external force in the sense of [[Newton's third law]], even though it is equal and opposite to the external force.

			Rather, the normal forces that the two bodies exert on each other form an action-reaction pair. Here is an elaboration using the previous examples:

			{\| class="wikitable" border="1"
			! Example !! False interpretation of Newton's third law !! Correct interpretation of Newton's third law
			\|-
			\| A block placed on a fixed horizontal surface \|\| The upward normal force exerted by the surface on the block forms an action-reaction pair with the downward gravitational force on the block \|\| The upward normal force exerted by the surface on the block, and the downward normal force exerted by the block on the surface, form an action-reaction pair. The gravitational force exerted by the earth on the block and the gravitational force exerted by the block on the earth form another action-reaction pair.
			\|-
			\| A block placed on a fixed inclined plane with angle <math>\theta</math> with the horizontal \|\| The upward/outward normal force exerted by the surface on the block forms an action-reaction pair with the component of gravitational force exerted on the block in the inward direction into the plane. \|\| The upward/outward normal force exerted by the surface on the block forms an action-reaction pair with an inward/downward normal force exerted by the block on the surface.
			\|}

	==Units and dimensions==		==Units and dimensions==