Dynamic of particles

Each system have the following conversion factors:

	SI system

	Symbol		Mean
	h			hour
	min			minute
	hp			horsepower
	cv			steam horses
	T			metric ton
	g			gram
	slug			slug
	km			kilometer
	cm			centimeter
	mm			millimeter
	mi			mile
	ft			feet
	in			inch
	km/h			kilometers per hour
	cm/s			centimeters per second
	mm/s		millimeters per second
	mph			miles per hour
	ft/s			feet per second
	in/s			inch per second
	kt			knot
	cm/s2		centimeters per squared second
	mm/s2		millimeters per squared second
	ft/s2			feet per squared second
	in/s2			inch per squared second

	English system

	Symbol		Mean
	h			hour
	min			minute
	hp			horsepower
	cv			steam horses
	kg			kilogram
	g			gram
	km			kilometer
	m			meter
	cm			centimeter
	mm			millimeter
	mi			mile
	in			feet
	km/h			kilometers per hour
	m/s			meters per second
	cm/s			centimeters per second
	mm/s		millimeters per second
	mph			miles per hour
	in/s			inch per second
	kt			knot
	m/s2			meters per squared second
	cm/s2		centimeters per squared second
	mm/s2		millimeters per squared second
	in/s2			inch per squared second
	lb/in			pounds per inch

In this module, the forces (elements Force, Friction or Contact) are added to the objects (elements Block, Pulley or Spring) placing the force in one of the cells around the object. Each object (if there isn’t in the chalkboard’s border) have 8 cells around it.

This module have 44 elements. Note that some elements have one or two equations, depending of the applied forces, or of the objects that interact with it.

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       ¬Stationary reference system

Stationary reference system, with X axis horizontal and positive to the right, and Y axis vertical an positive to upwards. 

Equations:	None.

Data:
	g:		Value of the gravity (absolute value). To default FisicaLab write the gravity
                           value to the selected system (9.81 m/s2 to SI, and 32.2 ft/s2 to English system).
	t:		End time to the problem.

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The following three elements, can be access with the icon:

¬

With a click above the desired mobile.
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       ¬Mobile

Mobile to collision problems. The angles are measured from the positive X axis, and the positive sense is the opposite of clockwise.

Equations:	None.

Data:
	Name:	Name of the mobile.
	m:		Mass of the mobile.
	vi: 		Initial velocity, in the direction specified by the initial angle.
	angi:		Initial angle.
	vf:		Final velocity, in the direction specified by the final angle.
	angf:		Final angle.

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       ¬Mobile in X    ¬Mobile in Y

Mobiles with movement along the X and Y axis, respectively.

Equations:	None.

Data:
	Name: 	Name of the mobile.
	m:		Mass of the mobile.
	vi:		Initial velocity.
	vf:		Final velocity.

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The following four elements, can be access with the icon:

¬

With a click above the arrow that specifies the direction of the movement.
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       ¬ Block with vertical movement

Block with vertical movement. Allows only one friction force, vertical or horizontal. 

Equations:		3 or 4 (if all the applied forces are vertical the block have 3 equation,
                                    otherwise have 4).

Data:
	Name:		Name of the block.
	m:			Mass block.
	a:			Acceleration of the block
	vi:			Initial velocity.
	vf:			Final velocity.
	d:			Travelled distance.
	Relative to:	To default is "sf" meaning that the data is measured from a stationary
                                    reference system. But you can set a block whit horizontal movement, if
                                    the data is relative to that block.

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       ¬ Block with horizontal movement

Block with horizontal movement. Allows only one horizontal friction force.

Equations:		4

Data:
	Name:		Name of the block.
	m:			Mass of the block.
	a:			Acceleration of the block.
	vi:			Initial velocity.
	vf:			Final velocity.
	d:			Travelled distance.
	Relative to:	To default is "sf" meaning that the data is measured from a stationary
                                    reference system. But you can set a block, if the data is relative to
                                    that block.

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       ¬ Block with movement along an inclined plane to the left

The data of this object are referring to a reference system, with the X axis along the plane and positive to upwards. And Y axis perpendicular to the plane and positive to upwards. Allows only one friction force parallel to the plane.

Equations:		4

Data:
	Name:		Name of the block.
	m:			Mass of the block.
	ang:			Angle of the plane, measured from the horizontal. 
	a:			Acceleration of the block.
	vi:			Initial velocity.
	vf:			Final velocity.
	d:			Travelled distance.
	Relative to:	To default is "sf" meaning that the data is measured from a stationary
                                    reference system. But you can set a block, if the data is relative to that
                                    block.

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       ¬ Block with movement along an inclined plane to the right

The data of this object are referring to a reference system, with the X axis along the plane and positive to upwards. And Y axis perpendicular to the plane and positive to upwards. Allows only one friction force parallel to the plane.

Equations:		4

Data:
	Name:		Name of the block.
	m:			Mass of the block.
	ang:			Angle of the plane, measured from the horizontal. 
	a:			Acceleration of the block.
	vi:			Initial velocity.
	vf:			Final velocity.
	d:			Travelled distance.
	Relative to:	To default is "sf" meaning that the data is measured from a stationary
                                    reference system. But you can set a block, if the data is relative to
                                    that block.

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       ¬ Pulley

Pulley without mass. Don’t allows frictions or contacts.

Equations:	1 or 2 (if all applied forces are vertical, or horizontal, the block have 1
                          equation, otherwise have 2).

Data:
	Name:	Name of the pulley (this data is irrelevant).

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       ¬  ¬  ¬  ¬Springs

Springs without mass, that satisfies the Hooke’s law. xi and xf are, respectively, the initial and end length that the spring is stretched or compressed. If the spring is stretched the length is positive, if is compressed is negative. Allow one or two forces. If have two forces these must have different sense (stretching or compressing the spring), and the same values or unknown data. Don’t allows frictions or contacts. The forces must be in the direction which will move the spring (see examples).

Equations:	1

Data:
	k:		Spring constant.
	xi: 		Initial length. 
	xf:		Final length.

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       ¬  ¬  ¬  ¬ Vertical or horizontal forces

Forces with the direction and sense of the arrow.

Equations:	None.

Data:
	f:		Magnitude of the force.

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       ¬  ¬  ¬  ¬ Oblique forces

Oblique forces with the sense of the arrow.

Equations:	None.

Data:
	f:		Magnitude of the force.
	ang:		Positive angle of the force, measured from the horizontal.

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       ¬  ¬  ¬  ¬ Vertical or horizontal friction forces
  
Friction forces with the direction and sense of the arrow.

Equations:	None.

Data:
	Normal:	Normal to calculate the friction force.
	u:		Friction coefficient, static or dynamic.

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       ¬  ¬  ¬  ¬ Oblique friction forces

Oblique frictions forces with the sense of the arrow. To be applied to a block on an inclined plane. The angle of force is the same as of the plane.

Equations:	None.

Data:
	Normal:	Normal to calculate the friction force.
	u:		Friction coefficient, static or dynamic.

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     ¬  ¬  ¬  ¬Vertical or horizontal friction forces between blocks

Friction forces between blocks, with the direction and sense of the arrows.

Equations:	None.

Data:
	Normal:	Normal to calculate the friction force.
	u:		Friction coefficient, static or dynamic.

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       ¬  ¬  ¬  ¬Oblique friction forces between blocks

Friction forces between blocks, with the sense of the arrows.

Equations:	None.

Data:
	Normal:	Normal to calculate the friction force.
	u:		Friction coefficient, static or dynamic.
	ang:		Positive angle of the friction force, measured from the horizontal.

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       ¬Relation between accelerations

Allows to make a relation between the magnitudes of accelerations measured in different reference systems.

Equations:	1

Data:
	a1:		Acceleration of the first block.
	a2:		Acceleration of the second block.
	z:		The relation factor, to default is -1.

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       ¬Relative motion

Allows get the acceleration, final velocity and travelled distance of a block in reference to the stationary system. When its data is relative to another block, that making a mobile reference system. The angles are measured from the positive X axis, and the positive sense is the opposite of clockwise.  

Equations:	6

Data:
	Object:		Name of the object that its data is relative.
	asf:			Magnitude of the acceleration.
	ang_asf:		Angle of the acceleration vector.
	vf_sf:		Magnitude of the final velocity.
	ang_vfsf:		Angle of the final velocity vector.
	dsf:			Travelled distance of the block.
	ang_dsf:		Angle of the travelled distance.

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       ¬Collision

Collision between mobiles. Allows collision between two Mobile in X, or two Mobile in Y. Or between two Mobile. Any other collision isn’t allowed.

Equations:	2 or 4 (if the collision is between two mobiles in x, or two mobiles in Y,
                          have 2 equations. Otherwise 4).

Data:
	Object 1:	Name of first mobile.
	Object 2:	Name of second mobile.
	e:		Coefficient of restitution.
	angn:	Angle of the normal between the objects (when collide). Measured from the
                           positive X axis. The positive sense is the opposite of clockwise.

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       ¬Energy

Set the principle of energy and work to 1, 2, 3, or 4 blocks or mobiles.

Equations:	1

Data:
	Object 1:	Name of the first block or mobile.
	Object 2:	Name of the second block or mobile.
	Object 3:	Name of the third block or mobile.
	Object 4:	Name of four block or mobile.
	Work:	External work to the system.

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       ¬Momentum

Set the principle of momentum and impulse, to one block or mobile.

Equations:	2

Data:
	Object:	Name of the block or mobile.
	Impulse:	Magnitude of the impulse’s vector.
	ang:		Angle of the impulse’s vector. Measured from the positive X axis. The
                           positive sense is the opposite of clockwise. 
	fImp:		Impulsive force.

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       ¬Power

Estimated the power developed.

Equations:	1

Data:
	Object:	Name of the block.
	Power:	Power.