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Elastic Collision

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter. Perfectly elastic collisions occur only if there is no net conversion of kinetic energy into other forms.

The final speeds depend on the sum of the initial momenta (masses times speeds) of the particles plus the mass of the other particle times the difference between the particle's intial speed minus the other particle's speed, all of which is divided by the sum of the masses.

Formula

{QuantityVariable[Subscript["v", "1", "f"], "Speed"] == (QuantityVariable[Subscript["m", "1"], "Mass"]*QuantityVariable[Subscript["v", "1", "i"], "Speed"] + QuantityVariable[Subscript["m", "2"], "Mass"]*QuantityVariable[Subscript["v", "2", "i"], "Speed"] + QuantityVariable[Subscript["m", "2"], "Mass"]*(-QuantityVariable[Subscript["v", "1", "i"], "Speed"] + QuantityVariable[Subscript["v", "2", "i"], "Speed"]))/(QuantityVariable[Subscript["m", "1"], "Mass"] + QuantityVariable[Subscript["m", "2"], "Mass"]), QuantityVariable[Subscript["v", "2", "f"], "Speed"] == (QuantityVariable[Subscript["m", "1"], "Mass"]*QuantityVariable[Subscript["v", "1", "i"], "Speed"] + QuantityVariable[Subscript["m", "1"], "Mass"]*(QuantityVariable[Subscript["v", "1", "i"], "Speed"] - QuantityVariable[Subscript["v", "2", "i"], "Speed"]) + QuantityVariable[Subscript["m", "2"], "Mass"]*QuantityVariable[Subscript["v", "2", "i"], "Speed"])/(QuantityVariable[Subscript["m", "1"], "Mass"] + QuantityVariable[Subscript["m", "2"], "Mass"])}

symbol description physical quantity
v1,f final speed 1 "Speed"
m1 mass 1 "Mass"
m2 mass 2 "Mass"
v1,i initial speed 1 "Speed"
v2,i initial speed 2 "Speed"
v2,f final speed 2 "Speed"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Elastic Collision"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Elastic Collision"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ResourceObject["Elastic Collision"], {QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("1", "f"\)]\),"Speed"] -> Quantity[1, ("Meters")/("Seconds")], QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("2", "i"\)]\),"Speed"] -> Quantity[-0.5`, ("Meters")/("Seconds")], QuantityVariable[ \!\(\*SubscriptBox[\("m"\), \("2"\)]\),"Mass"] -> Quantity[1, "Kilograms"]}]
Out[3]=

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