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Two-Dimensional Collisions
Unit 5, Presentation 3
Glancing Collisions
For a general collision of two objects in three-dimensional space, the conservation of momentum principle implies that the total momentum of the system in each direction is conserved
Use subscripts for identifying the object, initial and final velocities, and components
fy22fy11iy22iy11
fx22fx11ix22ix11
vmvmvmvm
andvmvmvmvm
Glancing Collisions
The “after” velocities have x and y components Momentum is conserved in the x direction and in the
y direction Apply conservation of momentum separately to each
direction
Problem Solving for Two-Dimensional Collisions
Coordinates: Set up coordinate axes and define your velocities with respect to these axes It is convenient to choose the x- or y-
axis to coincide with one of the initial velocities
Diagram: In your sketch, draw and label all the velocities and masses
Problem Solving for Two-Dimensional Collisions, 2
Conservation of Momentum: Write expressions for the x and y components of the momentum of each object before and after the collision
Write expressions for the total momentum before and after the collision in the x-direction and in the y-direction
Problem Solving for Two-Dimensional Collisions, 3
Conservation of Energy: If the collision is elastic, write an expression for the total energy before and after the collision Equate the two expressions Fill in the known values Solve the quadratic equations
Can’t be simplified
Problem Solving for Two-Dimensional Collisions, 4
Solve for the unknown quantities Solve the equations simultaneously There will be two equations for inelastic
collisions There will be three equations for elastic
collisions
2D Collision Example
Two cars enter an icy intersection and skid into each other. The 2500 kg sedan was originally heading south at 20.0 m/s, whereas the 1450 kg coupe was driving east at 30.0 m/s. On impact, the two vehicles become entangled and move off as one at an angle in a southeasterly direction. Determine and the speed at which they initially skid away after crashing.
First, note that the cars become entangled…an inelastic collision.
?
?
)(/0.30
1450
)(/0.20
2500
2
2
1
1
f
i
i
v
eastsmv
kgm
southsmv
kgm
sin)()0()/0.20(
cos)()/0.30()0(
2121
2121
f
f
vmmmsmm
DirectionY
vmmsmmm
DirectionX
2D Collision Example Continued
sin)14502500()/0.20(2500
cos)14502500()/0.30(1450
f
f
vkgkgsmkg
DirectionY
vkgkgsmkg
DirectionX
cos
01.11
cos01.11
cos395043500
f
f
f
v
v
v
DirectionX
Solve these two equations simultaneously in variables vf and
smv
v
v
DirectionY
f
f
f
/8.1649cos
01.11
49
tan15.1
sincos
01.1166.12
sin66.12
sin395050000
substitution
