Elastic Collisions in Two Dimensions

Question 1

Using unchanged parallel components wall

Answer 1

u cosα = v cosβ

Question 2

Using perpendicular components wall

Answer 2

e usinα = v sinβ

Perpendicular component changes due to coefficient of restitution

Question 3

Angles formula wall

Answer 3

e tanα = tanβ

Question 4

Angle of deflection wall

Answer 4

α + β

Question 5

A vertical ball hitting a plane at angle α to the horizontal

Answer 5

α is the angle between the vertical ball and the component of the velocity perpendicular to the plane

Question 6

Dot product parallel to the wall

Answer 6

u.W = v.W

where W is a vector parallel to the wall

Question 7

Dot product perpendicular to the wall

Answer 7

-e(u.I) = v.I

where I is a vector perpendicular to the wall

Question 8

Direction of impulse wall

Answer 8

Perpendicular to the wall

Question 9

Finding an impulse

Answer 9

Use I = m(v-u) using vectors

Question 10

Angle of deflection for spheres

Answer 10

Use cos θ = (a.b)/|a||b|

Keep negatives

Question 11

Line of centres

Answer 11

The line through the centres of both spheres

Question 12

Oblique impacts

Answer 12

The component perpendicular to the line of centres does not change
Parallel use e formula and momentum for each parallel component

Question 13

Direction of impulse with spheres

Answer 13

Parallel to the line of centres

Question 14

Where do impulses act in relation to each other?

Answer 14

Opposite directions so subtract the calculated change in velocity from the other

Question 15

Spheres dot product

Answer 15

e(ua.I - ub.I) = vb.I - va.I