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Date: 14-3-2021
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Date: 28-12-2016
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Date: 15-9-2020
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Collisions in 2-dimensions
Glancing collisions (i.e. not head-on) are more complicated to analyze. Figure 1.1 shows a typical configuration.
FIGURE 1.1 Glancing collision.
Example Write down the conservation of energy and momentum equations for the glancing collision depicted in Fig. 1.1 where the target ball is initially at rest.
Solution Conservation of momentum is
But In x and y components these are
or
If the collision is elastic we also have conservation of kinetic energy,
These three equations must then be solved for the quantities of interest.
Example A ball of mass m1 and speed v1i collides with a stationary target ball of mass m2, as shown in Fig. 1.1. If the target is scattered at an angle of θ2 what is the scattering angle θ1 of the projectile in terms of m1, m2, v1i, θ2 and v2f where v2f is the final speed of the target ?
Solution Conservation of momentum gives
or
The x direction gives
We want to find θ1. Solve the first and second equations for θ1 giving
and
giving
(Notice that this result is valid for both elastic and inelastic collisions. We did not use conservation of energy.)
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أمراض منتصف العمر.. "أعراض خطيرة" سببها نقص المغنيسيوم
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لماذا تتناقص أعداد النحل عالميا؟
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ممثل المرجعية العليا: العتبة الحسينية تخطط لإنشاء مراكز متخصصة للكشف المبكر عن (سرطان الثدي) بعموم العراق
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