Inelastic Non collinear angled collisions

[Probability]

This post may also in time help others!

Think of an "Intersection" and assume the traffic lights are malfunctioning. All traffic should give way and stop if necessary.

A car of kerb weight 1188 kg approaches the intersection and notices the traffic lights are inoperative. The car driver looks both ways (its dark at night) the streets are not brillinantly lit, however after starting to move off to the right, driving approximately 20 mph, an E bike runs straight into the nearside A post, swinging round approximately 90 degrees and his pedal collides with the door skin and tears it.

Legal E bikes can have a top speed of 15.5 mph, and it is assumed the E bike is travelling at that speed at the point of collision!

Looking at the damage and Momentum equations, the mass ratios are significantly different and it does not appear to be possible to do the math!

Lets say the E bike is U_1

Then...

U_1 = V (m_1 + m_2) - (m_2 * U_2) / m_1

The E bike is assumed to be travelling at 15.5 mph, so

U_1 = 6.93 (11.88 + 14) - (14 * 8.94) / 1188

U_1 = 6.91 m/s or 15.5 mph

Up to now to me that actually proves nothing I did not already assume.

So, lets look at the car as U_2...

U_2 = V (m_1 + m_2) - (m_1 * U_1) / m_2

U_2 = 8.94 (1188 + 14) - (1188 * 8.94) / 14

U_2 = 181.2 m/s or 405 mph

Clearly these momentum equations can't correctly workout these angled collisions when the mass ratios are significantly different.

Any view points or suggestions greatly appreciated.

 

[MarkOlwen]

This post may also in time help others!

Think of an "Intersection" and assume the traffic lights are malfunctioning. All traffic should give way and stop if necessary.

A car of kerb weight 1188 kg approaches the intersection and notices the traffic lights are inoperative. The car driver looks both ways (its dark at night) the streets are not brillinantly lit, however after starting to move off to the right, driving approximately 20 mph, an E bike runs straight into the nearside A post, swinging round approximately 90 degrees and his pedal collides with the door skin and tears it.

Legal E bikes can have a top speed of 15.5 mph, and it is assumed the E bike is travelling at that speed at the point of collision!

Looking at the damage and Momentum equations, the mass ratios are significantly different and it does not appear to be possible to do the math!

Lets say the E bike is U_1

Then...

U_1 = V (m_1 + m_2) - (m_2 * U_2) / m_1

The E bike is assumed to be travelling at 15.5 mph, so

U_1 = 6.93 (11.88 + 14) - (14 * 8.94) / 1188

U_1 = 6.91 m/s or 15.5 mph

Up to now to me that actually proves nothing I did not already assume.

So, lets look at the car as U_2...

U_2 = V (m_1 + m_2) - (m_1 * U_1) / m_2

U_2 = 8.94 (1188 + 14) - (1188 * 8.94) / 14

U_2 = 181.2 m/s or 405 mph

Clearly these momentum equations can't correctly workout these angled collisions when the mass ratios are significantly different.


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Any view points or suggestions greatly appreciated.

You’re running into problems because you’re applying 1-D, perfectly inelastic momentum equations to a 2-D angled collision, and that simply doesn’t work here—especially with such an extreme mass ratio.

A few key points:

1. Momentum must be conserved vectorially, not as a single scalar. You need separate x/y components based on approach angles.
2. This was not a perfectly inelastic collision (the bike didn’t stick to the car), so those equations aren’t applicable anyway.
3. Damage and rotation of the bike are dominated by impulse, contact geometry, and torque, not by transferring the car’s velocity to the bike.
4. With a 1188 kg car vs ~14 kg bike, the car’s velocity change is effectively ~0, so back-calculating speeds from momentum alone will always give nonsense results (like 400 mph).