How Do Coefficients of Restitution Affect Collision Outcomes?

[madmax2006]

Homework Statement

The driver of a 3850 lb Pontiac traveling East at 32 miles/hr has a collision with a 3100 lb Toyota traveling East at 24 miles/hr. The coefficient of restitution is .27. Find:
i) The final speed of the Pontiac after the collision
ii) The final speed of the Toyota after the collision

3850lb = 1744kg
3100lb = 1404kg
32 miles/hr = 46.93 ft/s
24 miles/hr = 35.2 ft/s
Cr = .27

Homework Equations

I'm attempting to solve i) and ii) using the equation:

The Attempt at a Solution

I need to do the work in ft/s & kg



Appx - 40.26 ft/s for m₁^'
Appx - 43.45 ft/s for m₂^'


Does it look right for this type of problem?

iii) The kinetic energy lost in the collision

KE = (1/2)(m)(v² )

KE (m₁) = (1/2)(1744kg)(14.3m/s)²
KE (m₁^') = (1/2)(1744kg)(12.27m/s)²
KE (m₂) = (1/2)(1404kg)(10.73m/s)²
KE (m₂^') = (1/2)(1404kg)(13.24m/s)²

KE (m₁) appx = 178315
KE (m₁^') appx = 131644
KE (m₂) appx = 80823
KE (m₂^') appx = 123058

(178315+80823) - (131644+123058)

4436 Joules lost :)

iv) Suppose the cars locked together during the collision. Find the final speed of the 2 cars after collision for this case

1744kg*46.93ft/s+1404kg*35.2ft/s
3148kg

= 41.7 ft/s

 

[Redbelly98]

Looks good. I haven't checked your arithmetic in detail, but your method looks sound.

 

[kerimek]

Your calculations for i) and ii) look correct for this type of problem. You have correctly used the equation for conservation of momentum, taking into account the coefficient of restitution to determine the final velocities of each car.

For iii), your calculations for the kinetic energy lost in the collision are also correct. This is an important quantity to consider in collisions, as it represents the energy that is dissipated or lost during the collision.

For iv), you have correctly used the concept of conservation of momentum to determine the final velocity of the two cars if they were to lock together during the collision. This scenario would result in a lower final velocity compared to the previous scenario, where the cars rebounded after the collision.

Overall, your approach to solving this problem is sound and your calculations are correct. Keep in mind that in real-life situations, there may be other factors at play that could affect the outcome of a collision, such as air resistance or friction. These factors would need to be taken into account for a more accurate analysis.