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.