Answer:
The coefficient of friction between the cars and the road is 0.859.
Explanation:
The two cars collide each other inelastically, then we can determine the resulting velocity by the Principle of Momentum Conservation:
(1)
Where:
,
- Masses of the cars, in kilograms.
,
- Initial velocities of the cars, in meters per second.
- Velocity of the resulting system, in meters per second.
If we know that ,
,
and
, then the velocity of the resulting system:
By Principle of Energy Conservation and Work-Energy Theorem, we understand that the initial translational kinetic energy (), in joules, is dissipated due to work done by friction (
), in joules, that is to say:
(2)
(2b)
Where:
- Coefficient of friction, no unit.
- Gravitational acceleration, in meters per square second.
- Travelled distance, in meters.
If we know that ,
and
, then the coefficient of friction is:
The coefficient of friction between the cars and the road is 0.859.