Finding initial speed in inelastic collision with friction

[formulajoe]

A car weighing 900 kg is waiting at a stop sign. A car weighing 1200 kg hits the oter car. The cars move .76 m after the collision. The coefficient of friction between the sliding tires and the pavement is .92. I need to find the speed of the car right before the collision.
I don't know what to use. Conservation of momentum doesn't work because I need at least one of the velocities.

 

[arcnets]

formulajoe,
I think conservation of momentum is the right idea. I think you got to use it.
You got to find the final momentum. The idea is that the cars stick together after collision. So the final momentum is $(m_1 + m_2)v_{final}$. You got to find $v_{final}$.
You can do that. The cars are decelerated by a constant force of friction. This force is $F = .92(m_1 + m_2)g$. From $F$ and $d = .76m$ you can calculate $v_{final}$.

 

[M98Ranger]

To solve this problem, you can use the conservation of energy principle. First, calculate the total kinetic energy of the cars before the collision using the formula KE = 1/2 * m * v^2, where m is the mass of the car and v is the velocity. Since the car at the stop sign is not moving, its initial kinetic energy will be zero.

Next, use the coefficient of friction and the distance the cars moved after the collision to calculate the work done by friction on the cars. This can be done using the formula W = F * d, where F is the force of friction and d is the distance. The force of friction can be calculated using the coefficient of friction and the weight of the cars (F = u * m * g).

Now, we can equate the initial kinetic energy to the final kinetic energy (after the collision) minus the work done by friction. This will give us an equation to solve for the initial velocity of the second car (since the first car is at rest). Once we have the initial velocity of the second car, we can use the conservation of momentum principle (m1v1 + m2v2 = m1v1' + m2v2') to find the initial velocity of the first car.

I hope this helps you solve the problem. Remember to always double check your units and make sure they are consistent throughout the calculations. Good luck!