A 2200 kg car traveling at 8.7 m/s collides with a 2750 kg car that is initially at rest at the stoplight. The cars stick together and move 2.00 m before friction causes them to stop. Determine the coefficient of kinetic friction between the cars and the road, assuming that the negative acceleration is constant and that all wheels on both cars lock at the time of impact.
To determine the coefficient of kinetic friction between the cars and the road, we need to follow a step-by-step approach:
Step 1: Calculate the total momentum before the collision.
Momentum is defined as the product of mass and velocity. The total momentum before the collision can be calculated by adding up the individual momenta of the cars.
Momentum of the first car = mass × velocity = 2200 kg × 8.7 m/s
Momentum of the second car = mass × velocity = 2750 kg × 0 m/s (since the second car is initially at rest)
Total momentum before the collision = momentum of first car + momentum of second car
Step 2: Calculate the total momentum after the collision.
Since the cars stick together and move as one unit after the collision, the total momentum after the collision is equal to the total momentum before the collision.
Total momentum after the collision = Total momentum before the collision
Step 3: Calculate the net force acting on the cars.
The net force acting on the cars is responsible for the deceleration and eventual stop. It can be calculated using Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.
Net force = mass × acceleration
Step 4: Calculate the distance traveled by the cars before stopping.
The cars travel a distance of 2.00 m before they come to a stop.
Step 5: Calculate the frictional force acting on the cars.
The frictional force can be calculated using the formula: Frictional force = coefficient of kinetic friction × normal force
The normal force is equal to the weight of the cars in this case, since the cars are on a flat road surface.
Step 6: Calculate the coefficient of kinetic friction.
Using the formula for frictional force, we can rearrange it to solve for the coefficient of kinetic friction:
coefficient of kinetic friction = frictional force / normal force
By following these steps, we can calculate the coefficient of kinetic friction between the cars and the road.