a 10,000kg boxcar rolling west at 60mph collides with an empty tanker of mass 7000kg sitting at rest on the track. The cars attach and continue to roll west on the track. What is the speed of the connected cars?
To find the speed of the connected cars after the collision, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by its mass multiplied by its velocity. Therefore, we can calculate the momentum of the boxcar and the momentum of the empty tanker before the collision.
Momentum of the boxcar before the collision:
Momentum = mass × velocity = 10,000 kg × 60 mph
Momentum of the empty tanker before the collision:
Momentum = mass × velocity = 7,000 kg × 0 mph (since it is at rest)
The total momentum before the collision is the sum of the individual momenta:
Total momentum before the collision = Momentum of the boxcar + Momentum of the empty tanker
Now, since the cars attach and continue to roll as one mass after the collision, we can consider them as a single object. Let's call the mass of the connected cars "M" and the velocity "V" (which is the speed we want to find).
Using the conservation of momentum principle:
Total momentum before the collision = Total momentum after the collision
(Momentum of the boxcar + Momentum of the empty tanker) = (Mass of connected cars) × (Velocity of connected cars)
Plugging in the values we know:
(10,000 kg × 60 mph) + (7,000 kg × 0 mph) = M × V
We need to convert the speed from mph to m/s to ensure consistent units. The conversion factor is 0.44704 (1 mph = 0.44704 m/s):
(10,000 kg × 60 mph) + (7,000 kg × 0 mph) = M × (V × 0.44704)
Now, solve the equation for V:
V = ((10,000 kg × 60 mph) + (7,000 kg × 0 mph)) / (M × 0.44704)
Now, plug in the values and calculate:
V = ((10,000 kg × 60 mph) + (7,000 kg × 0 mph)) / (17,000 kg × 0.44704)
V = (600,000 kg * mph) / (17,000 kg × 0.44704)
V = 26.59 mph
Therefore, the speed of the connected cars after the collision is approximately 26.59 mph.