7700-kg boxcar traveling 18m/s strikes a second car. The two stick together and move off with a speed of 5.0m/s. What is the mass of the second car?
Use the conservation of momentum equation to solve for the unknown M2.
M1*V1 + M2*V2 = (M1 + M2) Vfinal
V2 = 0 and Vfinal = 5.0 in this case, so
7700*18 = (7700 + M2)*5.0
20020
To solve this problem, we can use the principle of conservation of momentum. The initial momentum of the first boxcar is equal to the combined momentum of the two cars after they stick together.
Given:
Mass of first boxcar (m1) = 7700 kg
Initial velocity of first boxcar (v1) = 18 m/s
Final velocity after collision (vf) = 5.0 m/s
Let's assume the mass of the second car is m2.
Using the principle of conservation of momentum, we can write:
m1 * v1 = (m1 + m2) * vf
Substituting the given values:
7700 kg * 18 m/s = (7700 kg + m2) * 5.0 m/s
Now we can solve for m2:
138600 kg·m/s = (7700 kg + m2) * 5.0 m/s
Divide both sides by 5.0 m/s:
(138600 kg·m/s) / 5.0 m/s = 7700 kg + m2
27600 kg = 7700 kg + m2
Subtract 7700 kg from both sides:
27600 kg - 7700 kg = m2
19900 kg = m2
Therefore, the mass of the second car is 19900 kg.
To find the mass of the second car, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.
Let's denote the mass of the second car as m2.
Before the collision:
The momentum of the first car is given by momentum1 = mass1 * velocity1.
The momentum of the second car is given by momentum2 = mass2 * velocity2.
Given:
Mass of the first car (m1) = 7700 kg
Velocity of the first car (v1) = 18 m/s
Velocity of the combined cars after collision (v_combined) = 5.0 m/s
After the collision:
The combined momentum of the two cars is given by momentum_combined = (m1 + m2) * v_combined.
According to the conservation of momentum, the momentum before and after the collision is equal, so we have:
momentum1 + momentum2 = momentum_combined.
Substituting the values into the equation:
mass1 * velocity1 + mass2 * velocity2 = (mass1 + mass2) * v_combined.
Plugging in the known values:
(7700 kg * 18 m/s) + (mass2 * velocity2) = (7700 kg + mass2) * 5.0 m/s.
Simplifying the equation:
138600 kg·m/s + mass2 * velocity2 = (7700 kg + mass2) * 5.0 m/s.
Expanding the right side:
138600 kg·m/s + mass2 * velocity2 = 38500 kg·m/s + mass2 * 5.0 m/s.
Rearranging the equation to isolate mass2:
mass2 * 5.0 m/s - mass2 * velocity2 = 38500 kg·m/s - 138600 kg·m/s.
Combining like terms:
mass2 * (5.0 m/s - velocity2) = -100100 kg·m/s.
Dividing both sides by (5.0 m/s - velocity2):
mass2 = (-100100 kg·m/s) / (5.0 m/s - velocity2).
Substituting the given value for velocity2:
mass2 = (-100100 kg·m/s) / (5.0 m/s - 5.0 m/s).
Since velocity2 is 5.0 m/s, the denominator becomes zero, resulting in undefined mass2.
Therefore, the mass of the second car cannot be determined with the given information.