A 588.6 kN car moving at 1 km/hr instantaneously collides an stationary 392.40 kg car. If the collision is perfectly inelastic, what is the velocity of the car after collision?
Well, it seems like these cars are having quite the fender bender! Let's calculate the velocity of the car after the collision.
To solve this problem, we'll need to use the principle of conservation of momentum. Since the collision is perfectly inelastic, the two cars will stick together after the collision.
First, let's convert the velocity of the 588.6 kN car from km/hr to m/s. Since there are 1000 meters in a kilometer and 3600 seconds in an hour, we divide 1 km/hr by 3.6 to get the velocity in m/s.
1 km/hr / 3.6 = 0.278 m/s
Now we can calculate the momentum before the collision. Momentum is given by the equation:
Momentum = mass × velocity
For the 588.6 kN car:
Momentum1 = (mass1) × (velocity1)
Momentum1 = (mass1) × (0.278 m/s)
For the stationary car:
Momentum2 = (mass2) × (0 m/s) [since it's stationary]
Now, after the perfectly inelastic collision, the two cars stick together and move as a single unit. Let's call the mass of the combined cars as M' and the velocity after the collision as v'.
The momentum after the collision is given by:
Momentum' = (M') × (v')
Since momentum is conserved, we can set the initial momentum equal to the final momentum:
Momentum1 + Momentum2 = Momentum'
(mass1) × (0.278 m/s) + (mass2) × (0 m/s) = (M') × (v')
Now we can solve for the velocity after the collision (v').
However, it seems like there might be an error in the data. The given mass for the stationary car is extremely large compared to the force exerted by the moving car. This might lead to an unrealistic result. Could you please check and confirm the given values?
To find the velocity of the car after the collision, we need to use the principle of conservation of linear momentum.
Let's denote the initial velocity of the 588.6 kN car as v1 and the initial velocity of the 392.40 kg car as v2. Since the collision is perfectly inelastic, the two cars will stick together after the collision and move with a common final velocity, denoted as vf.
According to the principle of conservation of linear momentum, the total momentum before the collision is equal to the total momentum after the collision:
(m1 * v1) + (m2 * v2) = (m1 + m2) * vf
Where:
m1 = mass of the first car = 588.6 kN
m2 = mass of the second car = 392.40 kg
Converting the units:
m1 = 588.6 * 1000 kg
m2 = 392.40 kg
We are given the initial velocity of the first car (v1) as 1 km/hr. Converting it to m/s:
v1 = (1 km/hr) * (1000 m/km) * (1/3600 hr/s) = 0.2778 m/s
The initial velocity of the second car (v2) is 0 m/s since it is stationary.
We can now plug in the values into the conservation of momentum equation:
((588.6 * 1000 kg) * (0.2778 m/s)) + ((392.40 kg) * (0 m/s)) = ((588.6 * 1000 kg) + (392.40 kg)) * vf
Simplifying:
162999.48 kg*m/s = 581992.40 kg * vf
Dividing both sides by 581992.40 kg:
162999.48 kg*m/s / 581992.40 kg = vf
vf ≈ 0.2802 m/s
Therefore, the velocity of the car after the collision is approximately 0.2802 m/s.
To find the velocity of the car after the collision, we can use the principle of conservation of momentum. In an inelastic collision, the two objects stick together after the collision and move as one.
The principle of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
Now, let's calculate the initial momentum before the collision:
Initial momentum = mass * velocity
The mass of the first car is given as 588.6 kN, but we need to convert it to kg. Assuming you meant 588.6 kg, the initial momentum of the first car is:
Momentum1 = (mass1) * (velocity1)
= (588.6 kg) * (1 km/hr)
Next, let's calculate the initial momentum of the second car, which is stationary:
Momentum2 = (mass2) * (velocity2)
= (392.40 kg) * (0 km/hr) (since the second car is stationary)
Since the collision is perfectly inelastic, the two cars stick together, so they move as one. Therefore, the final velocity of the combined cars after the collision is the same. Let's call this final velocity "Vf."
Now, applying the conservation of momentum:
Initial momentum1 + Initial momentum2 = Final momentum
(588.6 kg * 1 km/hr) + (392.40 kg * 0 km/hr) = ( (588.6 + 392.40) kg) * (Vf)
Simplifying the equation:
588.6 kg * 1 km/hr = (588.6 + 392.40) kg * Vf
588.6 kg * 1 km/hr = 981 kg * Vf
Vf = (588.6 kg * 1 km/hr) / 981 kg
Vf ≈ 0.6 km/hr
Therefore, the approximate velocity of the car after the perfectly inelastic collision is 0.6 km/hr.
change weight of car to kg, by dividing by g.
588.6E3/g * 1km/hr=(588.6E3/g+392.40)V
solve for V.