A 1200.0kg car is moving east at 30.0 m/s and collides with a 3600.0 kg truck moving at 20 m/s in a direction 60 degrees north of east.The vehicles interlock and move off together.Find their common velocity.
Use the law of conservation of momentum. The resultant momentum of the two cars before collision equals the final momentum of the interlocked vehicles, which have a combined mass of 4800 kg.
If +y is north and +x is the east direction, the initial momentum has components
Px = (1200 * 30) + (3600 * 20 cos 60)
and
Py = 3600 * 20 sin 60
If Vx and Vy are the velocity componensts of the interlocked vehicles,
4800 Vx = Px
4800 Vy = Py
Solve for Vx and V
d12
To solve for the common velocity of the interlocked vehicles, we can use the law of conservation of momentum. The initial momentum of the vehicles is equal to the final momentum of the interlocked vehicles.
The initial momentum in the x-direction can be calculated as:
Px = (mass of car * velocity of car) + (mass of truck * velocity of truck * cos(angle))
Where,
mass of car = 1200.0 kg
velocity of car = 30.0 m/s
mass of truck = 3600.0 kg
velocity of truck = 20 m/s
angle = 60 degrees
Substituting the values:
Px = (1200 * 30) + (3600 * 20 * cos(60))
Simplifying:
Px = 36000 + 72000 * 0.5
Px = 36000 + 36000
Px = 72000 kg*m/s
The initial momentum in the y-direction can be calculated as:
Py = mass of truck * velocity of truck * sin(angle)
Substituting the values:
Py = 3600 * 20 * sin(60)
Simplifying:
Py = 3600 * 20 * (√3 / 2)
Py = 72000 * √3
Py = 72000√3 kg*m/s
Now, we can use the law of conservation of momentum:
The final momentum in the x-direction can be calculated as:
4800 * Vx = Px
Simplifying:
Vx = Px / 4800
Vx = 72000 / 4800
Vx = 15 m/s
The final momentum in the y-direction can be calculated as:
4800 * Vy = Py
Simplifying:
Vy = Py / 4800
Vy = 72000√3 / 4800
Vy = 15√3 m/s
The common velocity of the interlocked vehicles is the resultant velocity:
The magnitude of the velocity can be calculated using the Pythagorean theorem:
V = √(Vx^2 + Vy^2)
Substituting the values:
V = √(15^2 + (15√3)^2)
V = √(225 + 675)
V = √900
V = 30 m/s
Therefore, the common velocity of the interlocked vehicles is 30 m/s.
To solve for the common velocity of the two vehicles after the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
The initial momentum of the two cars in the x-direction can be calculated by multiplying the mass of each car by their respective velocities in the x-direction:
Px = (1200 kg * 30.0 m/s) + (3600 kg * 20.0 m/s * cos(60 degrees))
Here, we multiply the mass of the first car (1200 kg) by its velocity in the x-direction (30.0 m/s). We also multiply the mass of the second car (3600 kg) by its velocity in the x-direction (20.0 m/s) and then multiply by the cos(60 degrees) to account for the angle of 60 degrees north of east.
The initial momentum of the two cars in the y-direction can be calculated by multiplying the mass of the second car by its velocity in the y-direction:
Py = 3600 kg * 20.0 m/s * sin(60 degrees)
Here, we multiply the mass of the second car (3600 kg) by its velocity in the y-direction (20.0 m/s) and then multiply by the sin(60 degrees) to account for the angle of 60 degrees north of east.
Now, let's solve for Vx and Vy:
4800 kg * Vx = Px
4800 kg * Vy = Py
Dividing both equations by 4800 kg gives us:
Vx = Px / 4800 kg
Vy = Py / 4800 kg
Finally, substitute the values of Px and Py into these equations to find Vx and Vy. Once you have both components of the velocity, you can calculate the magnitude and direction of the common velocity using Pythagorean theorem and trigonometry.