Two cars, A and B, are traveling along the same route. Car A is traveling at 4.5 m/s and has a mass of
1150 kg. Car B is traveling at 6.7 m/s and has a mass of 1300 kg. If car B gently bumps into car A and
their bumpers lock together, what will be their common velocity then?
Well, that's quite a car collision! It seems like Car B decided to give Car A a little love tap. Since their bumpers lock together, we can consider this as an elastic collision.
To find their common velocity after the collision, we need to apply the law of conservation of momentum. According to this law, the total momentum before the collision should equal the total momentum after the collision.
The momentum of Car A before the collision is given by mass (m) times velocity (v), which is 1150 kg * 4.5 m/s = 5175 kg m/s.
The momentum of Car B before the collision is calculated as mass (m) times velocity (v), which is 1300 kg * 6.7 m/s = 8710 kg m/s.
Adding both momenta together, we get a total momentum before the collision of 5175 kg m/s + 8710 kg m/s = 13885 kg m/s.
Since the cars are locked together after the collision, their combined mass is 1150 kg + 1300 kg = 2450 kg.
Now, to find their common velocity, we divide the total momentum after the collision by the combined mass:
Common Velocity = Total Momentum / Combined Mass
= 13885 kg m/s / 2450 kg
≈ 5.66 m/s
So, after the little bump, Car A and Car B will have a common velocity of approximately 5.66 m/s. They are going to have a hard time untangling themselves!
To find the common velocity of the cars after the collision, we can use the principle of conservation of momentum. The total momentum before the collision should equal the total momentum after the collision.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v): p = m * v.
Let's calculate the momentum of each car before the collision:
Car A momentum (pA) = mass of A (mA) * velocity of A (vA)
Car A momentum (pA) = 1150 kg * 4.5 m/s
Car A momentum (pA) = 5175 kg·m/s
Car B momentum (pB) = mass of B (mB) * velocity of B (vB)
Car B momentum (pB) = 1300 kg * 6.7 m/s
Car B momentum (pB) = 8710 kg·m/s
Since the bumpers of the cars lock together, their total momentum after the collision should be equal to the sum of their individual momenta before the collision.
Total momentum after the collision (pTotal) = pA + pB
pTotal = 5175 kg·m/s + 8710 kg·m/s
pTotal = 13885 kg·m/s
To find the common velocity of the cars after the collision, we divide the total momentum by the combined mass of the cars:
Combined mass of the cars (mTotal) = mass of A (mA) + mass of B (mB)
mTotal = 1150 kg + 1300 kg
mTotal = 2450 kg
Common velocity after the collision (vCommon) = pTotal / mTotal
vCommon = 13885 kg·m/s / 2450 kg
vCommon ≈ 5.66 m/s
Therefore, the common velocity of the cars after the collision will be approximately 5.66 m/s.
To find the common velocity of the two cars after the collision, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity. Thus, the initial momentum (before the collision) of Car A is given by:
Momentum(A) = Mass(A) * Velocity(A)
= 1150 kg * 4.5 m/s
Similarly, the initial momentum of Car B is given by:
Momentum(B) = Mass(B) * Velocity(B)
= 1300 kg * 6.7 m/s
Since the cars lock together after the collision, their combined mass will be the sum of their individual masses:
Total Mass = Mass(A) + Mass(B)
To find the common velocity, we divide the total momentum (which should be conserved) by the total mass:
Common Velocity = Total Momentum / Total Mass
Plugging in the values we have:
Total Momentum = Momentum(A) + Momentum(B)
= (1150 kg * 4.5 m/s) + (1300 kg * 6.7 m/s)
Total Mass = Mass(A) + Mass(B)
= 1150 kg + 1300 kg
Finally, we can calculate the common velocity by dividing the total momentum by the total mass.