train car are coupled together by being bumped into one another. suppose two loaded train cars are moving toward one another, the first having a mass of 150000 kg and velocity of 0.30 m/sand the second havin a mass of 110000 kg and a velocity of (-0.12 m/s). what is their final velocity
conservation of momentum;
M1V1+M2V2=(M1+M2)V solve for V
0.122 m/s
To find the final velocity of the two coupled train cars, 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 defined as the product of its mass and velocity. Mathematically, momentum (p) is given by:
p = m * v
Where:
p = momentum
m = mass of the object
v = velocity of the object
Let's calculate the initial momentum (p_initial) of each train car separately:
The initial momentum of the first train car (train car 1) is:
p_initial1 = m1 * v1
= 150000 kg * 0.30 m/s
= 45000 kg⋅m/s
The initial momentum of the second train car (train car 2) is:
p_initial2 = m2 * v2
= 110000 kg * (-0.12 m/s) [Note: The negative sign indicates the opposite direction]
= -13200 kg⋅m/s
Now, since the two train cars are moving towards each other, we can add their respective momenta to get the total initial momentum (ptotal_initial):
ptotal_initial = p_initial1 + p_initial2
= 45000 kg⋅m/s -13200 kg⋅m/s
= 31800 kg⋅m/s
Next, we need to find the total mass of the coupled train cars (mtotal). This is simply the sum of the masses of train car 1 (m1) and train car 2 (m2):
mtotal = m1 + m2
= 150000 kg + 110000 kg
= 260000 kg
Finally, we can calculate the final velocity (v_final) of the coupled train cars using the formula for momentum:
v_final = ptotal_initial / mtotal
= 31800 kg⋅m/s / 260000 kg
= 0.122 m/s (rounded to three decimal places)
Therefore, the final velocity of the coupled train cars is approximately 0.122 m/s.
To find the final velocity of the two train cars after they collide, we can use the principle of conservation of momentum, which states that the total momentum of an isolated system remains constant before and after a collision.
The momentum of an object can be calculated by multiplying its mass by its velocity. Therefore, we need to calculate the initial momentum of each train car separately and then find the total initial momentum. We can then use this total initial momentum to determine the final velocity.
Let's label the first train car as A and the second train car as B.
The initial momentum of train car A (pA) is calculated as the product of its mass (mA) and velocity (vA):
pA = mA * vA
pA = 150000 kg * 0.30 m/s
pA = 45000 kg·m/s
Note: The direction of the velocity for train car A is positive since it is moving in the forward direction.
The initial momentum of train car B (pB) is calculated as the product of its mass (mB) and velocity (vB):
pB = mB * vB
pB = 110000 kg * (-0.12 m/s)
pB = -13200 kg·m/s
Note: The velocity of train car B is negative as it is moving in the opposite direction.
To find the total initial momentum (p𝚺), we simply add the individual momenta of the two train cars:
p𝚺 = pA + pB
p𝚺 = 45000 kg·m/s + (-13200 kg·m/s)
p𝚺 = 31800 kg·m/s
Now that we have the total initial momentum, we can find the final velocity (v𝚺) of the two train cars after the collision.
Using the principle of conservation of momentum, we can equate the total initial momentum to the total final momentum:
p𝚺 = (mA + mB) * v𝚺
v𝚺 = p𝚺 / (mA + mB)
v𝚺 = 31800 kg·m/s / (150000 kg + 110000 kg)
v𝚺 = 31800 kg·m/s / 260000 kg
v𝚺 ≈ 0.1223 m/s
Therefore, the final velocity of the two train cars after the collision is approximately 0.1223 m/s.