a 600 kg toy car moving at 3 m/s collides and hooks up with a 900 kg toy car at restand they move off together. What is their final velocity?
Hint: Total linear momentum is conserved.
M1*Vinitial = (M1 + M2)*Vfinal
600*3 = 1500*Vfinal
Solve for Vfinal
smn x
To find the final velocity of the two cars after the collision, we can use 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
We are given the following information:
Mass of the first car (m1) = 600 kg
Velocity of the first car (v1) = 3 m/s
Mass of the second car (m2) = 900 kg
Initially, the first car is moving, so its momentum is given by:
p1 = m1 * v1
Substituting the values, we have:
p1 = 600 kg * 3 m/s
= 1800 kg·m/s
Now, let's consider the final momentum of both cars together (pf). Since they move off together, their final velocity will be the same.
Therefore, the final momentum (pf) is given by the sum of the individual momenta of the two cars:
pf = p1 + p2
Where:
p2 = m2 * vf
vf = final velocity of both cars (which is the same)
Substituting the values, we have:
pf = 1800 kg·m/s + m2 * vf
Since the total momentum before the collision is equal to the total momentum after the collision, we can set up an equation:
1800 kg·m/s + m2 * vf = pf
Now, let's solve for vf:
1800 kg·m/s + 900 kg * vf = pf
Since the cars were at rest before the collision, the total momentum initially is zero:
1800 kg·m/s + 900 kg * vf = 0
Simplifying the equation:
900 kg * vf = -1800 kg·m/s
Dividing both sides by 900 kg:
vf = -1800 kg·m/s ÷ 900 kg
= -2 m/s
Therefore, the final velocity of both cars after the collision is -2 m/s. The negative sign indicates that they are moving in the opposite direction after the collision.
To find the final velocity of the two toy cars after the collision, we can use 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 (p) of an object is given by the product of its mass (m) and velocity (v). Therefore, the momentum of the 600 kg toy car before the collision is 600 kg * 3 m/s = 1800 kg·m/s.
The momentum of the 900 kg toy car before the collision is 900 kg * 0 m/s (since it is at rest) = 0 kg·m/s.
After the collision, the two cars move off together. Let's assume their final velocity is v_f.
So, according to the conservation of momentum, the total momentum after the collision is (600 kg + 900 kg) * v_f.
Since the total momentum before the collision is equal to the total momentum after the collision, we can set up the equation:
1800 kg·m/s + 0 kg·m/s = (600 kg + 900 kg) * v_f
1800 kg·m/s = 1500 kg * v_f
Now, we can solve for v_f:
v_f = 1800 kg·m/s / 1500 kg
v_f ≈ 1.2 m/s
Therefore, the final velocity of the two toy cars, after colliding and hooking up, is approximately 1.2 m/s.