A 13 g toy car moving to the right at 22 cm/s
has a head-on nearly elastic collision with a
22 g toy car moving in the opposite direction
at 30 cm/s. After colliding, the 13 g car moves
with a velocity of 43 cm/s to the left.
Find the speed of the second car after the
collision.
Answer in units of cm/s
M1*V1 + M2*V2 = M1*(-0.43) + M2*V.
0.13*0.22+0.22*(-0.30)=-0.43*0.13 + 0.22V.
V = ?
Multiply your answer by 100 to convert to cm/s.
To find the speed of the second car after the collision, we can use the law of conservation of momentum. The law states that the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity.
Let's denote the velocity of the second car after the collision as v2.
Before the collision, the total momentum is given by:
momentum1 + momentum2 = 0
momentum1 = 13 g * 22 cm/s
momentum2 = 22 g * 30 cm/s
momentum1 + momentum2 = 0
(13 g * 22 cm/s) + (22 g * 30 cm/s) = 0
Now, let's calculate the total momentum after the collision:
momentum1' + momentum2' = 0
momentum1' = 13 g * (-43 cm/s) (since the 13 g car moves to the left)
momentum2' = (22 g + 13 g) * v2 (since the second car's mass increases by the mass of the first car)
momentum1' + momentum2' = 0
(13 g * -43 cm/s) + ((22 g + 13 g) * v2) = 0
Now, we can solve for v2:
(13 g * -43 cm/s) + ((22 g + 13 g) * v2) = 0
-559 g * cm/s + (35 g * v2) = 0
35 g * v2 = 559 g * cm/s
v2 = (559 g * cm/s) / (35 g)
v2 ≈ 15.97 cm/s
Therefore, the speed of the second car after the collision is approximately 15.97 cm/s.
To find the speed of the second car 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. So, the momentum of the first car before the collision is given by:
momentum1_before = mass1 * velocity1_before
Substituting the given values:
mass1 = 13 g = 0.013 kg
velocity1_before = 22 cm/s
momentum1_before = 0.013 kg * 22 cm/s
Similarly, the momentum of the second car before the collision is given by:
momentum2_before = mass2 * velocity2_before
Substituting the given values:
mass2 = 22 g = 0.022 kg
velocity2_before = -30 cm/s (opposite direction)
momentum2_before = 0.022 kg * (-30 cm/s)
Now, since the collision is nearly elastic, the total momentum before the collision is equal to the total momentum after the collision. Therefore:
momentum1_before + momentum2_before = momentum1_after + momentum2_after
Substituting the values we have, and let's say the velocity of the second car after the collision is v2_after:
(0.013 kg * 22 cm/s) + (0.022 kg * (-30 cm/s)) = (0.013 kg * (-43 cm/s)) + (0.022 kg * v2_after)
Now we can solve this equation to find the value of v2_after, which will give us the speed of the second car after the collision.