a ball with a mass of 1.50 kg traveling + 2.00 m/s collides with a stationary ball with a mass of 1.00 kg. After the collision, the velocity of the 1.50 kg ball is + 0.40 m/s. What is the velocity of the 1.00 kg ball after the collision?
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To solve this problem, we can use 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.
First, let's calculate the initial momentum before the collision:
Initial momentum = mass * velocity
Initial momentum of the 1.50 kg ball = 1.50 kg * 2.00 m/s = 3.00 kg·m/s
Initial momentum of the 1.00 kg ball = 1.00 kg * 0 m/s (since it is stationary) = 0 kg·m/s
The total initial momentum before the collision is the sum of the individual momenta:
Total initial momentum = 3.00 kg·m/s + 0 kg·m/s = 3.00 kg·m/s
Now, let's calculate the final momentum after the collision:
Final momentum = mass * velocity
Final momentum of the 1.50 kg ball = 1.50 kg * 0.40 m/s = 0.60 kg·m/s
Final momentum of the 1.00 kg ball = 1.00 kg * v (let's assume the velocity of the 1.00 kg ball after the collision is v)
The total final momentum after the collision is the sum of the individual momenta:
Total final momentum = 0.60 kg·m/s + 1.00 kg * v
According to the conservation of momentum principle:
Total initial momentum = Total final momentum
3.00 kg·m/s = 0.60 kg·m/s + 1.00 kg * v
Now, let's solve for v:
2.40 kg·m/s = 1.00 kg * v
v = 2.40 kg·m/s / 1.00 kg
v = 2.40 m/s
Therefore, the velocity of the 1.00 kg ball after the collision is + 2.40 m/s.
To find the velocity of the 1.00 kg ball after the collision, we can use the conservation of momentum principle. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The formula for momentum is given by:
Momentum = mass × velocity
Let's denote the velocity of the 1.00 kg ball after the collision as v2. Now, let's set up the momentum equation using the given information:
Before collision:
Momentum1 = (mass1 × velocity1) + (mass2 × velocity2)
After collision:
Momentum2 = (mass1 × velocity1') + (mass2 × velocity2')
In this equation, momentum1 and momentum2 represent the total momentum before and after the collision, respectively.
Given:
Mass1 = 1.50 kg
Velocity1 = +2.00 m/s
Velocity1' = +0.40 m/s
Mass2 = 1.00 kg
Velocity2 = ? (to be determined)
Let's substitute these values into the momentum equation:
(1.50 kg × 2.00 m/s) + (1.00 kg × Velocity2) = (1.50 kg × 0.40 m/s) + (1.00 kg × Velocity2')
Now, we can solve for Velocity2 by rearranging the equation:
1.50 kg × 2.00 m/s + 1.00 kg × Velocity2 = 1.50 kg × 0.40 m/s + 1.00 kg × Velocity2'
Subtracting 1.50 kg × 0.40 m/s from both sides, we get:
1.50 kg × 2.00 m/s + 1.00 kg × Velocity2 - 1.50 kg × 0.40 m/s = 1.00 kg × Velocity2'
Simplifying further:
3.00 kg·m/s + 1.00 kg × Velocity2 - 0.60 kg·m/s = 1.00 kg × Velocity2'
Combining like terms and rearranging:
1.00 kg × Velocity2 - 0.60 kg·m/s = 1.00 kg × Velocity2' - 3.00 kg·m/s
1.00 kg × Velocity2 - 1.00 kg × Velocity2' = 3.00 kg·m/s - 0.60 kg·m/s
Now, we can substitute the given value of Velocity1' (0.40 m/s) into the equation:
1.00 kg × Velocity2 - 1.00 kg × 0.40 m/s = 3.00 kg·m/s - 0.60 kg·m/s
1.00 kg × Velocity2 - 0.40 kg·m/s = 2.40 kg·m/s
Now, we can solve for Velocity2:
1.00 kg × Velocity2 = 2.40 kg·m/s + 0.40 kg·m/s
1.00 kg × Velocity2 = 2.80 kg·m/s
Dividing both sides of the equation by 1.00 kg:
Velocity2 = 2.80 kg·m/s / 1.00 kg
Velocity2 = 2.80 m/s
Therefore, the velocity of the 1.00 kg ball after the collision is +2.80 m/s.