A 2 kg ball rolls at 2 m/s toward a 1 kg ball at rest. After the balls collide they stick together and move at _____ m/s.
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To find the final velocity of the balls 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.
Momentum is defined as the product of an object's mass and velocity. The momentum of an object can be calculated using the formula:
Momentum = mass × velocity
For the 2 kg ball rolling at 2 m/s, its momentum before the collision is:
Momentum1 = mass1 × velocity1
Momentum1 = 2 kg × 2 m/s
Momentum1 = 4 kg⋅m/s
Since the 1 kg ball is at rest, its momentum before the collision is zero:
Momentum2 = mass2 × velocity2
Momentum2 = 1 kg × 0 m/s
Momentum2 = 0 kg⋅m/s
The total momentum before the collision is the sum of the individual momenta:
Total Momentum_before = Momentum1 + Momentum2
Total Momentum_before = 4 kg⋅m/s + 0 kg⋅m/s
Total Momentum_before = 4 kg⋅m/s
After the collision, the balls stick together, meaning they move as a single combined object. Let's denote their combined mass as Mb and their final combined velocity as Vc.
Using the principle of conservation of momentum, we can equate the total momentum before and after the collision:
Total Momentum_before = Total Momentum_after
The total momentum after the collision is given by the combined mass multiplied by the final combined velocity:
Total Momentum_after = Mb × Vc
Therefore, we can rewrite the equation as:
Total Momentum_before = Total Momentum_after
4 kg⋅m/s = Mb × Vc
We know that the total mass after the collision is the sum of the masses of the two balls:
Mb = mass1 + mass2
Mb = 2 kg + 1 kg
Mb = 3 kg
Substituting this value into the equation:
4 kg⋅m/s = 3 kg × Vc
To find the final combined velocity (Vc), we can rearrange the equation as follows:
Vc = (4 kg⋅m/s) / 3 kg
Calculating the value:
Vc = 1.33 m/s
Therefore, after the collision, the balls stick together and move at a velocity of 1.33 m/s.