A 5 kg ball is moving 4m/s to the right when it collided least ally with a 2 kg ball moving at 6 m/s to the left. After the collision, the 5 kg ball is moving .8 m/s to the right. What is the velocity of the 2 kg ball?
let's call right positive
momentum is conserved
(5 * 4) - (2 * 6) = (5 * .8) + (2 * v)
8 = 4 + 2v
To solve this problem, we can use the principle of conservation of linear 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 given by the product of its mass and velocity. Mathematically, momentum (p) can be calculated as p = m * v, where m is the mass and v is the velocity.
Let's denote the velocity of the 2 kg ball after the collision as v_2.
Before the collision:
Momentum of the 5 kg ball = 5 kg * 4 m/s = 20 kg m/s (to the right)
Momentum of the 2 kg ball = 2 kg * (-6 m/s) = -12 kg m/s (to the left)
Total momentum before the collision = 20 kg m/s - 12 kg m/s = 8 kg m/s (to the right)
After the collision:
Momentum of the 5 kg ball = 5 kg * 0.8 m/s = 4 kg m/s (to the right)
Momentum of the 2 kg ball = 2 kg * v_2 m/s (to the left)
Total momentum after the collision = 4 kg m/s - 2 kg * v_2 m/s
According to the conservation of linear momentum, the total momentum before the collision is equal to the total momentum after the collision:
8 kg m/s = 4 kg m/s - 2 kg * v_2 m/s
To solve this equation for v_2, we can rearrange it:
8 kg m/s = 4 kg m/s - 2 kg * v_2 m/s
2 kg * v_2 m/s = 4 kg m/s - 8 kg m/s
2 kg * v_2 m/s = -4 kg m/s
v_2 m/s = -4 kg m/s / 2 kg
v_2 m/s = -2 m/s
Therefore, the velocity of the 2 kg ball after the collision is -2 m/s (to the left).
To find the velocity of the 2 kg ball after the collision, 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 can be calculated by multiplying its mass by its velocity. So, let's calculate the initial momentum before the collision:
Initial momentum of the 5 kg ball = mass of the 5 kg ball * velocity of the 5 kg ball
= 5 kg * 4 m/s = 20 kg·m/s to the right (since the velocity is positive)
Initial momentum of the 2 kg ball = mass of the 2 kg ball * velocity of the 2 kg ball
= 2 kg * (-6 m/s) = -12 kg·m/s to the left (since the velocity is negative)
The negative sign indicates that the direction of velocity is towards the left.
Now let's calculate the total momentum before the collision:
Total momentum before the collision = momentum of the 5 kg ball + momentum of the 2 kg ball
= 20 kg·m/s to the right + (-12 kg·m/s) to the left
= 20 - 12 kg·m/s = 8 kg·m/s to the right
Since momentum is conserved, the total momentum after the collision will also be equal to 8 kg·m/s to the right.
Now, we know the mass of the 2 kg ball after the collision, which is still 2 kg. Let's represent the velocity of the 2 kg ball after the collision as v.
So, the momentum of the 2 kg ball after the collision can be calculated as:
Momentum of the 2 kg ball after the collision = mass of the 2 kg ball * velocity of the 2 kg ball
= 2 kg * v
Now, using the principle of momentum conservation, we can write the equation:
Total momentum after the collision = Momentum of the 5 kg ball after the collision + Momentum of the 2 kg ball after the collision
8 kg·m/s to the right = 5 kg * 0.8 m/s to the right + 2 kg * v
Simplifying the equation:
8 kg·m/s = 4 kg·m/s + 2 kg * v
Rearranging the equation:
2 kg * v = 8 kg·m/s - 4 kg·m/s
2 kg * v = 4 kg·m/s
Finally, dividing both sides of the equation by 2 kg, we can find the velocity of the 2 kg ball after the collision:
v = 4 kg·m/s / 2 kg
v = 2 m/s
Therefore, the velocity of the 2 kg ball after the collision is 2 m/s to the right.