A 6.0 kg object at rest explodes into two parts. If part A has mass 2.0 kg and a velocity of 18.0 m/s right, what is the velocity of part B?
*The answer is 9 m/s, but I can't seem to get the answer. Any help would be appreciated!*
conserve momentum
6.0 * 0 = 2.0*18.0 + (6.0-2.0)v
Oh, I get it now! Thanks very much for your help!
Sure, I can help you with that!
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum before the explosion is equal to the total momentum after the explosion.
Given:
Mass of the object (m) = 6.0 kg
Mass of part A (m_A) = 2.0 kg
Velocity of part A (v_A) = 18.0 m/s
We need to find the velocity of part B (v_B).
The total momentum before the explosion is zero since the object is at rest:
Total momentum before = 0 kg∙m/s
The total momentum after the explosion is the sum of the individual momenta of part A and part B:
Total momentum after = (m_A * v_A) + (m_B * v_B)
Since we have the values for m_A and v_A, we can solve for m_B * v_B:
0 = (m_A * v_A) + (m_B * v_B)
Substituting the given values, we have:
0 = (2.0 kg * 18.0 m/s) + (m_B * v_B)
Simplifying the equation, we have:
0 = 36.0 kg∙m/s + (m_B * v_B)
Now, we can solve for v_B:
v_B = (-36.0 kg∙m/s) / m_B
We know that the mass of part B (m_B) is equal to the mass of the object (m) minus the mass of part A (m_A):
m_B = m - m_A
m_B = 6.0 kg - 2.0 kg
m_B = 4.0 kg
Substituting this value into the equation for v_B, we have:
v_B = (-36.0 kg∙m/s) / 4.0 kg
v_B = -9.0 m/s
Since velocity is a vector quantity, we take the magnitude of v_B, which is positive 9.0 m/s.
Therefore, the velocity of part B is 9.0 m/s right.
To find the velocity of part B, we can use the principle of conservation of momentum. The total momentum before the explosion should be equal to the total momentum after the explosion.
Before the explosion, the object is at rest, so the total momentum is zero (since momentum is mass times velocity).
After the explosion, the momentum of part A (m1) and part B (m2) should add up to zero:
m1 * v1 + m2 * v2 = 0
Given that the mass of part A (m1) is 2.0 kg and its velocity (v1) is 18.0 m/s to the right, we can substitute these values into the equation:
2.0 kg * 18.0 m/s + m2 * v2 = 0
Now, let's solve for the velocity of part B (v2).
First, multiply the mass and velocity of part A:
36 kg·m/s + m2 * v2 = 0
To isolate the velocity of part B, we need to move the term containing m2 to the other side of the equation:
m2 * v2 = -36 kg·m/s
Divide both sides of the equation by m2 to find v2:
v2 = -36 kg·m/s / m2
Since we know that m1 + m2 = 6.0 kg (the total mass of the object before the explosion), we can substitute m2 as 6.0 kg - 2.0 kg:
v2 = -36 kg·m/s / (6.0 kg - 2.0 kg)
v2 = -36 kg·m/s / 4.0 kg
v2 = -9 m/s
So, the velocity of part B after the explosion is -9 m/s (to the left).