2) Two objects, A and B, initially at rest, are "exploded" apart by the release of a coiled spring that was compressed between them. As they move apart, the velocity of object A is 5 m/s and the velocity of object B is -2 m/s. What is the ratio of the mass of object A to the mass of object B (mA/mB)?
2/5
2/5
To find the ratio of the mass of object A to the mass of object B (mA/mB), we need to consider the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. In this case, the initial momentum of the system is zero since both objects are initially at rest.
Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). Mathematically, momentum is given by the equation p = mv.
Using this equation, we can find the initial momentum (p_initial) of the system:
p_initial = (mass of A * velocity of A) + (mass of B * velocity of B)
Since both objects are initially at rest, their velocities are zero. Therefore, the initial momentum of the system is zero:
0 = (mass of A * 0) + (mass of B * 0)
Simplifying the equation above, we get:
0 = 0 + 0
This equation is true, which confirms the principle of conservation of momentum.
Next, we consider the final momentum (p_final) of the system after the objects move apart. The final momentum is given by:
p_final = (mass of A * velocity of A) + (mass of B * velocity of B)
From the given information, the velocity of object A is 5 m/s, and the velocity of object B is -2 m/s. However, to ensure the equation is balanced, we need to use the absolute value of the velocities:
p_final = (mass of A * 5) + (mass of B * 2)
Since the initial momentum is zero and the final momentum is determined by the masses and velocities, we can equate the two:
0 = (mass of A * 5) + (mass of B * 2)
Rearranging the equation:
(mass of A * 5) = -(mass of B * 2)
Now, we can divide both sides of the equation by 2:
(mass of A * 5) / 2 = -mass of B
Finally, to find the ratio of mA/mB, we divide both sides by the mass of B:
(mass of A * 5) / (2 * mass of B) = -1
Simplifying the equation, we get:
mass of A / mass of B = -1/5
Therefore, the ratio of the mass of object A to the mass of object B (mA/mB) is -1/5.
Write an equation that says the final momentum is zero. Zero was also the initial momentum, and it stays the same.
0 = mA*5 - mB*2
Solve for mA/mB