To determine the mass of the second body involved in the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant before and after a collision.
Mathematically, the conservation of momentum can be expressed as follows:
m1 * v1_initial + m2 * v2_initial = m1 * v1_final + m2 * v2_final
Where: m1 = mass of the first body (0.5 kg) v1_initial = initial velocity of the first body (15 m/s) m2 = mass of the second body (unknown, to be determined) v2_initial = initial velocity of the second body (-4.5 m/s, since it is moving in the opposite direction) v1_final = final velocity of the first body (to be determined) v2_final = final velocity of the second body (to be determined)
In this case, since the bodies collide and stick together, the final velocities can be considered the same for both bodies.
Using the given values, we can rearrange the equation and solve for m2:
m1 * v1_initial + m2 * v2_initial = (m1 + m2) * v_final
(0.5 kg) * (15 m/s) + m2 * (-4.5 m/s) = (0.5 kg + m2) * v_final
7.5 kg·m/s - 4.5 m2 kg·m/s = (0.5 kg + m2) * v_final
7.5 kg·m/s - 4.5 m2 kg·m/s = 0.5 kg·v_final + m2·v_final
Simplifying the equation, we have:
7.5 kg·m/s - 4.5 m2 kg·m/s = (0.5 kg + m2) * v_final
7.5 kg·m/s - 4.5 m2 kg·m/s = (0.5 kg + m2) * v_final
Let's solve for m2:
7.5 kg·m/s - 4.5 m2 kg·m/s = (0.5 kg + m2) * v_final
7.5 kg·m/s - 4.5 m2 kg·m/s = 0.5 kg·v_final + m2·v_final
Since the masses of the bodies are in kilograms and the velocities are in meters per second, the units on both sides of the equation are consistent.
To find the value of m2, we would need additional information, such as the final velocity (v_final) or any other known values related to the collision.