A(n) 3.91 kg sphere makes a perfectly inelastic collision with a second sphere that is
initially at rest. The composite system moves
with a speed equal to one-third the original
speed of the 3.91 kg sphere.
What is the mass of the second sphere?
Answer in units of kg
To solve this problem, we will use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system of objects remains constant before and after a collision, as long as no external forces act on the system.
In this case, we have two spheres: the 3.91 kg sphere with an initial speed, and the second sphere initially at rest.
Let's denote the mass of the second sphere as m2.
Before the collision, the momentum of the 3.91 kg sphere is given by p1 = m1 * v1, where m1 is the mass of the sphere and v1 is its initial speed.
After the collision, the composite system of both spheres moves with a speed equal to one-third the original speed of the 3.91 kg sphere, which we can denote as v_comp.
The momentum of the composite system after the collision is given by p_comp = (m1 + m2) * v_comp.
According to the conservation of momentum, the momentum before the collision should be equal to the momentum after the collision:
p1 = p_comp
m1 * v1 = (m1 + m2) * v_comp
Now, we can substitute the given values into the equation:
3.91 kg * v1 = (3.91 kg + m2) * (1/3) * v1
Simplifying the equation:
3.91 kg = (3.91 kg + m2) / 3
Multiplying both sides by 3 to eliminate the fraction:
11.73 kg = (3.91 kg + m2)
Rearranging the equation to isolate m2:
11.73 kg - 3.91 kg = m2
7.82 kg = m2
Therefore, the mass of the second sphere is 7.82 kg.