A(n) 1.62 kg sphere makes a perfectly inelastic collision with a second sphere that is initially at rest. The composite system moveswith a speed equal to one-third the originalspeed of the 1.62 kg sphere.
What is the mass of the second sphere
To find the mass of the second sphere, we can use the principle of conservation of momentum. In an inelastic collision, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the mass of the second sphere as m2.
The equation for conservation of momentum is:
(m1 * v1) + (m2 * v2) = (m1 + m2) * vf
Where:
m1 = mass of the first sphere (1.62 kg)
v1 = initial velocity of the first sphere (unknown)
m2 = mass of the second sphere (unknown)
v2 = initial velocity of the second sphere (0 m/s since it is initially at rest)
vf = final velocity of the composite system (1/3 * v1)
We can rearrange the equation to solve for m2:
m1 * v1 = (m1 + m2) * vf - m2 * v2
m1 * v1 = (m1 + m2) * (1/3 * v1) - m2 * 0
m1 * v1 = (m1 + m2) * (1/3 * v1)
3 * m1 * v1 = (m1 + m2) * v1
3 * m1 = m1 + m2
3 * m1 - m1 = m2
2 * m1 = m2
Now we can substitute the value of m1 (1.62 kg) and calculate m2:
2 * 1.62 kg = m2
m2 = 3.24 kg
Therefore, the mass of the second sphere is 3.24 kg.
To find the mass of the second sphere, we can use the principle of conservation of momentum.
The equation for conservation of momentum in a one-dimensional collision is:
m1 * v1 = (m1 + m2) * v2
Where:
m1 = mass of the first sphere = 1.62 kg
v1 = original speed of the first sphere
m2 = mass of the second sphere (unknown)
v2 = speed of the composite system after collision
Given that the composite system moves with a speed equal to one-third the original speed of the 1.62 kg sphere, we have:
v2 = (1/3) * v1
Substituting this value into the conservation of momentum equation:
m1 * v1 = (m1 + m2) * [(1/3) * v1]
Simplifying the equation:
v1 cancels out on both sides:
m1 = (m1 + m2) / 3
Multiplying both sides by 3:
3 * m1 = m1 + m2
2 * m1 = m2
Substituting the given value for m1:
2 * 1.62 kg = m2
m2 = 3.24 kg
Therefore, the mass of the second sphere is 3.24 kg.