A 4-kg object moving 12 m/s in the positive x direction has a one-dimensional elastic collision with an object (mass = M) initially at rest. After the collision the object of unknown mass has a velocity of 6.0 m/s in the positive x direction. What is M
To find the mass of the second object (M), we can use the principle of conservation of momentum. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.
Before the collision:
The momentum of the 4-kg object is 4 kg * 12 m/s = 48 kg⋅m/s, since it is initially moving at a velocity of 12 m/s.
Since the second object is initially at rest, its momentum is 0 kg⋅m/s.
After the collision:
The 4-kg object still has a momentum, which is now 4 kg * 6 m/s = 24 kg⋅m/s, since its velocity is now 6 m/s.
The second object, with mass M, now has a momentum of M kg * 6 m/s = 6M kg⋅m/s.
Since momentum is conserved, we can set up the equation:
Before collision momentum = After collision momentum
48 kg⋅m/s + 0 kg⋅m/s = 24 kg⋅m/s + 6M kg⋅m/s
Simplifying the equation:
48 kg⋅m/s = 24 kg⋅m/s + 6M kg⋅m/s
Subtracting 24 kg⋅m/s from both sides:
24 kg⋅m/s = 6M kg⋅m/s
Dividing both sides by 6 kg⋅m/s:
4 = M
Therefore, the mass of the second object (M) is 4 kg.