In a closed system, an object with a mass of 1.5 kg
collides with a second object. The two objects then move together at a velocity of 50 m/s . The total momentum of the system is 250 kg⋅m/s . What is the mass of the second object? (1 point)
Responses
3.5 kg
3.5 kg
3.0 kg
3.0 kg
5.0 kg
5.0 kg
1.5 kg
To calculate the mass of the second object, we can use the conservation of momentum principle, which states that the total momentum before the collision is equal to the total momentum after the collision in a closed system.
Let's denote the mass of the second object as m2. We know that the total momentum before the collision is 250 kg·m/s and that the total mass of the two objects is 1.5 kg + m2.
Using the equation for momentum (momentum = mass × velocity), we can set up the equation:
1.5 kg × 0 m/s + m2 × 0 m/s = (1.5 kg + m2) × 50 m/s
Simplifying the equation:
0 kg·m/s + 0 kg·m/s = (1.5 kg + m2) × 50 m/s
0 = (1.5 kg + m2) × 50 m/s
To solve for m2, we can divide both sides of the equation by 50 m/s:
0 / 50 m/s = (1.5 kg + m2)
0 = 1.5 kg + m2
Subtracting 1.5 kg from both sides of the equation:
0 - 1.5 kg = m2
m2 = -1.5 kg
Since mass cannot be negative, this solution is invalid. Therefore, the mass of the second object must be one of the given valid options, 3.5 kg, 3.0 kg, 5.0 kg, or 1.5 kg.
The correct answer based on the information given is 3.5 kg.