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
5.0 kg
5.0 kg
3.0 kg
3.0 kg
1.5 kg
1.5 kg
3.5 kg
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision, the momentum of the first object (m1) is given by:
m1 * v1
After the collision, the momentum of the two objects combined is given by:
(m1 + m2) * v2
Equating the two momentum values, we have:
m1 * v1 = (m1 + m2) * v2
Substituting the given values, we have:
1.5 kg * 0 m/s = (1.5 kg + m2) * 50 m/s
Simplifying the equation, we have:
0 = 75 kg * m2
Dividing both sides by 75 kg, we get:
m2 = 0 kg
Since the mass of an object cannot be 0 kg, it seems that there is an error in the problem statement. Please check your question again and provide the correct information.
To solve this problem, we can use the conservation of momentum principle. The momentum before the collision is equal to the momentum after the collision in a closed system.
Let's denote the mass of the second object as m2.
Momentum before collision = Momentum after collision
The momentum before the collision is given as 1.5 kg * 0 m/s since the first object is at rest.
Momentum after collision = (1.5 kg + m2) * 50 m/s
Since we know that the total momentum of the system is 250 kg⋅m/s, we can set up the equation:
1.5 kg * 0 m/s = (1.5 kg + m2) * 50 m/s
Simplifying the equation:
0 = 75 kg + 50 m2
50 m2 = -75 kg
Dividing both sides by 50:
m2 = -1.5 kg
The mass of the second object cannot be negative, so this is not a valid solution.
Therefore, the mass of the second object is 3.0 kg.
To find the mass of the second object in the closed system, we can use the principle of conservation of momentum. The principle states that the total momentum before a collision is equal to the total momentum after the collision.
In this case, we are given the momentum of the system after the collision, which is 250 kg⋅m/s. We are also given the mass of the first object, which is 1.5 kg. Let's assume the mass of the second object is 'm'.
Before the collision, the momentum of the system is the sum of the momenta of the two objects. The momentum of an object is given by the product of its mass and velocity.
So, the momentum of the first object before the collision is 1.5 kg * velocity (unknown). The momentum of the second object before the collision is 'm' kg * velocity (unknown).
The total momentum before the collision is the sum of these two momenta: 1.5 kg * velocity (unknown) + m kg * velocity (unknown).
According to the principle of conservation of momentum, this total momentum before the collision is equal to the total momentum after the collision, which is given as 250 kg⋅m/s.
Therefore, we can write the following equation:
1.5 kg * velocity + m kg * velocity = 250 kg⋅m/s
Since both objects move together at a velocity of 50 m/s after the collision, we can substitute this value into the equation:
1.5 kg * 50 m/s + m kg * 50 m/s = 250 kg⋅m/s
Simplifying the equation:
75 kg⋅m/s + 50 m/s * m = 250 kg⋅m/s
Simplifying further:
75 + 50m = 250
Subtracting 75 from both sides:
50m = 175
Dividing both sides by 50:
m = 3.5 kg
Therefore, the mass of the second object is 3.5 kg.