In a collision, Object 1 moving to the right with momentum
|
p
1
i
|
=
25
kg-m/s collides with Object 2 moving to the left with momentum
|
p
2
i
|
=
35
kg-m/s.

After the collision Object 1 moves to the left with momentum
|
p
1
f
|
=
10
kg-m/s.

What is
|
p
2
f
|
, the magnitude of the final momentum of Object 2?

(a)
50 kg-m/s

(b)
20 kg-m/s

(c)
0 kg-m/s

To solve for the final momentum of Object 2 (\(p_{2f}\)), we can use the principle of conservation of momentum. The total momentum before the collision must equal the total momentum after the collision, assuming there are no external forces.

### Step 1: Write the conservation of momentum equation:
\[
p_{1i} + p_{2i} = p_{1f} + p_{2f}
\]
Where:
- \(p_{1i} = 25 \, \text{kg·m/s}\) (initial momentum of Object 1)
- \(p_{2i} = -35 \, \text{kg·m/s}\) (initial momentum of Object 2, negative because it’s moving to the left)
- \(p_{1f} = -10 \, \text{kg·m/s}\) (final momentum of Object 1, negative because it's now moving to the left)
- \(p_{2f}\) is what we want to find.

### Step 2: Solve for \(p_{2f}\)
Using the conservation of momentum equation:
\[
25 \, \text{kg·m/s} - 35 \, \text{kg·m/s} = -10 \, \text{kg·m/s} + p_{2f}
\]
Simplifying:
\[
-10 \, \text{kg·m/s} = -10 \, \text{kg·m/s} + p_{2f}
\]
\[
p_{2f} = 0 \, \text{kg·m/s}
\]

Thus, the magnitude of the final momentum of Object 2 is:
\[
\boxed{0 \, \text{kg·m/s}}
\]
This corresponds to option **(c) 0 kg-m/s**.

Would you like further explanation or details?

Here are 5 related questions:
1. What conditions must hold true for momentum to be conserved in a collision?
2. What is the difference between elastic and inelastic collisions in terms of momentum and energy?
3. How do we calculate the velocities of objects after a collision from their momentum?
4. In what situations would the final momentum of both objects be zero?
5. How can the impulse-momentum theorem be applied in this scenario?

**Tip:** Remember that momentum is a vector quantity, so direction is important when solving problems involving collisions.

In a collision, Object 1 moving to the right with momentum |p1i| = 25 kg-m/s collides with Object 2 moving to the left with momentum |p2i| = 35 kg-m/s. After the collision Object 1 moves to the left with momentum |p1f| = 10 kg-m/s. What is |p2f|, the magnitude of the final momentum of Object 2? (a) 50 kg-m/s (b) 20 kg-m/s (c) 0 kg-m/s

Learn how to solve a collision problem using the conservation of momentum principle. This problem involves calculating the final momentum of Object 2 after a collision with given initial and final momentum values. Suitable for students in Grades 9-12.

Math Problem Statement

In a collision, Object 1 moving to the right with momentum | p 1 i |

25 kg-m/s collides with Object 2 moving to the left with momentum | p 2 i |

After the collision Object 1 moves to the left with momentum | p 1 f |

Solution

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