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Sagot :
Alright, let's carefully examine the situation step-by-step with the given data and fill in the sentences appropriately.
### Step-by-Step Solution:
1. Determine Initial Conditions:
- Mass of Glider 1 (m1) = 0.5 kg
- Mass of Glider 2 (m2) = 0.8 kg
- Velocity of Glider 1 before collision (v1_before) = 3.00 m/s
- Velocity of Glider 2 before collision (v2_before) = -3.00 m/s
2. Calculate Momenta Before Collision:
- Momentum of Glider 1 before collision (p1_before) = m1 v1_before = 0.5 kg 3.00 m/s = 1.50 kg·m/s
- Momentum of Glider 2 before collision (p2_before) = m2 v2_before = 0.8 kg (-3.00 m/s) = -2.40 kg·m/s
3. Total Momentum Before Collision:
- Total momentum before collision = p1_before + p2_before = 1.50 kg·m/s + (-2.40 kg·m/s) = -0.90 kg·m/s
4. Conditions After Collision:
- Total mass after collision = m1 + m2 = 1.3 kg
- Velocity after collision (v_after) = -0.69 m/s
- Total momentum after collision (from the table) = -0.90 kg·m/s
5. Compare Directions:
After the collision, the gliders move together with a velocity of -0.69 m/s.
- Since the velocity after collision is negative, they travel in the same direction as Glider 1 before the collision (Glider 1 had a positive momentum, meaning it was initially moving in a positive direction before collision).
6. Magnitude of Velocity:
- The magnitude of the post-collision velocity (-0.69) is less than the velocity of Glider 1 before the collision (3.00 m/s).
7. Momentum Comparison:
- The momentum magnitude of Glider 2 before the collision (| -2.40 |) is greater than Glider 1 (| 1.50 |) because its mass is greater.
8. Percent Difference Between Total Momentum Before and After Collision:
- The calculated percent difference was found to be approximately \(3.700743415417187 \times 10^{-14} \%\), which is extremely close to zero, indicating conservation of momentum within a very small error margin.
### Filling in the Sentences:
After colliding, [tex]\( G1 + G2 \)[/tex] travels in a negative direction as [tex]\( G1 \)[/tex] travels before the collision, but at about one-fourth the magnitude in velocity. The initial momentum of [tex]\( G2 \)[/tex] (the magnitude or absolute value) is greater than [tex]\( G1 \)[/tex] because its mass is greater than [tex]\( G1 \)[/tex]. The percent difference between the total momentum before and after the collision is 3.700743415417187 \times 10^{-14} %.
### Step-by-Step Solution:
1. Determine Initial Conditions:
- Mass of Glider 1 (m1) = 0.5 kg
- Mass of Glider 2 (m2) = 0.8 kg
- Velocity of Glider 1 before collision (v1_before) = 3.00 m/s
- Velocity of Glider 2 before collision (v2_before) = -3.00 m/s
2. Calculate Momenta Before Collision:
- Momentum of Glider 1 before collision (p1_before) = m1 v1_before = 0.5 kg 3.00 m/s = 1.50 kg·m/s
- Momentum of Glider 2 before collision (p2_before) = m2 v2_before = 0.8 kg (-3.00 m/s) = -2.40 kg·m/s
3. Total Momentum Before Collision:
- Total momentum before collision = p1_before + p2_before = 1.50 kg·m/s + (-2.40 kg·m/s) = -0.90 kg·m/s
4. Conditions After Collision:
- Total mass after collision = m1 + m2 = 1.3 kg
- Velocity after collision (v_after) = -0.69 m/s
- Total momentum after collision (from the table) = -0.90 kg·m/s
5. Compare Directions:
After the collision, the gliders move together with a velocity of -0.69 m/s.
- Since the velocity after collision is negative, they travel in the same direction as Glider 1 before the collision (Glider 1 had a positive momentum, meaning it was initially moving in a positive direction before collision).
6. Magnitude of Velocity:
- The magnitude of the post-collision velocity (-0.69) is less than the velocity of Glider 1 before the collision (3.00 m/s).
7. Momentum Comparison:
- The momentum magnitude of Glider 2 before the collision (| -2.40 |) is greater than Glider 1 (| 1.50 |) because its mass is greater.
8. Percent Difference Between Total Momentum Before and After Collision:
- The calculated percent difference was found to be approximately \(3.700743415417187 \times 10^{-14} \%\), which is extremely close to zero, indicating conservation of momentum within a very small error margin.
### Filling in the Sentences:
After colliding, [tex]\( G1 + G2 \)[/tex] travels in a negative direction as [tex]\( G1 \)[/tex] travels before the collision, but at about one-fourth the magnitude in velocity. The initial momentum of [tex]\( G2 \)[/tex] (the magnitude or absolute value) is greater than [tex]\( G1 \)[/tex] because its mass is greater than [tex]\( G1 \)[/tex]. The percent difference between the total momentum before and after the collision is 3.700743415417187 \times 10^{-14} %.
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