A 0.500 kg sphere moving with a velocity given by (2.001 - 3.40 + 1.00k) m/s strikes another sphere of mass 1.50 kg moving with an initial velocity of (-1.00 +2.00 - 3.10k) m/s. (a) The velocity of the 0.500 kg sphere after the collision is (-0.601 +3.00 -8.00k) m/s. Find the final velocity of the 1.50 kg sphere. m/s Identify the kind of collision (elastic, inelastic, or perfectly inelastic). O elastic O inelastic O perfectly inelastic (b) Now assume the velocity of the 0.500 kg sphere after the collision is (-0.2501 + 0.650 - 2.08k) m/s. Find the final velocity of the 1.50 kg sphere. V= m/s Identify the kind of collision. O elastic O inelastic O perfectly inelastic (c) Take the velocity of the 0.500 kg sphere after the collision as (-1.00 +2.601 + ak) m/s. Find the value of a and the velocity of the 1.50 kg sphere after an elastic collision. (Two values of a are possible, a positive value and a negative value. Report each with their corresponding final velocities.) a (positive value) a (negative value) V₂f V2f km/s km/s
A 0.500 kg sphere moving with a velocity given by (2.001 - 3.40 + 1.00k) m/s strikes another sphere of mass 1.50 kg moving with an initial velocity of (-1.00 +2.00 - 3.10k) m/s. (a) The velocity of the 0.500 kg sphere after the collision is (-0.601 +3.00 -8.00k) m/s. Find the final velocity of the 1.50 kg sphere. m/s Identify the kind of collision (elastic, inelastic, or perfectly inelastic). O elastic O inelastic O perfectly inelastic (b) Now assume the velocity of the 0.500 kg sphere after the collision is (-0.2501 + 0.650 - 2.08k) m/s. Find the final velocity of the 1.50 kg sphere. V= m/s Identify the kind of collision. O elastic O inelastic O perfectly inelastic (c) Take the velocity of the 0.500 kg sphere after the collision as (-1.00 +2.601 + ak) m/s. Find the value of a and the velocity of the 1.50 kg sphere after an elastic collision. (Two values of a are possible, a positive value and a negative value. Report each with their corresponding final velocities.) a (positive value) a (negative value) V₂f V2f km/s km/s
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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![### Collision Problem Involving Two Spheres
Consider a collision scenario where a 0.500 kg sphere moves with a velocity of \((2.00\hat{i} - 3.40\hat{j} + 1.00\hat{k})\) m/s and collides with another sphere of mass 1.50 kg. This second sphere is initially moving with a velocity of \((-1.00\hat{i} + 2.00\hat{j} - 3.10\hat{k})\) m/s.
#### (a) Calculate the Final Velocity of the 1.50 kg Sphere
After the collision, the velocity of the 0.500 kg sphere is given as \((-0.60\hat{i} + 3.00\hat{j} - 8.00\hat{k})\) m/s. Your task is to find the final velocity of the 1.50 kg sphere.
\[ \vec{v} = \_\_\_\_ \]
Identify the type of collision:
- ○ Elastic
- ○ Inelastic
- ○ Perfectly Inelastic
#### (b) Altered Scenario: New Velocity for 0.500 kg Sphere
Now, if the velocity of the 0.500 kg sphere after the collision is \((-0.250\hat{i} + 0.650\hat{j} - 2.08\hat{k})\) m/s, determine the final velocity of the 1.50 kg sphere.
\[ \vec{v} = \_\_\_\_ \]
Identify the type of collision:
- ○ Elastic
- ○ Inelastic
- ○ Perfectly Inelastic
#### (c) Solve for Variable and Velocity in Elastic Collision
Consider the final velocity of the 0.500 kg sphere as \((-1.00\hat{i} + 2.60\hat{j} + a\hat{k})\) m/s and calculate the value of \(a\) for both possible outcomes. Report the velocity of the 1.50 kg sphere for an elastic collision with these values.
**Positive \(a\):**
- \(a = \_\_\_\_\)
- \(v_{2f} = \_\_\_\_\hat{i} + \_\_\_\_\hat{j} + \_\_\_\_\hat{k}\) m/s
**Negative \(a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08aa0b19-cba0-4fd4-b1f6-356b8c0f7ad5%2F4b6a722b-1761-455d-87ed-ec9bc1a90aaf%2F032ufyo_processed.png&w=3840&q=75)
Transcribed Image Text:### Collision Problem Involving Two Spheres
Consider a collision scenario where a 0.500 kg sphere moves with a velocity of \((2.00\hat{i} - 3.40\hat{j} + 1.00\hat{k})\) m/s and collides with another sphere of mass 1.50 kg. This second sphere is initially moving with a velocity of \((-1.00\hat{i} + 2.00\hat{j} - 3.10\hat{k})\) m/s.
#### (a) Calculate the Final Velocity of the 1.50 kg Sphere
After the collision, the velocity of the 0.500 kg sphere is given as \((-0.60\hat{i} + 3.00\hat{j} - 8.00\hat{k})\) m/s. Your task is to find the final velocity of the 1.50 kg sphere.
\[ \vec{v} = \_\_\_\_ \]
Identify the type of collision:
- ○ Elastic
- ○ Inelastic
- ○ Perfectly Inelastic
#### (b) Altered Scenario: New Velocity for 0.500 kg Sphere
Now, if the velocity of the 0.500 kg sphere after the collision is \((-0.250\hat{i} + 0.650\hat{j} - 2.08\hat{k})\) m/s, determine the final velocity of the 1.50 kg sphere.
\[ \vec{v} = \_\_\_\_ \]
Identify the type of collision:
- ○ Elastic
- ○ Inelastic
- ○ Perfectly Inelastic
#### (c) Solve for Variable and Velocity in Elastic Collision
Consider the final velocity of the 0.500 kg sphere as \((-1.00\hat{i} + 2.60\hat{j} + a\hat{k})\) m/s and calculate the value of \(a\) for both possible outcomes. Report the velocity of the 1.50 kg sphere for an elastic collision with these values.
**Positive \(a\):**
- \(a = \_\_\_\_\)
- \(v_{2f} = \_\_\_\_\hat{i} + \_\_\_\_\hat{j} + \_\_\_\_\hat{k}\) m/s
**Negative \(a
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