Section B: Choose 3 out o 5. A 120 g marble I is releas It slides dowm an inclined tra an angle of 30° with the hori: A. If the marble is releas m, will it make it arou B. Determine the height the block just makes i

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Physics Problem: Motion on an Inclined Track with a Loop

#### Problem Statement:
A 120 g marble is released from rest at point A, at a vertical distance \(h\) above the ground. It slides down an inclined track around a circular loop of radius \(R=0.5\ m\), then up another incline that forms an angle of 30° with the horizontal. Assuming the track is frictionless and air resistance is negligible:

##### Part A:
If the marble is released from a height of 0.8 m, will it make it around the loop?

##### Part B:
Determine the height \(h\) necessary so that the block just makes it around the loop.

#### Diagram Explanation:
The diagram illustrates a track setup:
1. **Inclined Track**: The marble starts at a height \(h\).
2. **Loop**: The circular loop has a radius \(R=0.5\ m\).
3. **Variables**: 
   - Height of release point A (\(h\)).
   - Radius of the loop (\(R = 0.5\ m\)).
   - Height at the top of the loop (\(2R = 1\ m\)).

```plaintext
   h      A
   |      .
   |     / \
   |    /---\
   |   /     \
   |  /       \
   | /         \ F
   |/___________\
       R = 0.5 m

Note: 
- \(F\) is the point at the bottom of the loop.
- \(R\) is the radius of the loop.
- \(h\) is the initial height from which the marble is released.
```

---

This problem requires a fundamental understanding of energy conservation principles and dynamics in circular motion.
Transcribed Image Text:--- ### Physics Problem: Motion on an Inclined Track with a Loop #### Problem Statement: A 120 g marble is released from rest at point A, at a vertical distance \(h\) above the ground. It slides down an inclined track around a circular loop of radius \(R=0.5\ m\), then up another incline that forms an angle of 30° with the horizontal. Assuming the track is frictionless and air resistance is negligible: ##### Part A: If the marble is released from a height of 0.8 m, will it make it around the loop? ##### Part B: Determine the height \(h\) necessary so that the block just makes it around the loop. #### Diagram Explanation: The diagram illustrates a track setup: 1. **Inclined Track**: The marble starts at a height \(h\). 2. **Loop**: The circular loop has a radius \(R=0.5\ m\). 3. **Variables**: - Height of release point A (\(h\)). - Radius of the loop (\(R = 0.5\ m\)). - Height at the top of the loop (\(2R = 1\ m\)). ```plaintext h A | . | / \ | /---\ | / \ | / \ | / \ F |/___________\ R = 0.5 m Note: - \(F\) is the point at the bottom of the loop. - \(R\) is the radius of the loop. - \(h\) is the initial height from which the marble is released. ``` --- This problem requires a fundamental understanding of energy conservation principles and dynamics in circular motion.
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