Hasbro is (hypothetically) contracting you to help design a new series of Nerf railguns e patent pending, Here is the current schematic of the Nerf railgun: Uniform magnetic field caused by ceramic magnets Bullet loaded Battery supply at rest Barrel width x x x x X Muzzle Barrel length speed Trigger Here are the desired statistics: • Use of ceramic magnets, which provide a 0.35 T uniform magnetic field. • Barrel length of 0.21 m. • Barrel width of 2 cm (or 0.02 m). • Bullet mass of 1 g (or 0.001 kg). • Bullet resistance of 12 Q (from electrically conductive foampatent pending). • Muzzle speed of 25 m/s. Assuming the wires and the rails of the gun are ideal conductors, what voltage is needed to make the gun work to these specifications? Give you answer in units of kV".

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**Nerf Railgun Schematic and Design Specifications**

Hasbro is (hypothetically) contracting you to help design a new series of Nerf railguns. Here is the current schematic of the Nerf railgun:

### Diagram Explanation:
- **Uniform Magnetic Field**: Created by ceramic magnets, represented by a series of "X" marks across the top and bottom of the diagram.
- **Bullet Loaded at Rest**: Indicated by a shaded circle within the barrel, connected to a battery supply via a trigger mechanism.
- **Barrel Width and Length**: The dimensions of the railgun’s barrel are annotated, showing the width at the opening and the length stretching from the bullet position to the muzzle.
- **Muzzle Speed**: Illustrated with an arrow pointing outwards from the muzzle, indicating the direction of bullet ejection.

### Design Specifications:
- **Magnetic Field**: Utilizes ceramic magnets with a strength of 0.35 Tesla (T).
- **Barrel Dimensions**:
  - Length: 0.21 meters
  - Width: 2 centimeters (0.02 meters)
- **Bullet Mass**: 1 gram (0.001 kilograms)
- **Bullet Resistance**: 12 Ohms, using electrically conductive foam.
- **Muzzle Speed**: 25 meters per second

### Task:
Assuming the wires and rails of the gun are ideal conductors, calculate the voltage needed to achieve these specifications. Provide your answer in units of kilovolts (kV).
Transcribed Image Text:**Nerf Railgun Schematic and Design Specifications** Hasbro is (hypothetically) contracting you to help design a new series of Nerf railguns. Here is the current schematic of the Nerf railgun: ### Diagram Explanation: - **Uniform Magnetic Field**: Created by ceramic magnets, represented by a series of "X" marks across the top and bottom of the diagram. - **Bullet Loaded at Rest**: Indicated by a shaded circle within the barrel, connected to a battery supply via a trigger mechanism. - **Barrel Width and Length**: The dimensions of the railgun’s barrel are annotated, showing the width at the opening and the length stretching from the bullet position to the muzzle. - **Muzzle Speed**: Illustrated with an arrow pointing outwards from the muzzle, indicating the direction of bullet ejection. ### Design Specifications: - **Magnetic Field**: Utilizes ceramic magnets with a strength of 0.35 Tesla (T). - **Barrel Dimensions**: - Length: 0.21 meters - Width: 2 centimeters (0.02 meters) - **Bullet Mass**: 1 gram (0.001 kilograms) - **Bullet Resistance**: 12 Ohms, using electrically conductive foam. - **Muzzle Speed**: 25 meters per second ### Task: Assuming the wires and rails of the gun are ideal conductors, calculate the voltage needed to achieve these specifications. Provide your answer in units of kilovolts (kV).
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