Piston 1 in the figure has a diameter of 1.48 cm. m 2 2 in. 10 in. (1 LL Piston 2 has a diameter of 8.47 cm. In the absence of friction, determine the force required on piston 1 necessary to support an object with a mass of 989 kg placed on piston 2. (Neglect the height difference between the bottom of the two pistons, and assume that the pistons are massless).

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### Educational Content: Hydraulic Pistons

#### Text Description:
- Piston 1 in the figure has a diameter of 1.48 cm.
- Piston 2 has a diameter of 8.47 cm. 
- In the absence of friction, determine the force required on piston 1 necessary to support an object with a mass of 989 kg placed on piston 2.
  - **Assumptions:**
    - Neglect the height difference between the bottom of the two pistons.
    - Assume that the pistons are massless.

#### Diagram Explanation:
The image illustrates a hydraulic system consisting of two pistons connected by a fluid. Here is a detailed explanation of the diagram components:

- **Piston 1:**
  - Located on the right side, with a smaller diameter of 1.48 cm.
  - Attached to a handle held by a hand, applying force \( F \).
  
- **Piston 2:**
  - Located on the left side, with a larger diameter of 8.47 cm.
  - Holds a mass \( m \) of 989 kg on top.
  
- **Connecting Arm:**
  - Horizontal arm measuring 10 in. with a 2 in. section leading to Piston 1.
  
- **Force Diagram:**
  - Shows the application of force \( F \) vertically downward on Piston 1 via the handle.

#### Problem Questions:
- **Primary Question:** What is the magnitude of the force \( F \), required at the end of the handle?
Transcribed Image Text:### Educational Content: Hydraulic Pistons #### Text Description: - Piston 1 in the figure has a diameter of 1.48 cm. - Piston 2 has a diameter of 8.47 cm. - In the absence of friction, determine the force required on piston 1 necessary to support an object with a mass of 989 kg placed on piston 2. - **Assumptions:** - Neglect the height difference between the bottom of the two pistons. - Assume that the pistons are massless. #### Diagram Explanation: The image illustrates a hydraulic system consisting of two pistons connected by a fluid. Here is a detailed explanation of the diagram components: - **Piston 1:** - Located on the right side, with a smaller diameter of 1.48 cm. - Attached to a handle held by a hand, applying force \( F \). - **Piston 2:** - Located on the left side, with a larger diameter of 8.47 cm. - Holds a mass \( m \) of 989 kg on top. - **Connecting Arm:** - Horizontal arm measuring 10 in. with a 2 in. section leading to Piston 1. - **Force Diagram:** - Shows the application of force \( F \) vertically downward on Piston 1 via the handle. #### Problem Questions: - **Primary Question:** What is the magnitude of the force \( F \), required at the end of the handle?
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