https://r2.erweima.ai/mathbot/image/1724469833994xq6wfucs.jpg

Câu trắc nghiệm đúng sai Trong kĩ thuật cơ khí, để biến chuyển động tròn đều thành chuyển động thẳng, người ta dùng một cơ cấu như hình vẽ bên. Bánh xe trong mô hình có bán kính R = 0,2 m. Cho bánh xe quay đều với tốc độ góc 20 rad/s
	a) Chiều dài quỹ đạo chuyển động của pit - tông bằng bán kính của bánh xe.
	b) Tốc độ cực đại của pit-tông là 40 m/s.
	c) Quãng đường pit-tông di chuyển được trong thời gian bánh xe quay 120 vòng là 96 m.
	d) Quãng đường lớn nhất khi bánh xe quay được góc 600 là 0,2 m

The image you provided shows a mechanical system typically used in converting rotational motion to linear motion. The system consists of a wheel (which rotates) and a piston (which moves linearly). This setup is often found in engines or pumps.

Let’s analyze each statement one by one:

### Given Data:
- Radius of the wheel \( R = 0.2 \) m
- Angular velocity \( \omega = 20 \) rad/s

### Statement Analysis:

**(a) "Chiều dài quỹ đạo chuyển động của pit-tông bằng bán kính của bánh xe."**
- The length of the trajectory of the piston (which moves back and forth in a straight line) is twice the radius of the wheel. This is because the piston moves from one end of its stroke to the other as the wheel completes half a turn. Thus, the length of the trajectory is \( 2R \), not \( R \).

- **This statement is incorrect.**

**(b) "Tốc độ cực đại của pit-tông là 40 m/s."**
- The maximum linear speed \( v_{\text{max}} \) of the piston is given by:
  \[
  v_{\text{max}} = \omega \cdot R = 20 \text{ rad/s} \times 0.2 \text{ m} = 4 \text{ m/s}
  \]
  
- **This statement is incorrect.**

**(c) "Quãng đường pit-tông di chuyển được trong thời gian bánh xe quay 120 vòng là 96 m."**
- The piston moves a distance equal to \( 2R \) for each full rotation of the wheel.
- For 120 rotations, the distance \( d \) the piston moves is:
  \[
  d = 120 \times 2R = 120 \times 2 \times 0.2 \text{ m} = 48 \text{ m}
  \]
  
- **This statement is incorrect.**

**(d) "Quãng đường lớn nhất khi bánh xe quay được góc 60° là 0,2 m."**
- A 60° angle corresponds to \( \frac{1}{6} \) of a full circle. The maximum linear distance covered by the piston for this rotation is:
  \[
  d = R \times \sin(60^\circ) = 0.2 \times \frac{\sqrt{3}}{2} \approx 0.173 \text{ m}
  \]
  
- **This statement is incorrect.**

### Summary:
- All four statements are incorrect based on the given data and physical principles.

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:
1. How does the angular velocity of the wheel affect the speed of the piston in such a system?
2. What is the relationship between the radius of the wheel and the stroke length of the piston?
3. How can the design of the system be modified to increase the maximum speed of the piston?
4. What factors could influence the accuracy of the piston’s movement in this setup?
5. How would the system behave if the wheel had a non-uniform angular velocity?

**Tip:** Always double-check the units and dimensional consistency when solving mechanical problems, especially in scenarios involving rotational and linear motion conversion.

Explore the analysis of a mechanical system converting rotational motion to linear motion. Understand the principles behind wheel and piston interactions with angular velocity and linear speed calculations. Detailed solutions and explanations included.

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