According to the previous analysis, we first examine a college entrance examination simulation question. In month 3x and month 43x, a block is released from the rightmost position. At this point, the left spring force F is greater than the right friction force f, causing the block to accelerate to the left. As it moves, the frictional resistance remains constant. Compared to vertical spring oscillations, it's straightforward to show that the block undergoes simple harmonic motion. However, its equilibrium position is not at point O, but rather at a point closer to the right.
Note: The amplitude calculation is taken with respect to point O as the reference. The movement time corresponds to only half a cycle. Points A and B are both located to the right of O, with point A being closer to O and point B closer to C. Both are on the right side of O, and point D coincides with O. Therefore, the correct answer is option C. When the block is pulled to point P and released, it undergoes harmonic motion. The equilibrium position—where the velocity is maximum—is located to the right of O, at a distance x. Calculations involving time, distance, and other parameters in such oscillations exceed the scope of the college entrance exam, but they align with competition-level knowledge. Hence, similar questions often appear in competition tests.
From the earlier analysis, we can conclude that the nth vibration amplitude of the block follows an arithmetic progression: A_n = A(2n - 1). (Note: the amplitude is calculated using the equilibrium position O1 and the starting point as the reference.) The distance between the nth end position and point O, which represents the elongation or compression of the spring, also follows an arithmetic progression.
What is the coefficient of friction between the block and the table? (2) Determine the maximum distance between the stopping point and O, and check whether this is the farthest point the block reaches during its motion. It is assumed that the dynamic friction coefficient equals the static one. After n vibrations, the total vibration time can be calculated using the path method.
If the block vibrates only once, it moves to the left with an initial amplitude A. Eventually, the two blocks will come to rest. The final position cannot be outside the region between O and O', because within that area, the spring force is greater than the friction force, resulting in a net non-zero force. Therefore, the resting position must lie within the interval O to O'. If the block is at rest within O to O', it will remain stationary.
Then: (1) If the nth end position is at a distance A_n from O, then the block is still within the oscillation range, and the next vibration will continue in the opposite direction. (2) If the nth end position is at a distance A_n - x from O, where A_n > 2x, the block will stop within the region O to O' and remain there. For example, when A_n = 2x, the block stops at either equilibrium position O1 or O2.
At this point, the distance between the stopping position and O is A_n - x (with x < A_n). To ensure multiple oscillations, the spring must not reach its maximum compression. When the block moves from the rightmost point to the right, it reaches the farthest possible position. This is because the rightmost point is the maximum extension of the spring. If the spring reaches the right side of the block, it may suffer irreversible deformation.
Weighing Cabinet With High Precision
Weighing cabinets are equipped with high-precision scales that can measure objects with extreme accuracy. These scales are often calibrated regularly to maintain their accuracy.
Temperature Control: To ensure accurate weighing results, weighing cabinets often have temperature control features. This helps to prevent fluctuations in temperature that can affect the accuracy of the scale.
Vibration Isolation: Vibrations can interfere with the accuracy of weighing. Weighing cabinets are designed to isolate vibrations, ensuring that the scale remains stable during the weighing process.
Draft Shields: Draft shields are used to protect the scale from air currents that can affect the weighing process. These shields create a still environment around the scale, ensuring accurate measurements.
Security Features: Some weighing cabinets may have security features such as locks or alarms to prevent unauthorized access and protect valuable equipment.
Customization Options: Weighing cabinets can be customized to meet specific requirements, such as size, scale type, and additional features.
Types of Weighing Cabinets
Product weight: 200KG
Dimension: 1372mm long; 593mm wide;1950mm high
Scale plate size: 200mm long; 338mm wide
Screen size: 10 inch touch screen
Product color: White yellow (customizable)
Capacity: 30 scales
Freight lane type: 6 floors * 5 lanes
Weighing sensor: A single weighing position can weigh up to 20 kg, a small weighing capacity of 5g, and an error of 1gram
Applicable system: optional card swiping, facial recognition, and fingerprint recognition
Power supply: AC220V/50HZ.No packaging required, can be weighed separately, and high-precision sensors automatically calculate weight
Open material requisition, convenient material requisition, and simple replenishment.Fasteners such as screws and nuts, various spare materials, and office supplies.Weighing cabinets, also known as balance enclosures or safety cabinets, are specialized pieces of laboratory equipment designed to provide a safe and controlled environment for precision weighing operations. These cabinets are particularly important when handling hazardous materials, such as powders, chemicals, or toxic substances.
Weighing cabinets protect the operator and the laboratory environment from exposure to hazardous materials.
Accuracy: The controlled environment within a Weighing Cabinet can help to ensure accurate and precise weighing results.
Compliance: Weighing cabinets are often required to comply with safety regulations and standards in industries such as pharmaceuticals, chemicals, and research.
Efficiency: By providing a dedicated space for weighing operations, weighing cabinets can improve efficiency and productivity in the laboratory.
Applications:
Pharmaceutical industry: Weighing cabinets are essential for handling and measuring pharmaceutical ingredients, ensuring product quality and safety.
Chemical laboratories: These cabinets are used for weighing chemicals and other hazardous substances in research and development settings.
Research laboratories: Weighing cabinets are valuable tools for scientists conducting various experiments and analyses.
Quality control: In industries where precision weighing is critical, such as food and beverage manufacturing, weighing cabinets are used for quality control purposes.
Types of Weighing Cabinets:
Standard weighing cabinets: These are general-purpose cabinets suitable for a wide range of applications.
Powder weighing cabinets: Designed specifically for handling powders, these cabinets often have specialized ventilation systems to prevent the spread of airborne particles.
Hazardous substance weighing cabinets: These cabinets are equipped with advanced safety features to protect operators from exposure to highly toxic or hazardous substances.
Factors to Consider When Choosing a Weighing Cabinet:
Safety requirements: Consider the specific hazards associated with the materials you will be handling and choose a cabinet that meets the appropriate safety standards.
Ventilation system: Evaluate the ventilation system to ensure it is adequate for your needs and complies with relevant regulations.
Size and capacity: Select a cabinet that is large enough to accommodate your weighing equipment and the materials you will be handling.
Ergonomics: Ensure that the cabinet's design is comfortable and ergonomic for the operator.
Additional features: Consider any additional features that may be beneficial, such as built-in lighting or power outlets.
By investing in a high-quality weighing cabinet, you can create a safe and controlled environment for your precision weighing operations, ensuring accurate results and protecting the health and safety of laboratory personnel.
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