Talking about the Relationship between Light Rope, Light Rod and Light Spring
August 11 07:44:00, 2025
The light bar can exert both tension and support forces on an object, unlike a light rope that only provides tension. This allows the pendulum ball to perform a complete circular motion in the vertical plane. At the lowest point of the motion, the ball must have a minimum velocity vâ‚€ in order to maintain the circular path. At the highest point, the ball can experience either a pulling force or a supporting force from the light bar, which means that the velocity at this point can be zero. Therefore, the minimum speed required at the top is such that the ball does not lose contact with the track.
The critical velocity at the highest point is given by v = √(gL). If the velocity is less than √(gL), the bar will exert a downward pull on the ball. Using the principle of conservation of mechanical energy from the bottom to the top of the circle, we get ½mv₀² = 2mgL, which leads to v₀ = √(4gL). Thus, for the ball to complete the circular motion, its velocity at the bottom must be greater than √(4gL).
This situation is similar to a mass moving inside a vertical circular tube, where the tube can provide both pushing and pulling forces depending on the position of the mass. In both cases, the ability to sustain a full circular motion depends on the minimum velocity at the lowest point.
In another example, consider a light spring with original length L₀ and spring constant k, attached to a block of mass m at one end and fixed at point O on a rotating turntable. The block rotates along with the turntable at a certain angular velocity. The maximum static friction between the block and the turntable is fm. The block’s position on the turntable is constrained based on the balance of forces.
When the block is at the smallest radius râ‚, the spring is compressed by an amount (Lâ‚€ - râ‚). The net centripetal force is provided by the static friction and the spring force: fm - k(Lâ‚€ - râ‚) = mrâ‚ω². Solving for râ‚ gives râ‚ = (fm - kLâ‚€) / (mω² - k).
When the block is at the largest radius r₂, the spring is stretched by (r₂ - L₀). The net centripetal force is now provided by the spring force minus the static friction: k(r₂ - L₀) - fm = mr₂ω². Solving for r₂ gives r₂ = (fm + kL₀) / (k - mω²).
Therefore, the block can rotate within the range: (fm - kL₀) / (mω² - k) ≤ r ≤ (fm + kL₀) / (k - mω²). This shows how the interplay between the spring force and static friction determines the possible positions of the block on the turntable.
Brass is a special copper alloy. Brass is an object made of an alloy of copper and zinc. It gets its name from its yellow color. Brass with 56% to 68% copper has a melting point of 934 to 967 degrees. Brass has good mechanical properties and wear resistance. Because of its unique advantages, it has become an important part of the parts manufacturing industry. It is generally used for precision copper parts such as automobile parts, medical parts and electrical parts.