In a lecture demonstration , a 3.0 m long vertical string wuth ten bolts tied to it at equal intervals is dropped from the ceiling of the lecture hall. The string falls on a tin plate, and the class hears the clink of each bolt as it hits the plate.the sounds will not occur at equal time intervals.WHY? will the time between the clinks increase or decrease near the end of the fall? How could the bolts be tied so that the clinks occur at equal intervals.
The bolt at the bottom of the string will have a lesser distance to fall than the one at the top. It will therefore arrive at a slower speed. Each successive bolt will arrive a bit faster. The time intervals between equally spaced bolts wil therefore become less each time. Think about how you could make them equal by adjusting the spacing.
The sounds of the bolts hitting the tin plate will not occur at equal time intervals due to the effects of gravity and air resistance. As the string falls, the bolts closer to the top will have a shorter distance to travel and will reach the plate first. The bolts near the bottom of the string will have a longer distance to cover, so they will take a longer time to reach the plate. This difference in distance traveled results in uneven time intervals between the clinks.
Near the end of the fall, the time intervals between the clinks will decrease. This is because the bolts near the bottom of the string are falling faster due to the acceleration of gravity. As a result, they cover equal distances in decreasing time intervals, causing the clinks to occur closer together.
To ensure that the clinks occur at equal intervals, the bolts should be tied in such a way that they experience the same acceleration due to gravity. One approach is to attach additional strings, also with bolts tied at equal intervals, to the main string. This will create a parallel arrangement of strings, known as a parallel array. The additional strings will distribute the tension and allow each bolt to fall independently, ensuring that they experience similar acceleration and resulting in the clinks occurring at equal intervals.
The clinks of the bolts will not occur at equal time intervals because the speed of the string's fall is not constant. As the string falls, it gains speed due to the force of gravity. The speed increase leads to each bolt hitting the tin plate faster than the previous one, resulting in varying time intervals between the clinks.
Near the end of the fall, the time between the clinks will decrease. This is because the string is reaching its maximum speed, so the bolts will hit the tin plate more rapidly as they are closer together.
To tie the bolts so that the clinks occur at equal intervals, you would need to account for the increasing speed of the falling string. An approach to achieve this would be to tie the bolts at intervals that are proportional to the square of the time. By doing so, the bolts would hit the tin plate at equal time increments. For example, you could tie the first bolt at 0 seconds, the second bolt at 1 second, the third bolt at 4 seconds (2^2), and so on, with each subsequent bolt tied at intervals that increase by the square of the time.