We appreciate your visit to A plant is suspended from the ceiling by two ropes that make angles of 20 and 60 with the ceiling Find the weight of the. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The weight of the plant is approximately 21.98 kg
The term "plant weight" describes the measurement of the mass or volume of a plant. Usually, the plant or specific portions of the plant, such as the leaves, stems, roots, or the total biomass, are weighed. In several scientific fields, including botany, agriculture, ecology, and plant physiology, plant weight is a crucial statistic.
It is used to examine how plants respond to environmental conditions including nutrient availability, water stress, or pollution exposure as well as their growth, biomass output, productivity, and reactions to those factors. Understanding plant physiology and ecological dynamics can be aided by knowing a plant's weight, which can reveal information about the health, development, and resource distribution of the plant.
To solve for the weight of the plant, we can use the concept of resolving forces and trigonometry. The diagram below shows the forces acting on the plant:
Here, T1 and T2 are the tension in the ropes, and W is the weight of the plant.Using trigonometry, we can relate the tensions T1 and T2 to the angle they make with the ceiling. From the diagram, we can see that:T1 = W sin 20°T2 = W sin 60°We are given that T2 = 187N.
Substituting into the equation for T2 above:187 = [tex]W sin 60°[/tex]
Dividing both sides by[tex]sin 60°[/tex]:
W = [tex]187/sin 60[/tex]°≈ 215.51 N
To convert to kilograms, we can divide by the acceleration due to gravity, g = 9.8 [tex]m/s^2[/tex]:
Weight of plant = 215.51 N ÷ 9.8 [tex]m/s^2[/tex]≈ 21.98 kg
Therefore, the weight of the plant is approximately 21.98 kg.
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