Answer:
1/2mv² = ke²
Explanation:
Let's suppose the material in question is a spring with spring constant k, mass m and position k, the kinetic energy possessed by the string will be;
K.E = 1/2mass×velocity² i.e 1/2mv²
Its elastic potential energy will be the work done on the spring when stretched which is equal to 1/2kx²
E.P = 1/2kx²
The equation describing the case where the kinetic energy is twice the elastic potential energy will be;
K.E = 2EP... 1)
Substituting the KE and EP formula into (1), we have;
1/2mv² = 2(1/2ke²)
1/2mv² = ke² which gives the required equation
Answer:
Final Length = 30 cm
Explanation:
The relationship between the force applied on a string and its stretching length, within the elastic limit, is given by Hooke's Law:
F = kΔx
where,
F = Force applied
k = spring constant
Δx = change in length of spring
First, we find the spring constant of the spring. For this purpose, we have the following data:
F = 50 N
Δx = change in length = 25 cm - 20 cm = 5 cm = 0.05 m
Therefore,
50 N = k(0.05 m)
k = 50 N/0.05 m
k = 1000 N/m
Now, we find the change in its length for F = 100 N:
100 N = (1000 N/m)Δx
Δx = (100 N)/(1000 N/m)
Δx = 0.1 m = 10 cm
but,
Δx = Final Length - Initial Length
10 cm = Final Length - 20 cm
Final Length = 10 cm + 20 cm
<u>Final Length = 30 cm</u>
Answer:
The first flowering plants appeared in the Mesozoic era, not the Paleozoic era
Explanation:
The Mesozoic era is well known and most famous because of the rule of the dinosaurs which were the dominant animals for most of this are. Also, it is the era in which the mammals appeared, though they lived in the shadows of the dinosaurs and only became dominant after their extinction. Another important evolution that took place and is not mentioned very often is the appearance of the first flowering plants. This was a revolutionary trait for the plants, and it helped them to survive in the changing climate on Earth. Soon this trait enabled this type of plants to spread out significantly and to become one of the most dominant organisms on the planet in the following era.
