Using law of conservation of energy, "Energy can neither be created nor be destroyed but it can be transformed from one form to another".
That is, sum of Kinetic energy and Potential energy at initial point is equal to the sum of Kinetic energy and Potential energy at final point.
We can say that,
(K.E)1 + (P.E.)1 = (K.E)2 + (P.E)2
1/2 m1 * v1² + m1*g*h1 = 1/2 m2 * v2² + m2* g*h2
For motion in circular path,
Initial velocity v1 is at h1 =0
Final velocity v2 is at h2= d
For rotational motion, inertia is denoted by I.
1/2 I1 * v1² = 1/2 I2* v2² + I2 gd
1/2 I2*v2² = 1/2 I1*v1²- I2 gd
v2²= I1/I2 * v1²- 2 gd
v2= √(I1/12* v1²- 2gd)
The above equation gives the speed of the ball when it reaches the top of circular path in term of I, g and d.
Answer:
Difference in height = 7.5 cm
Explanation:
We are given;.
Height of ethyl alcohol;h2 = 20 cm = 0.2 m
Density of glycerin: ρ1 = 1260 kg/m³
Density of ethyl alcohol; ρ2 = 790 kg/m³
To get the difference in height, the pressure at the top of the open end must be equal to the pressure at the point where the liquids do not mix since both points will be at different levels after the pouring.
Thus;
P1 = P2
Formula for pressure is; P = ρgh
Thus;
ρ1 × g × h1 = ρ2 × g × h2
g will cancel out to give;
ρ1 × h1 = ρ2× h2
Making h1 the subject, we have;
h1 = (ρ2× h2)/ρ1
h1 = (790 × 0.2)/1260
h1 = 0.125 m
Difference in height will be;
Δh = h2 - h1
Δh = 0.2 - 0.125
Δh = 0.075 m = 7.5 cm
Bacteria and Binary Fission-
Many single-celled organisms rely on binary fission to reproduce themselves. All bacteria reproduce by binary fission.
Budding and Hydras-
Hydras are a type of freshwater cnidarian related to jellyfish, sea anemones and corals. Hydras reproduce asexually by developing small, genetically identical polyps that protrude from the parent. These polyps break off from the parent to form a new organism in a process called "budding."
Parthenogenesis and Copperheads- Though most of the organisms that use asexual reproduction are invertebrates, several species of vertebrate animals do make use of it. Some, like copperhead snakes, can reproduce asexually as an alternative to their typical sexual reproduction. Through a process called parthenogenesis -- literally "virgin birth" -- copperhead females can give birth to live young without having been inseminated by a male, even when males are available, according to National Geographic. In this form of parthenogenesis, the polar body, or a cell produced alongside the female's egg, acts as a sperm cell and essentially "fertilizes" the egg. Parthenogenesis has been observed in several species of reptiles, birds and sharks, and is especially common in insects.
The egg was dropped from a height of 24.7 m (free fall motion)
Explanation:
The motion of the egg is a free fall motion (uniformly accelerated motion), so we can use the following suvat equation:
where
v is the final velocity
u is the initial velocity
a is the acceleration
s is the displacement
For the egg in this problem, we have:
u = 0 is the initial velocity
v = 22 m/s is the final velocity
is the acceleration of gravity
s is the vertical displacement (the height from which the egg was dropped)
Solving for s, we find:
Learn more about free fall here:
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