Answer:
dr/dt = -2 cm/s.
Explanation:
The volume of a cone is given by:
(1)
- r is the radius
- h is the height
Let's take the derivative with respect to time in each side of (1).
(2)
We know that:
- dh/dt = 10 cm / s (rate increasing of height)
- dV/dt = 0 (constant volume means no variation with respect of time)
- r = 4 cm
- h = 10 cm
We can calculate how fast is the radius changing using the above information.
Therefore dr/dt will be:
The minus signs means that r is decreasing.
I hope it helps you!
To find the change in centripetal acceleration, you should first look for the centripetal acceleration at the top of the hill and at the bottom of the hill.
The formula for centripetal acceleration is:
Centripetal Acceleration = v squared divided by r
where:
v = velocity, m/s
r= radium, m
assuming the velocity does not change:
at the top of the hill:
centripetal acceleration = (4.5 m/s^2) divided by 0.25 m
= 81 m/s^2
at the bottom of the hill:
centripetal acceleration = (4.5 m/s^2) divided by 1.25 m
= 16.2 m/s^2
to find the change in centripetal acceleration, take the difference of the two.
change in centripetal acceleration = centripetal acceleration at the top of the hill - centripetal acceleration at the bottom of the hill
= 81 m/s^2 - 16.2 m/s^2
= 64.8 m/s^2 or 65 m/s^2
Answer:
Buoyant Force: Cause and Calculation
The result is a net upward force (a buoyant force) on any object in any fluid. If the buoyant force is greater than the object's weight, the object will rise to the surface and float. If the buoyant force is less than the object's weight, the object will sink.
The answers are as follows:
1. B.
A typical atom is made up of three different particles, which are electron, proton and neutron. The proton and the neutron are located inside the nucleus of the atom while the electron orbit round the nucleus.
2. C
The number of proton in an atom determines the atomic number of that atom. Atom are positively charged particles and they do no participate in chemical reactions. The number of proton of an element remain constant at all time while the number of neutrons and the electrons in the atom may change.
3. B.
The first periodic table was created by Dmitri. He arranged the periodic table in such a way that, elements with similar properties fall into the same column in his periodic table. This was because, he arranged the periodic table on the basis of their physical and chemical properties.
4. A
The elements in the periodic table are arranged in horizontal row and vertical column. The column on the periodic table divides the elements into groups.
A row of element on the periodic table is called PERIOD. For elements on the same period, they have the same number of atomic orbitals.
5. A
Chemical symbol refers to the one or two letters which are used to represent a particular element. Chemical symbols are derived in a variety of ways. The chemical symbols make it possible for one to recognize an element quickly and to write it in an abbreviated form when writing chemical equations.
6. A.
An object is said to be ductile if it can be pulled into a long wire. It refers to an element's capacity to be pulled into a thin wire without the element been deformed. This is one of the properties of metals. Ductability makes it easier for one to work with a metal.
7. C
When metals atoms react with other atoms, the metal atoms lose electrons, this is because, metals usually have a low number of electrons in their outermost shells, which they always preferred to donate in order to achieve octet form.
8. B
Particle accelerator is a machine that accelerate elementary particles to very high energies, thus producing beam of charged particles which can be used for a lot of different purposes.
