# A pendulum built from a steel sphere with radius r cm 5 and density stl kg m S 3 7800 is attached to an aluminum bar with length l m 1 thickness t cm 0 8. and width w cm 4 and density . al kg m S 3 2820 a. Calculate the mass moment of inertia of the pendulum about its center of mass, . cm I b. Calculate the mass moment of inertia of the pendulum about its pivot point, o

1)   I_ pendulum = 2.3159 kg m², 2)  I_pendulum = 24.683 kg m²

Explanation:

In this exercise we are asked to calculate the moment of inertia of a physical pendulum, let's start by calculating the center of mass of each elements of the pendulum and then the center of mass of the pendulum

Sphere

They indicate the density of the sphere roh = 37800 kg / m³ and its radius

r = 5 cm = 0.05 m

we use the definition of density

ρ = M / V

M = ρ V

the volume of a sphere is

V = 4/3 π r³

we substitute

M = ρ 4/3 π r³

we calculate

M = 37800  4/3 π 0.05³

M = 19,792 kg

Bar

the density is ρ = 32800 kg / m³ and its dimensions are 1 m,

0.8 cm = 0.0008 m and 4cm = 0.04 m

The volume of the bar is

V = l w h

m = ρ l w h

we calculate

m = 32800 (1   0.008   0.04)

m = 10.496 kg

Now we can calculate the center of mass of the pendulum, we use that the center of mass of the sphere is its geometric center, that is, its center and the center of mass of the bar is where the diagonals intersect, in this case it is a very bar. long and narrow, whereby the center of mass is about half the length. It's mass scepter of the pendulum is

r_cm = 1 / M (M r_sphere + m r_bar)

M = 19,792 + 10,496 = 30,288 kg

r_cm = 1 / 30,288 (10,496 0.5 + 19.792 (1 + 0.05))

r_cm = 1 / 30,288 (5,248 + 20,7816)

r_cm = 0.859 m

This is the center of mass of the pendulum.

1) Now we can calculate the moment of inertia with respect to this center of mass, for this we can use the theorem of parallel axes and that the moments of inertia of the bodies are:

Sphere I = 2/5 M r2

Bar I = 1/12 m L2

parallel axes theorem

I = I_cm + m D²

where m is the mass of the body and D is the distance from the body to the axis of rotation

Sphere

m = 19,792 ka

the distance D is

D = 1.05 -0.85

D = 0.2 m

we calculate

I_sphere = 2/5 19.792 0.05 2 + 19.792 0.2 2 = 0.019792 +0.79168

I_sphere = 0.811472 kg m²

Bar

m = 10.496 kg

distance D

D = 0.85 - 0.5

D = 0.35 m

I_bar = 1/12 10.496 0.5 2 + 10.496 0.35 2 = 0.2186 + 1.28576

I_bar = 1.5044 kg m²

The moment of inertia is a scalar quantity whereby the moment of inertia of the body is the sum of the moment of the parts

I_pendulum = I_sphere + I_bar

I_pendulum = 0.811472 +1.5044

I_ pendulum = 2.3159 kg m²

this is the moment of inertia of the pendulum with respect to its center of mass located at r = 0.85 m

2) The moment is requested with respect to the pivot point at r = 0 m

Sphere

D = 1.05 m

I_sphere = 2/5 M r2 + M D2

I_sphere = 2/5 19.792 0.05 2 + 19.792 1.05 2 = 0.019792 +21.82

I_sphere = 21.84 kg m²

Bar

D = 0.5 m

I_bar = 1/12 10.496 0.5 2 + 10.496 0.5 2 = 0.21866 + 2.624

I_bar = 2,84266 kg m 2

The pendulum moment of inertia is

I_pendulum = 21.84 +2.843

I_pendulum = 24.683 kg m²

This moment of inertia is about the turning point at r = 0 m

## Related Questions

If the solution described in the introduction is cooled to 0 ∘c, what mass of kno3 should crystallize? enter your answer numerically in grams.

14 g is the solubility per 100 g water, since it is difficult to read the graph.
Then, in 130 g H20 the solubility would be 14 g KNO3/100 g H2O x 130 g H2O = 18 g KNO3
The question asks how much crystallizes.
Initial 34.0 g minus 18.0 g still dissolved = 16.0 g crystallizes.

KNO3 of 10g will undergo crystallization at 0 °

Because the heavier the KNO3 mass will require a higher temperature in the dissolution process.

## Further explanation

Potassium nitrate is a nitrate salt compound from potassium with the molecular formula KNO3. Potassium nitrate salt can be made by reacting potassium chloride with sodium nitrate. If the saturated solution each of the solution is mixed with each other, then it will form sodium chloride salt because NaCl in water is small, the salt will settle. By cooling the filtered filtrate KNO3 will undergo crystallization

This compound decomposes with oxygen evolution at 500 ° C according to the reaction equation:

2 NaNO3 (s) -> 2NaNO 2 (s) + O2 (g)

Crystallization is separation by forming crystals so that the mixture can be separated. A gaseous or liquid substance can cool or condense and form crystals because it undergoes a crystallization process. Crystals will also form from a solution that will be saturated with a certain solvent. The more the number of crystals, the better, because the less likely to be polluted by dirt.

Potassium Nitrate has a physical white powder that is easily soluble in water and odorless. Meanwhile, to analyze the structure and characteristics of Potassium Nitrate MM2 data processing is used in the Chemoffice 15.0 application. This data processing is used to determine the shape of compounds, types of bonds in molecular movement compounds and other parts that can not be observed directly by the eye without the aid of tools. And for the form of compounds in 2 dimensions and 3 dimensions used Chemdraw 15.0 and Chem3D 15.0 applications

Potassium nitrate brainly.com/question/10847775

Crystallization brainly.com/question/2575925

Details

Subject: Chemistry

Keyword: kno3, nitrate, crystallization

A 17.0 resistor and a 6.0 resistor are connected in series with a battery. The potential difference across the 6.0 resistor is measured as 15 V. Find the potential difference across the battery.

V= 57.5 V

Explanation:

• If the resistors are in the linear zone of operation, the potential difference across them, must obey Ohm's law:

• For the 6.0 Ω resistor, if the potential difference across it is 15 V, we can find the current flowing through it as follows:

• In a series circuit, the current is the same at any point of it, so the current through the battery is I = 2.5 A
• The equivalent resistance of a series circuit is just the sum of the resistances, so, in this case, we can write the following equation:

• Applying Ohm's Law to the equivalent resistance, we can find the potential difference through it, that must be equal to the potential difference across the battery, as follows:

Two small objects each with a net charge of +Q exert a force of magnitude F on each other. We replace one of the objects with another whose net charge is + 4Q. We move the +Q and +4Q charges to be 3 times as far apart as they were. What is the magnitude of the force on the +4Q charge ?A. F

B. 4F

C. 4F/3

D. 4F/9

E. F/3

F'= 4F/9

Explanation:

Two small objects each with a net charge of +Q exert a force of magnitude F on each other. If r is the distance between them, then the force is given by :

...(1)

Now, if one of the objects with another whose net charge is + 4Q is replaced and also the distance between +Q and +4Q charges is increased 3 times as far apart as they were. New force is given by :

.....(2)

Dividing equation (1) and (2), we get :

Hence, the correct option is (d) i.e. " 4F/9"

The magnitude of the force on the +4Q charge, after replacing one of the original +Q charges and moving the charges three times farther apart, is calculated to be 4F/9 using Coulomb's Law. Therefore, the correct answer is D.

### Explanation:

The magnitude of the electrostatic force between two charges can be described by Coulomb's Law, which states that F = k × (q1 × q2) / r^2, where F is the force between the charges, k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the centers of the two charges. Originally, two objects each with charge +Q exert a force of magnitude F on each other. After one charge is replaced with a +4Q charge and they are moved to be three times as far apart, the force on the +4Q charge can be calculated using the modified version of Coulomb's Law that takes into account the new charges and distance.

Using the original scenario as a reference, where F = k × (Q × Q) / r^2, when the charge is replaced and the distance is tripled, the new force F' = k × (Q × 4Q) / (3r)^2 = 4kQ^2 / 9r^2. By comparing F' with F, we find that F' = (4/9)F. Thus, the magnitude of the force on the +4Q charge is 4F/9.

Planets A and B have the same size, but planet A is half the mass of planet B.Which statement correctly explains the weight you would experience on each
planet?
A. You would weigh the same on both planets because the planets
are the same size.
B. You would weigh less on planet A because it has less mass than
planet B.
C. You would weigh the same on both planets because your mass
would be the same on both.
D. You would weigh more on planet A because it has less mass than
planet B.

The statement which correctly explains the weight you would experience on each planet is: B. You would weigh less on planet A because it has less mass than  planet B.

Weight can be defined as the force acting on a body or an object as a result of gravity.

Mathematically, the weight of an object is given by the formula;

Where;

• m is the mass of the object.
• g is the acceleration due to gravity.

Hence, we can deduce that the weight and gravity acting on an object is highly dependent on the mass of an object.

Therefore, the higher the mass in a planet, the higher the gravity existing there.

B

Explanation:

The more mass an object has, the more gravity it has.

So to deal with the irrational belief in REBT, we must Group of answer choices

A. Consult with a friend and get their feeback

B. Dispute the beliefs by asking if these are true and examining the evidence

C. Seek mental health counseling

D. It is just too hard so let's just forget it.

i believe the answer is B

Explanation:

Seeking the right answer is the best thing to do

Consider a space shuttle which has a mass of about 1.0 x 105 kg and circles the Earth at an altitude of about 200.0 km. Calculate the force of gravity that the space shuttle experiences

The force of gravity that the space shuttle experiences is 9.8 x 10^5 Newtons.

### Explanation:

To calculate the force of gravity that the space shuttle experiences, we can use the equation F = mg, where F represents the force of gravity, m is the mass of the object, and g is the acceleration due to gravity (approximately 9.8 m/s² on Earth). In this case, the mass of the space shuttle is given as 1.0 x 10^5 kg. However, we need to convert the altitude of the shuttle into meters, so 200.0 km becomes 200,000 meters.

Now we can calculate the force of gravity:

F = (1.0 x 10^5 kg)(9.8 m/s²)

F = 9.8 x 10^5 N

Therefore, the space shuttle experiences a force of gravity of 9.8 x 10^5 Newtons.