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24.12.2021

If the diameter of the black marble is 3.0 cm, and by using the formula for volume, what is a good approximation of its volume? record to the ones place. determine the initial volume of water in the graduated cylinder. if you added the black marble to the graduated cylinder and it sinks, what final volume should the water level indicate? record to the ones place.

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17.02.2022, solved by verified expert

Sachin Kumar

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Chemistry, Q&A Expert, I am a Assistant Professor in Maharaj Singh College Saharanpur, Uttar Pradesh, India

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Assuming the marble has an spherical shape, its volume can be calculated by the following formula:

(1)

where is the radius of the sphere and also is the half of its diameter :

(2)

Now, if we know the diameter of the black marble is , its radius is:

(3)

Substituting this value on equation (1):

Simplifying:

>>>>>This is an approximation of the volume of the marble

Note that , therefore the result above can be also written as

According to the Archimedes’ Principle a body totally or partially immersed in a fluid at rest, experiences a vertical upward thrust equal to the mass weight of the body volume that is displaced.

In this case, if we have a graduated cylinder with the capacity to contain 100 ml of water, and we fill it with 50 ml of water (as shown in the image attached) and then we add the black marble until it sinks; the water level will increase according to the principle explained above.

As the marble does not absorb water, the space it occupies displaces the water upwards and, in this way, it is possible to determine its volume or the final volume the water level indicates in the cylinder.

We already know the initial volume of water in the graduated cylinder, which is 50 ml, and we know the volume of the marble because we calculated it above. If we want to know the final volume of water level we have to use the following relation:

(4)

and find :

(5)

Finally:

>>>>>This is the final volume of the water level indicated in the graduated cylinder

If the diameter of the black marble is 3.0 cm,, №15221818, 24.12.2021 21:53

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Chemistry

If the diameter of the black marble is 3.0 cm, and by using the formula for volume, what is a good approximation of its volume? record to the ones place. cm3 determine the initial volume of water in the graduated cylinder. if you added the black marble to the graduated cylinder and it sinks, what final volume should the water level indicate? record to the ones place.

Step-by-step answer

P Answered by PhD

The rise in liquid is 4.33-3 = 1.33 cm

Explanation:

Volume of the given marble can be found out using the formula for volume = $4/3 \pi r3$

Radius is given as 3/2 cm

$4/3 \times 22/7 \times 3/2 \times 3/2 = 66/7 cm3= 9.42$

Now if the graduated cylinder has same diameter and the level of liquid is 3 cm then volume of cylinder can be calculated by the following formula = $\pi r2h = 22/7 \times 3/2 \times 3/2 \times 3 = 21.21cm$

When the marble ball completely sinks the new volume is = 21.21 + 9.42 = 30.63

The rise in height will be $\pi r2h = 22/7 \times 3/2 \times 3/2 \times h = 30.63$

H= 4.33 so rise in liquid is 4.33-3 = 1.33 cm

Chemistry

Step-by-step answer

P Answered by PhD

The rise in liquid is 4.33-3 = 1.33 cm

Explanation:

Volume of the given marble can be found out using the formula for volume = $4/3 \pi r3$

Radius is given as 3/2 cm

$4/3 \times 22/7 \times 3/2 \times 3/2 = 66/7 cm3= 9.42$

When the marble ball completely sinks the new volume is = 21.21 + 9.42 = 30.63

The rise in height will be $\pi r2h = 22/7 \times 3/2 \times 3/2 \times h = 30.63$

H= 4.33 so rise in liquid is 4.33-3 = 1.33 cm

Physics

An amateur player is about to throw a dart with an initial velocity of 15 meters/second onto a dartboard that is at a distance of 2.7 meters. Calculate the vertical distance by which the player will miss the target if he throws the dart horizontally, in line with the dartboard.

Step-by-step answer

P Answered by Specialist

Options:
a. 0.08 meters
b. 0.16 meters
c. 0.32 meters
d. 1.8 meters

Answer:
b. 0.16 meters

Explanation:
In the picture
Options:
a. 0.08 meters
b. 0.16 meters
c. 0.32 meters
d. 1.8 meters

Answer:
b. 0.16 meters

Physics

Abbey always gets zits on her chin and she can t figure out the best method to get rid of them. She decides to test several products to see which clears her face up fastest: washing with soap and water, washing with an acne face wash from the pharmacy, and washing her face with organic oils. For one week she just washes her face with water. The next week she washes every day with soap and water. The following week she uses the acne wash, and the last week she uses the organic oils. Each week she records the number of zits she has on her chin at

Step-by-step answer

P Answered by PhD

Independent variable: the best method to get rid of them.

Dependent variable: washing with soap and water.

Hypothesis: Organic oils

Control group: water

Physics

A proton (1.6726 ? 10-27 kg) and a neutron (1.6749 ? 10-27 kg) at rest combine to form a deuteron, the nucleus of deuterium or “heavy hydrogen.” In this process, a gamma ray (high-energy photon) is emitted, and its energy is measured to be 2.2 MeV (2.2 ? 10 6 eV).

Step-by-step answer

P Answered by Master

Answer:

see below.

Step-by-step explanation:

To solve this problem, we can use the conservation of energy and conservation of momentum principles.

Conservation of energy:

The total initial energy is the rest energy of the proton and neutron, which is given by:

Ei = (mp + mn)c^2

where mp and mn are the masses of the proton and neutron, respectively, and c is the speed of light.

The total final energy is the rest energy of the deuteron plus the energy of the gamma ray, which is given by:

Ef = (md)c^2 + Eg

where md is the mass of the deuteron and Eg is the energy of the gamma ray.

According to the conservation of energy principle, the initial energy and final energy must be equal, so we have:

Ei = Ef

(mp + mn)c^2 = (md)c^2 + Eg

Conservation of momentum:

The total initial momentum is zero because the proton and neutron are at rest. The total final momentum is the momentum of the deuteron and the momentum of the gamma ray. Since the gamma ray is massless, its momentum is given by:

pg = Eg/c

where pg is the momentum of the gamma ray.

According to the conservation of momentum principle, the total final momentum must be equal to zero, so we have:

0 = pd + pg

where pd is the momentum of the deuteron.

Solving for md and pd:

From the conservation of energy equation, we can solve for md:

md = (mp + mn - Eg/c^2)/c^2

Substituting this expression into the conservation of momentum equation, we get:

pd = -pg = -Eg/c

Substituting the given values, we have:

mp = 1.6726 × 10^-27 kg mn = 1.6749 × 10^-27 kg Eg = 2.2 × 10^6 eV = 3.52 × 10^-13 J

Using c = 2.998 × 10^8 m/s, we get:

md = (1.6726 × 10^-27 kg + 1.6749 × 10^-27 kg - 3.52 × 10^-13 J/(2.998 × 10^8 m/s)^2)/(2.998 × 10^8 m/s)^2 = 3.3435 × 10^-27 kg

pd = -Eg/c = -(3.52 × 10^-13 J)/(2.998 × 10^8 m/s) = -1.1723 × 10^-21 kg·m/s

Therefore, the mass of the deuteron is 3.3435 × 10^-27 kg, and its momentum is -1.1723 × 10^-21 kg·m/s.

Physics

tomatoes are being thrown horizontally off the top of a building 50.0 meters above the ground at 3.00 m/s. How far will the tomatoes travel horizontally by the time it hits the ground? Use significant figures, and estimate g to be equal to 9.81 m/s^2

Step-by-step answer

P Answered by PhD

Answer:

9.6 meters

Step-by-step explanation:

Time taken by the tomatoes to each the ground

using h = 1/2 g t^2

t^2 = 2h/g = 2 x 50/ 9.8 = 10.2

t = 3.2 sec

horizontal ditance = speed x time = 3 x 3.2 = 9.6 meters

Physics

a screw has a head diameter of 0.812 m and a thread width of 0.318 cm. What is the ideal mechanical advantage?

Step-by-step answer

P Answered by PhD

The question specifies the diameter of the screw, therefore the IMA of this screw is 0.812? / 0.318 = 8.02

Physics

compare the momentum of a 6,300 kg elephant walking 0.11 m/s and a 50-kg dolphins swimming 10.m/s

Step-by-step answer

P Answered by PhD

First sum applied the Newton's second law motion: F = ma
Force = mass* acceleration
This motion define force as the product of mass times Acceleration (vs.Velocity). Since acceleration is the change in velocity divided by time,
force=(mass*velocity)/time
such that, (mass*velocity)/time=momentum/time
Therefore we get mass*velocity=momentum
Momentum=mass*velocity
Elephant mass=6300 kg; velocity=0.11 m/s
Momentum=6300*0.11
P=693 kg (m/s)
Dolphin mass=50 kg; velocity=10.4 m/s
Momentum=50*10.4
P=520 kg (m/s)
The elephant has more momentum(P) because it is large.

Physics

Jordan lifts a 100-kilogram barbell from the floor to a height of 2.0 meters in 1.5 seconds. The amount of power he generates is about ____ watts.

Step-by-step answer

P Answered by PhD

Weight of barbell (m) = 100 kg
Uplifted to height (h) = 2m
Time taken= 1.5 s
Work done by Jordan = potential energy stored in barbell = mgh
= 100×2×9.8
= 1960J
Power = energy/time
= 1960/1.5
1306.67watts

Physics

Jasmine, who weighs 400 newtons, moves up a 5.0-meter climbing wall in 15 seconds. The amount of power generated by Jasmine as she climbs the wall is about ____ watts.

Step-by-step answer

P Answered by PhD

Weight of jasmine (m) = 400 N
Height climbed on wall (h) = 5m
Total time taken in climbing = 5 sec
Work done in climbing the wall = rise in potential energy = mgh
= 400×9.8×51
= 19600J
Power generated by Jasmine = potential energy / time
= 19600/5
= 3920Watts

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