1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zavuch27 [327]
2 years ago
15

A ball with a mass of 2000 g is floating on the surface of a pool of water. What is the minimum volume that the ball could have

without sinking below the surface of the water? (Note that water has a density of 1.00 g/cm³.)
Physics
1 answer:
Doss [256]2 years ago
3 0

Answer:

2000\; {\rm cm^{3}}.

Explanation:

When the ball is placed in this pool of water, part of the ball would be beneath the surface of the pool. The volume of the water that this ball displaced is equal to the volume of the ball that is beneath the water surface.

The buoyancy force on this ball would be equal in magnitude to the weight of water that this ball has displaced.

Let m(\text{ball}) denote the mass of this ball. Let m(\text{water}) denote the mass of water that this ball has displaced.

Let g denote the gravitational field strength. The weight of this ball would be m(\text{ball}) \, g. Likewise, the weight of water displaced would be m(\text{water})\, g.

For this ball to stay afloat, the buoyancy force on this ball should be greater than or equal to the weight of this ball. In other words:

\text{buoyancy} \ge m(\text{ball})\, g.

At the same time, buoyancy is equal in magnitude the the weight of water displaced. Thus:

\text{buoyancy} = m(\text{water}) \, g.

Therefore:

m(\text{water})\, g = \text{buoyancy} \ge m(\text{ball})\, g.

m(\text{water}) \ge m(\text{ball}).

In other words, the mass of water that this ball displaced should be greater than or equal to the mass of of the ball. Let \rho(\text{water}) denote the density of water. The volume of water that this ball should displace would be:

\begin{aligned}V(\text{water}) &= \frac{m(\text{water})}{\rho(\text{water})} \\ &\ge \frac{m(\text{ball}))}{\rho(\text{water})}  \end{aligned}.

Given that m(\text{ball}) = 2000\; {\rm g} while \rho = 1.00\; {\rm g\cdot cm^{-3}}:

\begin{aligned}V(\text{water}) &\ge \frac{m(\text{ball}))}{\rho(\text{water})}  \\ &= \frac{2000\; {\rm g}}{1.00\; {\rm g\cdot cm^{-3}}} \\ &= 2000\; {\rm cm^{3}}\end{aligned}.

In other words, for this ball to stay afloat, at least 2000\; {\rm cm^{3}} of the volume of this ball should be under water. Therefore, the volume of this ball should be at least 2000\; {\rm cm^{3}}\!.

You might be interested in
Rahul wants to change the motion map shown so that it shows uniform circular motion. What change should Rahul make?
saw5 [17]

Answer:

B. He should change the lengths of the vectors that point tangent to the circle so that each is the same length.

Explanation:

A uniform circular motion is a motion in a circle where the tangential speed of the object is constant.

In the motion map:

- The arrows pointing towards the centre of the circle represent the centripetal acceleration, and their length represent the magnitude of the acceleration

- The arrows pointing tangential to the circle represent the tangential speed, and their length represent the magnitude of the speed

In this motion map, we see that the length of the vectors pointing tangent to the circle is not constant: this means that the speed is not constant. In order to have a uniform circular motion, the speed must be constant, therefore the lengths of the vectors that point tangent to the circle must be the same.

6 0
3 years ago
Read 2 more answers
People in the future may well live inside a rotating space structure that is more than 2 km in diameter. Inside the structure, p
Sergeeva-Olga [200]

Answer:

option B

Explanation:

given,

diameter of the rotating space = 2 Km

Force exerted at the edge of the space = 1 g

force experienced at the half way = ?

As the object is rotating in the circular part

Force is equal to centripetal acceleration.

at the edge

g = ω² r

ω is the angular velocity of the particle

r is the radius.

now, acceleration at the half way

g' = ω² r'

g' = \omega^2 (\dfrac{r}{2})

g' =\dfrac{1}{2}(\omega^2 r)

g'=\dfrac{g}{2}

People at the halfway experience g/2

hence, the correct answer is option B

7 0
3 years ago
Winds tend to rotate in a counter clockwise direction in the ___ (northern or southern) Hemisphere as they move into a low press
lana [24]

Answer:

Winds tend to rotate in a counter clockwise direction in the center of northern and southern hemisphere.

Explanation:

The wind blows clockwise around a high pressure area  in the northern hemisphere and the wind blows counter - clockwise around low pressure.  

In the northern hemisphere High-pressure systems rotate clockwise direction and in the southern hemisphere  low-pressure systems rotate clockwise direction.

 

8 0
3 years ago
Read 2 more answers
What is the force felt by the electrons and the nuclei in the rod when the external field described in the problem introduction
fomenos

Complete Question

The complete question is shown on the uploaded image

Answer:

The nuclei experience a force that will move it to the right of the conductor rod while the electrons experience a force that will move it to the left side of the conductor rod.

Explanation:

The force that act on the charges(both the positive and the negative charge ) is Mathematically expressed as

                      F = qE   => E = F/q

where F is the force, q is the charge and E is the electric field

we can see that the force is directly proportional to the electric field,so an increase in the electric field would increase the force.

we can also see that the electric field is given as force per unit charge and generally the direction of this field is taken to be the direction of the force it would exert on a positive test charge

Now from the question we are being told that the external electric field is the direction of the positive x axis

Hence this field would drive the positive charge i.e the nuclei to the right.

In order to further explain let consider this

Generally the electric field is always radially outward  originating from a positive point charge and radially in toward a negative point charge.

what  this means for this question, is that the positive point charge is on the left side of the electric field while the negative point charge is at the right side of the field.

According to Coulomb's law which states that unlike term attract while like terms repel, it means that  the electron would move to the left of the conductor rod   while the nuclei would move to the right side of the conductor rod.

7 0
3 years ago
Why is water always used in energy generation (water -> steam -> turbine) instead of a liquid with a lower specific heat c
frez [133]

There are multiple reasons for this. First of all, water is available in almost every place on the Earth. It doesn't pollute the air, doesn't cause health use and is easily handle.

Other factor is the fact that water has a really high specific heat. This means that water, and more specifically steam, can aborb and transport more energy. A lower heat capacity would imply the need to boil more of the liquid to obtain the same amount of energy. This combine with the fact that water expands at a large rate when boiling, combine with everything mentioned previously, and you get a liquid with all the characteristics that a efficient turbine requires to work.

8 0
3 years ago
Other questions:
  • What force is required to accelerate a body with a mass of 15 kilograms at a rate of 8 m/s²?
    7·1 answer
  • What information can be deduced by analyzing the graph?
    5·2 answers
  • What is the experimental group(s)?
    8·1 answer
  • A gasoline engine transform approximately 34 percent of the fuel's chemical energy into mechanical energy. if energy is conserve
    15·1 answer
  • A car with bad shock absorbers bounces up and down with a period of 1.50 s after hitting a bump. The car has a mass of 1 500 kg
    5·1 answer
  • A new school is being built in a field of wildflowers. A class wanted to develop a research project to predict the effects of th
    9·1 answer
  • If the horse lifts a 50 kilogram mass a vertical distance of 3 meters in 2 seconds, what is the horse’s minimum power output?
    9·1 answer
  • Explain whether there can be forces act-
    15·1 answer
  • Erwin Schrödinger developed the quantum model of the atom. What scientific knowledge was necessary for Schrödinger’s work?
    11·1 answer
  • What is the motional kinetic energy of a 25 kg object moving at a speed of 10 m/s?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!