A small sphere 0.70 times as dense as water is dropped from a height of 8 m above the surface of a smooth lake. Determine the maximum depth to which the sphere will sink. Neglect any energy transferred to the water during impact and sinking.

Answers

Answer 1

Answer:

18.66m

Explanation:

This was actually fun! Let set up the problem first: As you drop the sphere, it will accelerate till it hits the water with a given speed [tex]\dot z[/tex]. Once sinking the ball is subjected to two forces: its own weight [tex]m_sg = \rho_sVg[/tex] directed towards the bottom of the lake, and buoyancy (Archimedes law), ie a force upward equal to the volume of displaced water, [tex]m_wg=\rho_wVg[/tex]. At this point it's the classical "how high can I toss a ball before it falls down" with a water twist. Please note that I'm using z as the height of the sphere, and [tex]\dot z; \ddot z[/tex] represent the velocity (with one dot) and the acceleration (with two dots) in the z direction .Let's assume the sign of all quantities being positive if directed upwards, and negative if towards the bottom of the lake.

Let's first determine how fast the ball hit the water. For me the easiest way is saying "at 8m it has a given potential energy, and 0 kinetic energy. When it hits the water it loses all potential energy and has only kinetic energy". In numbers:

[tex]m_sgz=\frac12m_s\dot z_0^2[/tex] Let's divide by the masses, g is a known value ([tex]9.81 ms^{-2}[/tex]), z is 8 meters, and we get that [tex]\dot z_0 = 4\sqrt g =12.52 m/s[/tex]

At this point, let's determine the force acting on the sphere, courtesy of Newton second law and the debate we had earlier:

[tex]m_s \ddot z = -m_sg + m_wg\\\rho_sV \ddot z = -\rho_sVg + \rho_wV g[/tex]

At this point we can divide by the volume of the sphere, and make use of the fact that [tex]\rho_s = 0.7 \rho_w[/tex]

[tex]0.7\rho_w \ddot z = -.7\rho_w g+ \rho_wg \rightarrow 0.7 \ddot z = 0.3 g\\\ddot z = \frac {0.3}{0.7} g= \frac 37g = 4.2 ms^-2[/tex]

We're almost there. At this point we can write the law of motion for the sphere.

[tex]\dot z = \dot z_0 + \ddot z t[/tex] that we will use to find the time for the ball to stop sinking - ie reaches 0 velocity.

[tex]0 = -12.52 +4.2t \rightarrow t= 12.52/4.2 \approx 3s[/tex]

At this point we can use the other law of motion to find out the distance traveled

[tex]z= z_0 + \dot z_ot + \frac12 \ddot z t^2\\z= 0 -12.52 (3) + \frac12 (4.2)(3)^2 = -37.56+18.90 = -18.66 m[/tex]

as usual, please double and triple check all the calculations, it's almost 1.30 am here and I am not the most confident number cruncher even when fully awake.


Related Questions

Energy a substance or system has because of its motion Is what?

light energy
chemical energy
sound energy
electrical energy
thermal energy
mechanical energy

Answers

Answer:

Mechanical energy is the energy a substance or system has because of its motion. For example machines use mechanical energy to do work.

Block 1, of mass m1, moves across a frictionless surface with speed ui. It collides elastically with block 2, of mass m2, which is at rest (vi=0). (Figure 1)After the collision, block 1 moves with speed uf, while block 2 moves with speed vf. Assume that m1>m2, so that after the collision, the two objects move off in the direction of the first object before the collision. What is the final speed vf of block 2?

Answers

The conservation of the momentum allows to find the velocity of the second body after the elastic collision is:

           [tex]v_f = \frac{2u_o}{1- \frac{m_2}{m_1} }[/tex]  

the momentum is defined by the product of the mass and the velocity of the body.

        p = mv

The bold letters indicate vectors, p is the moment, m the mass and v the velocity of the body.

If the system is isolated, the forces during the collision are internal and the it  is conserved. Let's find the momentum is two instants.

Initial instant. Before crash.

      p₀ = m₁ u₀ + 0

Final moment. After crash.

      [tex]p_f = m_1 u_f + m_2 v_f[/tex]  

The momentum is preserved.

      p₀ = [tex]p_f[/tex]  

      [tex]m_1 u_o = m_1 u_f + m_2 v_f[/tex]  

Since the collision is elastic, the kinetic energy is conserved.

      K₀ = [tex]K_f[/tex]

      ½ m₁ u₀² = ½ m₁ [tex]u_f^2[/tex]  + ½ m₂  [tex]v_f^2[/tex]  

       

Let's write our system of equations.

       [tex]m_1 u_o = m_1 u_f + m_2 v_f \\m_1 u_o^2 = m_1 u_f^2 + m_2 v_f^2[/tex]

       

Let's solve

       [tex]u_f = u_o - \frac{m_2}{m_2} \ v_f \\u_f^2 = u_o^2 - \frac{m_2}{m_1} \ v_f^2[/tex]

       

       [tex]( u_o - \frac{m_2}{m_1} v_f)^2 = u_o - \frac{m_2}{m_1} \ v_f^2 \\u_o^2 - 2 \frac{m_2}{m_1} \ u_o v_f + (\frac{m_2}{m_1} )^2 v_f^2 = u_o^2 - \frac{m_2 }{m_1} \ v_f^2[/tex]  

         

        [tex]2 \frac{m_2}{m_1} \ u_o = \frac{m_2}{m_1} v_f \ ( 1 - \frac{m_2}{m_1}) \\v_f = \frac{2u_o}{1-\frac{m_2}{m_1} }[/tex]

In conclusion, using the conservation of momentum, we can find the velocity of the second body after the elastic collision is:

           [tex]v_f = \frac{2u_o}{1-\frac{m_2}{m_1} }[/tex]  

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An element with a force of 0.00SN moves at a minimum: 0.2m / s². Calculate the mass of that element.

Answers

Please find attached photograph for your answer.

Hope it helps.

Do comment if you have any query.

A ball of mass 2.0 kg is travelling at a speed of 12 m/s. It moves towards an object of mass 3.0 kg which is at rest.

The ball hits the object and sticks to it.

Which row gives the total momentum, and the speed of both objects immediately after the collision?

total momentum (kg m/s)
A- 0
B- 0
С- 24
D- 24

AND..

speed (m/s)
A- 4.8
B- 8.0
C- 4.8
D- 8.0

Answers

Please find attached photograph for your answer.

Hope it helps.

Do comment if you have any query.

The velocity for the entire trip is 0.4 m/s as It takes her 500 seconds to make the round trip and 60 kg • m/s2 = (45 kg • v) + (20 kg • 3 m/s).

Path 1 = 400 m В B. A Path 2 = 200 m Path 3 = 300 m. Thus, option C is correct.

What is velocity?

A particle's settling velocity known as the rate at which is travels through a still fluid. The specific gravity of the particles, their size, and their shape all have an impact on settling velocity.

A particle in still air will gravitationally settle and reach its terminal velocity fairly quickly. A particle's terminal velocity in a still fluid is referred to as the settling velocity (also known as the "sedimentation velocity").

Understanding variations in the hydraulic regime and interactions between sediment and fluid in the surf zone depends heavily on the particle settling velocity at the foreshore region. In contrast to sedimentation, which is the end product of the settling process, settling is the movement of suspended particles through the liquid.

Therefore, Thus, option C is correct.

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how do mechanical waves compare with electromagnetic waves?

Answers

Answer:

Electromagnetic waves are waves that have no medium to travel whereas mechanical waves need a medium for its transmission. Electromagnetic waves travel in a vacuum whereas mechanical waves do not. The mechanical waves need a medium like water, air, or anything for it to travel.

Explanation:

A car of mass 1500 kg is moving with a velocity of 30 m/s. If the velocity-time graph for this car
is a horizontal line parallel to the time axis, then the velocity of the car at the end of 25 s will be

Answers

Answer:

v=30m/s

Explanation:

m = 1500kg

v = 30m/s

t = 25s

The velocity time graph is parallel to the time axis,

that means The Velocity is constant. ('constant' means remains same).

Therefore, after 25s, v=30m/s

Do you think humans will ever walk on the sun?

Answers

[tex] \: \: \: \: \: [/tex]

yes

because sun have a super nova and if someone get it there that person definitely get burn

hope it helps

[tex] \: \: \: \: \: [/tex]

3. What happens if an object has a negative acceleration?​

Answers

Answer:

They will go backwards?

Explanation:

If positive they go forward but is negative they go backwards.


2. Given what you know about the acceleration of Earth's gravity (g = 9.8 m/s2), is this number accurate?
accurate. If not explain why you think it is not accurate. Pleaseee help mee

Answers

Answer:

it is correct

Explanation:

Though no rounded numbers can be defined as accurate, if we were going by people's discovery, and research, we can define that the number, g = 9.8m/s^2, is accurate

A wrecking ball has a mass of 650 kg. It swings from a cable that is 21 m long. The centripetal force on the ball is 56 N. What is the tangential speed of the wrecking ball? 1. 3 m/s 1. 8 m/s 46 m/s 870 m/s.

Answers

Hi there!

For an object moving in a circle:

Centripetal force = ∑F = mv²/r

Thus:

56 = mv²/r

Rearrange to solve for velocity:

√(56r/m) = v

√(56 × 21)/650 = 1.345 m/s

Answer:

A

Explanation:

have a good day

Calculate the force applied if 100 N/m² pressure is exerted over the area of 0.2m²​

Answers

Answer: 100 pascals times 0.2 m^2= 20 N force is applied.

Explanation:

help me solve please ​

Answers

Answer:

please check the image

Explanation:

I hope this image helps you please follow the steps. Thank you

Answer:

1kg/```````2

Explanation:

solution

the small lightweight particles outside the nucleus of an atom are called___.​

Answers

The neutron has no charge, and a mass of slightly over 1 amu. Some scientists propose the neutron is made up of a proton and electron-like particle. The electron is a very small particle located outside the nucleus.

Electron: -1

Neutron: 0

Proton: +1

You increase your walking speed from 1 m/s to 3 m/s in a period of 1 s.

What is your acceleration?

5 m/s2
3 m/s2
2 m/s2
4 m/s2

Answers

Answer:

2 m/s2

Explanation:

the answer is 2 m/s2

The initial temperature of the mixture was +20 °C. The mixture froze at -1.5 °C.
A total of 165 kJ of internal energy was transferred from the mixture to cool and
freeze it.
specific heat capacity of the mixture = 3500 J/kg °C
specific latent heat of fusion of the mixture = 255 000 J/kg
Calculate the mass of the mixture.
Give your answer to 2 significant figures.
[6
M

Answers

Answe16000/3500(-1.5-2-)225000= 1.1

Explanation:

The mass of the mixture will be 2.19 ×10⁻³ kg. The unit of mass is kg and it is a scalar quantity.

What is mass?

Mass is a numerical measure of inertia, which is a basic feature of all matter. It is, in effect, a body of matter's resistance to a change in speed or position caused by the application of a force.

In the International System of Units (SI), the kilogram is the unit of mass.

The given data in the problem is;

The initial temperature of the mixture was, [tex]\rm T_i = 20 ^0 \ C[/tex]

The mixture froze at the temperature of, [tex]\rm T_F = -1.5 ^0 \ C[/tex]

The internal energy is,[tex]\rm E = \rm 165 \ kJ[/tex]

The specific heat capacity of the mixture is,[tex]\rm C = 3500 J/kg ^0C[/tex]

The specific latent heat of fusion of the mixture is,[tex]\rm l = 255 000 J/kg[/tex]

m is the mass of the mixture,

The latent heat is equal to the heat transfer. Because the net work done is zero.

The formula for the heat transfer is found as;

[tex]\rm Q = mCdt \\\\ m = \frac{Q}{Cdt} \\\\ m = \frac{165 }{3500(20-(-1.5)} \\\\ m = 2.19 \times 10^{-3} \ kg[/tex]

Hence the mass of the mixture will be 2.19 ×10⁻³ kg.

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2hrt 20 min +60 sec ​

Answers

Answer:

2hr 21 min

Explanation:

0 days 2 hours 20 minutes 0 seconds

+ 0 days 0 hours 0 minutes 60 seconds

= 0 days 2 hours 21 minutes 0 seconds

According to the table, what was the hiker's average speed for
the entire hike?
A: 2.0 km/h B: 5.7 km/h C: 6.7 km/h D: 10 km/h

Answers

Answer:

6.7 km/h (C)

Explanation:

According to the table, the hiker's average speed for the entire hike would be 6.7 kilometers/hour.

What is speed?

The total distance covered by any object per unit of time is known as speed. It depends only on the magnitude of the moving object. The unit of speed is a meter/second. The generally considered unit for speed is a meter per second.

The total distance traveled by the hiker = 4 kilometers  + 6 kilometers + 4 kilometers west + 6 kilometers north

                                                                  = 20 kilometers

The total time is taken by the hiker = 45 min + 60 min + 30 min+ 45 min

                                                           = 180 min

                                                           =3 hours

                                               

The average speed of the hiker = 20 kilometers / 3 hours

                                                     = 6.7 kilometers / hours

Thus, the hiker's average speed for the entire hike would be 6.7 kilometers/hour.

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The energy transferred per unit electric charge in a circuit is .
A current
B charge
C power
D potential difference​

Answers

Answer:

(D)

E = V Q      energy of charge Q  thus V = E / Q

what is the medium for the sound waves for whales to communicate with each other?

Answers

Answer:

SONGS CLICKS AND WHISTLE

Explanation:

A ____ is a region where jets of gas from young stars impact and heat the gas surrounding the young star.

Answers

Bipolar outflow is the blank

how much of the light that reaches the earth from the sun is used for photosynthesis

Answers

Answer:

Less than one percent of the total energy that reaches Earth is used by plants for photosynthesis

The weight of a 1,000 kg car is ______________ (pick best answer)

Group of answer choices

9800 N

102.4 N

1000 N

10000 N​

Answers

What is the weight of a car with the mass of 1000 kg?

Answer: it is 9800 N.

How is the input energy carried to the light bulb's energy stores?

Answers

Answer:

the electric energy travels through the plug or wire or whatever is connecting the energy source to the lightbulb, which conducts electricity, and to the light bulb. the electric energy is transfered into light energy and thermal energy

Explanation:

i hope i understood this question and answered it correctly XD

A 100 kg roller coaster comes over the first hill at 2 m/sec (vo). The height of the first hill (h) is 20 meters. See roller diagram below.

1) Find the total energy for the roller coaster at the initial point.

2) Find the potential energy at point A using the PE formula.

3) Use the conservation of energy to find the kinetic energy (KE) at point B.

4) Find the potential energy at point C.

5) Use the conservation of energy to find the Kinetic Energy (KE) of the roller coaster at point C.

6) Use the Kinetic Energy from C, find velocity of the roller coaster at point C.

Answers

For the 100 kg roller coaster that comes over the first hill of height 20 meters at 2 m/s, we have:

1) The total energy for the roller coaster at the initial point is 19820 J

2) The potential energy at point A is 19620 J

3) The kinetic energy at point B is 10010 J

4) The potential energy at point C is zero

5) The kinetic energy at point C is 19820 J

6) The velocity of the roller coaster at point C is 19.91 m/s

1) The total energy for the roller coaster at the initial point can be found as follows:

[tex] E_{t} = KE_{i} + PE_{i} [/tex]

Where:

KE: is the kinetic energy = (1/2)mv₀²

m: is the mass of the roller coaster = 100 kg

v₀: is the initial velocity = 2 m/s

PE: is the potential energy = mgh

g: is the acceleration due to gravity = 9.81 m/s²

h: is the height = 20 m

The total energy is:

[tex] E_{t} = KE_{i} + PE_{i} = \frac{1}{2}mv_{0}^{2} + mgh = \frac{1}{2}*100 kg*(2 m/s)^{2} + 100 kg*9.81 m/s^{2}*20 m = 19820 J [/tex]

Hence, the total energy for the roller coaster at the initial point is 19820 J.

   

2) The potential energy at point A is:

[tex] PE_{A} = mgh_{A} = 100 kg*9.81 m/s^{2}*20 m = 19620 J [/tex]

Then, the potential energy at point A is 19620 J.

3) The kinetic energy at point B is the following:

[tex] KE_{A} + PE_{A} = KE_{B} + PE_{B} [/tex]

[tex] KE_{B} = KE_{A} + PE_{A} - PE_{B} [/tex]

Since

[tex] KE_{A} + PE_{A} = KE_{i} + PE_{i} [/tex]

we have:

[tex] KE_{B} = KE_{i} + PE_{i} - PE_{B} =  19820 J - mgh_{B} = 19820 J - 100kg*9.81m/s^{2}*10 m = 10010 J [/tex]

Hence, the kinetic energy at point B is 10010 J.

4) The potential energy at point C is zero because h = 0 meters.

[tex] PE_{C} = mgh = 100 kg*9.81 m/s^{2}*0 m = 0 J [/tex]

5) The kinetic energy of the roller coaster at point C is:

[tex] KE_{i} + PE_{i} = KE_{C} + PE_{C} [/tex]            

[tex] KE_{C} = KE_{i} + PE_{i} = 19820 J [/tex]      

Therefore, the kinetic energy at point C is 19820 J.

6) The velocity of the roller coaster at point C is given by:

[tex] KE_{C} = \frac{1}{2}mv_{C}^{2} [/tex]

[tex] v_{C} = \sqrt{\frac{2KE_{C}}{m}} = \sqrt{\frac{2*19820 J}{100 kg}} = 19.91 m/s [/tex]

Hence, the velocity of the roller coaster at point C is 19.91 m/s.

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the following can increase the amount of friction in the surface, except ______.
a. glue
b. paper
c. lubricant
d. foil​

Answers

Answer:

c. lubricant..........

How much work must be done to stop a 925-kg car traveling at 95 km/h?

Answers

The amount of work done to stop the car is equal to 322,099.85 Joules.

Given the following data:

Mass = 925 kilogramsVelocity = 95 km/h

Conversion:

Velocity = 95 km/h = [tex]\frac{95 \times 1000}{60 \times 60} = 26.39 \;m/s^2[/tex]

To determine the amount of work done to stop the car, we would apply the work-energy theorem:

Note: The amount of work done must balance the kinetic energy possessed by the car due to its motion.

From the work-energy theorem, we have:

[tex]Work\done = \Delta K.E\\\\Work\done = \frac{1}{2} MV^2[/tex]

Substituting the given parameters into the formula, we have;

[tex]Work\;done = \frac{1}{2} \times 925 \times (26.39)^2\\\\Work\;done =462.5 \times 696.4321[/tex]

Work done = 322,099.85 Joules

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How much potential energy did the the milkshake have after it fell off of the counter, just before it hit the ground (at the bottom)? Make sure to write the correct units with

your answer!

Answers

Answer:

The formula for potential energy depends on the force acting on the two objects. For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m / s2 at the surface of the earth) and h is the height in meters.

Imagine you have a ball tied to the end of a string. You hold the other end of the string and swing it around. Suppose the string breaks, what direction will the ball travel

Answers

It will move in a curving motion starting in the direction where it snapped from. In the end it goes down :D

Does the volume of a gas affect the rate of diffusion in a porous material​

Answers

Answer:

No

Explanation:

The rate of diffusion defines the gas that passes through some area over the course of time.

please no irrelevant answers!
Light enters a glass block at an angle of incidence of 46°. The light refracts at an angle of refraction of 26°. What is the refractive index of the glass?
A 0.57
B 0.61
C 1.64
D 1.77​

Answers

Answer:

Choice C: Approximately [tex]1.64[/tex].

(Assuming that light entered into this glass block from air.)  

Explanation:

Let [tex]n_{1}[/tex] denote the refractive index of the first medium (in this example, air.) Let [tex]\theta_{1}[/tex] denote the angle of incidence.

Let [tex]n_{2}[/tex] denote the refractive index of the second medium (in this example, the glass block.) Let [tex]\theta_{2}[/tex] denote the angle of refraction.

By Snell's Law:

[tex]n_{1} \, \sin(\theta_{1}) = n_{2}\, \sin(\theta_{2})[/tex].

Rearrange the equation to find an expression for [tex]n_{2}[/tex], the refractive index of the second medium (the glass block.)

[tex]\begin{aligned}n_{2} = \left(\frac{\sin(\theta_{1})}{\sin(\theta_{2})}\right)\, n_{1}\end{aligned}[/tex].

The refractive index of air is approximately [tex]1.00[/tex]. Substitute in the values and solve for [tex]n_{2}[/tex], the refractive index of the glass block:

[tex]\begin{aligned}n_{2} &= \left(\frac{\sin(\theta_{1})}{\sin(\theta_{2})}\right)\, n_{1} \\ &= \left(\frac{\sin(46^{\circ})}{\sin(26^{\circ})}\right)\times 1.00 \\ &\approx 1.64\end{aligned}[/tex].

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