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
svlad2 [7]
3 years ago
8

is a constant related to the size and composition of the ball as well as the viscosity of the syrup. Find the rate at which grav

itational energy is converted to thermal energy once the ball reaches terminal velocity.
Physics
1 answer:
Neporo4naja [7]3 years ago
4 0

Answer:

Thermal = 0.48 W

Explanation:

Given:

- The complete question is:

" Starting from rest, a 0.0367-kilogram steel ball sinks into a vat of corn syrup. The thick syrup exerts a viscous drag force that is proportional to the ball's velocity: where C = 0.270 N- s/m is a constant related to the size and composition of the ball as well as the viscosity of the syrup. Find the rate at which gravitational energy is converted to thermal energy once the ball reaches terminal velocity. After the ball reaches terminal velocity its kinetic energy is constant Any further work done by gravity is therefore directly transferred to the syrup and ball as thermal energy The rate at which the energy is converted is the power supplied by gravity: where F is the force, v is the speed of the ball and B is the relative angle between the force and velocity vectors. The terminal velocity of the ball can be determined from the given information using Newton's Laws. "

Solution:

- Once the terminal velocity Vt of the body is reached, it begins to move downward  at constant speed. The drag force Fd then attains a constant value:

                                         Fd = - C • Vt

- Instant the rate of conversion of gravitational potential energy to thermal  energy becomes equal to the power dissipated by the drag force at the terminal  velocity is given by:

                                        Fd • Vt = - C • Vt ²

- To get the general velocity V , solve the equation of motion:

                                        mv' = -m*g - C*V

                                        v' = -g - [C/ m] * V

Where,

                                        v' = dv / dt

                                        dv / dt =  -g - [C/ m] * V

- We will denote [C/ m]  as constant B:

                                        dv / dt =  -B*[ g/B +  V ]

- Separate variables:

                                        dv / [ g/B +  V ]  =  -B*dt

- Integrate both sides:

                                        Ln | g/B +  V | = -B*t + C

                                        g/B +  V = C*e^( -B*t )

                                        V = C*e^( -B*t ) - g/B

- The above expression for velocity gives the velocity of the steel ball at any time t. We know that terminal velocity Vt is achieved when t - > ∞. Then we have:

                                       Vt = 0 - g/B = -m*g/C

- Then from power equation we have:

                                        P = - C*Vt^2

                                        P = -C ( -m*g/C )^2

                                        P = -(mg)^2 / C

                                        P = -(0.0367*9.81)^2 / 0.27

                                        P = - 0.48 W

- The rate at which gravitational energy is lost to surrounding gives rise to thermal energy of surrounding fluid Thermal = 0.48 W .

You might be interested in
What is matter? Give a grade 10/11/12 understanding.
lara [203]

Matter can be many things, but is mostly made of atoms. Atoms are small things that cannot be seen directly, as lights either passes through it or alters it. However, we know that atoms are made of 3 parts, those being the proton, neutron, and electron.

Protons have a positive electromagnetic charge.

Neutrons have no charge.

Electrons have a negative charge equal to the protons positive charge.

Protons and neutrons make up what's called the nucleus, which is orbited by the electrons.

Protons and neutrons also share another thing in common, that being their composition.

Until relatively recently, we thought that these were the smallest particles in the universe, and indestructible. However, modern discoveries have revealed that they are actually made of quarks and gluons.

These are actually indestructible, being part of the group that is elementary particles.

3 0
3 years ago
The key to making a concise mathematical definition of escape velocity is to consider the energy. If an object is launched at it
aleksklad [387]

Answer:

The total Mechanical energy will be zero

Explanation: Escape velocity is the velocity required by a free object in order to overcome the impact of the force of gravity. The total mechanical energy of an object is the total energy possessed by an object which includes its kinectic and potential energy.

since the object is moving at an escape velocity which is 11.2m/s the object will be assumed to be weightless

Etotal = kinetic energy + potential energy

kinetic energy= 1/2*M*V*V

Potential energy=MGH

Etotal=1/2*0*11.2*11.2+0*0*0

Etotal=0+0

Etotal=0.

3 0
3 years ago
This version of Einstein’s equation is often used directly to find what value?
Setler [38]
This version of Einstein’s equation is often used directly to find what value? E = ∆mc2

Answer: This version of Einstein’s equation is often used directly to find the mass that is lost in a fusion reaction. Therefore the correct answer to this question is answer choice C).

I hope it helps, Regards.
8 0
2 years ago
Read 2 more answers
Pls help me, tomorrow is the deadline of my assignment ​
elena-14-01-66 [18.8K]

Answer:

6- B

7- I think A

8-B

9-D

10-A

3 0
2 years ago
The length of a 100 mm bar of metal increases by 0.3 mm when subjected to a temperature rise of 100°C. The coefficient of linear
Juli2301 [7.4K]

Answer:

α = 3×10^-5 K^-1

Explanation:

let ΔL be the change in length of the bar of metal, ΔT be the change in temperature, L be the original length of the metal bar and let α be the coefficient of linear expansion.

then, the coefficient of linear expansion is given by:

α = ΔL/(ΔT×L)

   = (0.3×10^-3)/(100)(100×10^-3)

   = 3×10^-5 K^-1

Therefore, the coefficient of linear expansion is 3×10^-5 K^-1

5 0
3 years ago
Other questions:
  • An object starts at rest then accelerates at a rate of 5m/s^2 for 1 second and then 2m/s^2 for 2 seconds. What is the average ac
    10·1 answer
  • What’s the similarity between nuclear fission and nuclear fusion
    15·1 answer
  • How does the water cycle affect weather and climate?
    14·2 answers
  • The ancient city of Pompeii was destroyed when a mixture of hot volcanic gasses, ash, and rock pored down Mount Vesuvius and cov
    7·2 answers
  • Suppose you wish to construct a motor that produces a maximum torque whose magnitude is 1.7 × 10-2 N·m. The coil of the motor ha
    11·1 answer
  • This DNA strand consists of eight pairs of nitrogenous bases. How many different sequences of eight bases can you make?
    8·1 answer
  • Short wavelengths, from high-pitched sounds, cause displacement of the basilar membrane near the oval window. true false
    15·2 answers
  • What is the best explanation for seasons?
    7·2 answers
  • Please help it’s multiple choice
    7·1 answer
  • A copper calorimeter of mass 120g contains 70g of water and 10g of ice at 0°C. What mass of steam at 100°C must be passed into t
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!