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
Dmitry [639]
3 years ago
12

Newton's law of cooling is , where is the temperature of an object, is in hours, is a constant ambient temperature, and is a pos

itive constant. Suppose a building loses heat in accordance with Newton's law of cooling. Suppose that the rate constant has the value Assume that the interior temperature is , when the heating system fails. If the external temperature is , how long will it take for the interior temperature to fall to

Physics
1 answer:
kirill [66]3 years ago
3 0

Complete Question

The complete question is shown on the first uploaded image

Answer:

The time taken  is  t  = 6.89 \ hrs

 

Explanation:

From the question we are told that

       The value of  k = 0.15hr^{-1}

       The  the interior temperature is  u(t = 0) =  70 ^oF

         The external temperature is  T  = 11 ^oF

          The required interior temperature is  u_{t} = 32 ^oF

      The newton cooling law is

                      \frac{du}{dt}  =  -k (u -T)

=>                 \frac{du}{u-T}  = - kdt

  Now integrate both sides we have  

                 \int\limits \frac{du}{u-T}  =\int\limits   - kdt

                   ln (u - T) =  -kt + c    

Since c is a constant lnC = c   will also give a constant so

                 ln (u - T) =  -kt + ln C    

       =>       \frac{(u -T)}{C}  =  e^{-kt}

     =>        u = T + Ce^{-kt}  

          substituting value

                  70 = 11 +Ce^{-0* 0.15}

                  C = 59

Hence

        u_t =  11 + 59 e^{-0.15 *t}

       32=  11 + 59 e^{-0.15 *t}

=>     t  =  -\frac{ln(\frac{21}{59} )}{0.15}

         t  = 6.89 \ hrs

 

You might be interested in
Write a question you would like to see on a quiz to calculate NET FORCE.
Pie

Answer:

How do you find the net force?

Explanation:

i think this is want you asked for?

5 0
3 years ago
Two bodies are falling with negligible air resistance, side by side, above a horizontal plane. If one of the bodies is given an
tankabanditka [31]

Answer:4-strikes the plane at same time as the other body

Explanation:

Given

If both bodies is falling on a horizontal plane and second body is given an acceleration in horizontal direction then it does not change the time to reach the Horizontal Plate as there is no change in vertical direction.

Horizontal acceleration will give only horizontal range and horizontal velocity.

8 0
3 years ago
Read 2 more answers
More Density Graphi Questions
nata0808 [166]

Answer:

?

Explanation:

6 0
3 years ago
In any problems involving circular motion, which way does the tangential speed vector point?
Anton [14]

In what may be one of the most remarkable coincidences in
all of physical science, the tangential component of circular
motion points along the tangent to the circle at every point. 

The object on a circular path is moving in that exact direction
at the instant when it is located at that point in the circle.  The
centripetal force ... pointing toward the center of the circle ...
is the force that bends the path of the object away from a straight
line, toward the next point on the circle.  If the centripetal force
were to suddenly disappear, the object would continue moving
from that point in a straight line, along the tangent and away from
the circle.

4 0
3 years ago
The length of a football field is closest to<br> (1) 1000 cm (3) 1000 km<br> (2) 1000 dm (4) 1000 mm
Sergeu [11.5K]

For this case, the first thing you should know is that the length of a football field is around 100 meters.

We must then look for a measure close to this value.

We have the following unit conversion:

1 meter = 10 decimeters

Applying the conversion we have:

(1000 dm)*(\frac{1}{10} \frac{m}{dm}) = 100 m

Therefore, the measure closest to a soccer field is:

1000 dm

Answer:

The length of a football field is closest to:

(2) 1000 dm

5 0
4 years ago
Read 2 more answers
Other questions:
  • What will be the force if the particle's charge is tripled and the electric field strength is halved? Give your answer in terms
    6·1 answer
  • Calculate the speed of an 8.0 x 10^4 kg airliner with a kinetic energy of 1.1 x 10^9 J.
    9·1 answer
  • I. The spring does work on the box from the moment the box first hits the spring to the moment the spring first reaches its maxi
    6·1 answer
  • list all the storage forms of energy that forms of energy that you are familiar with. for each storage form, give an example of
    15·1 answer
  • 1. How much heat energy is required to raise the temperature of a 5 kg aluminium bar
    14·1 answer
  • A space vehicle deploys its re–entry parachute when it's traveling at a vertical velocity of –150 meters/second (negative becaus
    8·1 answer
  • A sprinter accelerates from rest to 10.0 m/s in 1.28 s . Part A Part complete What is her acceleration in m/s2? a a = 7.81 m/s2
    6·1 answer
  • A turtle and a rabbit are in a 150 meter race. The rabbit decides to give the turtle a 1 minute head start. The turtle moves at
    11·1 answer
  • The unit of area is derived unit why​
    6·2 answers
  • You are at a 4-way stop, and it is your turn to go. However, the car across from you starts to go. Explain.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!