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
masha68 [24]
2 years ago
14

Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te

mperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 205 degrees Fahrenheit when freshly poured, and 2.5 minutes later has cooled to 195 degrees in a room at 70 degrees, determine when the coffee reaches a temperature of 160 degrees.
Physics
1 answer:
Maksim231197 [3]2 years ago
8 0

Answer:

Tt = 70 + 135e^-0.031t

13 minutes

Explanation:

Given that :

Initial temperature, Ti = 205°

Temperature after 2.5 minutes = 195°

Temperature of room, Ts= 70

Using the relation :

Tt = Ts + Ce^-kt

Temperature after time, t

When freshly poured, t = 0

205 = 70 + Ce^-0k

205 = 70 + C

C = 205 - 70 = 135°

T after 2.5 minutes to find proportionality constant, k

Tt = Ts + Ce^-kt

195 = 70 + 135e^-2.5k

125 = 135e^-2.5k

125 / 135 = e^-2.5k

0.9259 = e^-2.5k

Take In of both sides :

−0.076989 = - 2.5k

k = −0.076989 / - 2.5

k = 0.031

Equation becomes :

Tt = 70 + 135e^-0.031t

t when Tt = 160

160 = 70 + 135e^-0.031k

90 = 135e^-0.031t

90/135 = e^-0.031t

0.6667 = e^-0.031t

In(0.6667) = - 0.031t

−0.405465 = - 0.031t

t = 0.405465/ 0.031

t = 13.071

t = 13 minutes

You might be interested in
7. A car moving at 10m/s (about 22.4 mph) crashes into a barrier and stops in 0.25 m.
Galina-37 [17]

Answer:

a) 0.05s

b) 4000N

Explanation:

a)When car is stopped its final velocity become zero

U- 10 m/s

V- 0 m/s

S - 0.25 m

t -?

S = (v+u)*t/2

0.25 =(10+0)*t/2

t = 0.05s

b) If we happened to calculate the avarage force we have to consider about acceleration

V= 0

U = 10

t = 0.05 s

a =?

V = U + at

0 = 10 -a * 0.05

a = 200 m/s2

F = m *a

= 20 * 200

= 4000N

6 0
3 years ago
A hiker starts at point P and walks 2.0 km due east and then walks at an angle of 30 degrees north of east for 1.4 km.
olchik [2.2K]

Answer:

The magnitude of the hiker’s displacement is 2.96 km

Explanation:

Let the initial displacement of the hiker, = x = 2km

the final displacement of the hiker, = y = 1.4 km

The resultant of the two vectors, According to Pythagorean theorem is the vector sum of the two vectors.

R' = x' + y'

Check the image uploaded for solution;

8 0
3 years ago
Figure 21.62 shows a box on whose surfaces the electric field is measured to be horizontal and to the right. On the left face (3
natima [27]

(a) The electric flux on left face is 0.24 Vm and on the right face is 1 Vm.

(b) The total flux is 1.24 Vm.

(c) The total amount of charge that is inside the box is  1.1 x 10⁻¹¹ C.

<h3>Area of the left face</h3>

The area of the left face is calculated as follows;

A1 = 0.03 m x 0.02 m = 0.0006 m²

<h3>Electric flux on the left face</h3>

Ф1 = EA1

Ф1 = (400 V/m)( 0.0006 m²) = 0.24 Vm

Let the dimension of the right face = 5 cm by 2 cm

<h3>Area of the right face</h3>

A2 = 0.05 m x 0.02 m = 0.001 m²

<h3>Electric flux on the right face</h3>

Ф2 = EA2

Ф2 = (1000 V/m)( 0.001 m²) = 1 Vm

<h3>Total flux</h3>

Ф = Ф1 + Ф2

Ф = 0.24 Vm + 1 Vm = 1.24 Vm

<h3>Total charge inside the box</h3>

Ф = Q/ε

Q = εФ

Q = (8.85 x 10⁻¹²)(1.24)

Q = 1.1 x 10⁻¹¹ C

Thus, the electric flux on left face is 0.24 Vm and on the right face is 1 Vm.

The total flux is 1.24 Vm and the total amount of charge that is inside the box is  1.1 x 10⁻¹¹ C.

Learn more about total flux here: brainly.com/question/26289097

#SPJ1

7 0
2 years ago
In the ___________ biome, plants typically have deep roots, reduced leaves, and photosynthetic stems.
Yakvenalex [24]
The Desert Biome is your answer. They have deep roots because it receives little to no rainfall
3 0
3 years ago
Read 2 more answers
Which psychiatrist believed the environment was more important to a child's intellectual development than biology? A. B. F. Skin
Ugo [173]
The accurate answer is
The psychiatrist that <span>believed the environment was more important to a child's intellectual development than biology was "D" </span>Sigmund Freud.
8 0
3 years ago
Other questions:
  • Materials that are magnetic have_________that are lined up in the same orientation?
    14·1 answer
  • A combination of two or more simple machines is a (n)
    10·1 answer
  • Which of the following is not a multicellular organism?
    13·2 answers
  • A 238 92U nucleus is moving in the x-direction at 5.0 × 105 m/s when it decays into an alpha particle 4 2He and a 234 90Th. If t
    6·1 answer
  • Which of the following BEST describes sports etiquette?
    12·1 answer
  • A cell supplies current of 0.6A and 0.2A through 1ohms and 4.0ohms resistor respectively. Calculate the internal resistance of t
    13·1 answer
  • Which refers to the rate of change in velocity?
    13·1 answer
  • can you suggest improvement that can be made towards the design of siphon so that the transfer of liquid is much higher.​
    13·1 answer
  • Which data set has the largest range?
    7·1 answer
  • PLEASE HELP ASAP I WILL GIVE YOU BRAINLEAST (15 POINTS)
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!