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ella [17]
3 years ago
12

Newton’s empirical law of cooling/warming of an object is given by ( ), T Tm k dt dT = − where k is a constant of proportionalit

y, T(t) is the temperature of the object for t  0, and Tm is the ambient temperature –that is, the temperature of the medium around the object. When a cake is removed from an oven, its temperature is measured at 300 . 0 F Three minutes later its temperature is F 0 200 . How long will it take for the cake to cool off to a room temperature of F 0 70 ? (Assume that Tm =70.)
Physics
1 answer:
pychu [463]3 years ago
4 0

Answer:

The time for the cake to cool off to room temperature is

approximately 30 minutes.

Let T_{0} = 70^{0}F be the temperature and T that of the body

Explanation:

 Our Tm = 70, the initial-value problem is

\frac{DT}{dt} = <em>k</em>(T − 70), T(0) = 300

Solving the equation, we get

\frac{DT}{t-70} = <em>kdt</em>

In [T-70]= <em>kt </em>+C_{1}

    T   =  70  + C_{2} e^{kt}

Finding he value for C_{2} using the initial value of T (0)= 300, therefore we get:

300=70+C_{2}

C_{2} = 230 therefore

T= 70+ 230 e^{kt}

Finding the value for <em>k </em>using T (3)  = 200, therefore we get

T (3) = 200

e^{3k} = \frac{13}{23}

<em>K </em>= \frac{1}{3} in \frac{13}{23}

= -0.19018

Therefore

T(t) = 70+230e^{-0.19018}

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amm1812

Answer:

q=3.5*10^-4

Explanation:

<u>concept:</u>

The force acting on both charges is given by the coulomb law:

F=kq1q2/r^2

the centripetal force is given by:

Fc=mv^2/r

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KE=1/2mv^2

<u>The tension force:</u>

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T=mv^2/r

T=2(K.E)/r

T=2(50 J)/r

T=100/r

<u><em>when the plane is charged </em></u>

T+k*|q|^2/r^2=2(K.E)charged/r

100/r+k*|q|^2/r^2=2(53.5 J)/r

q=√(2r[53.5 J-50 J]/k)                                          √= square root on whole

q=√2(2)(53.5 J-50 J)/8.99*10^9

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5 0
3 years ago
A box with a mass of 40 kg sits at rest on a frictionless tile floor. with your foot, you apply a 20 N force in a horizontal dir
Grace [21]

Answer:

0.5 m/s²

Explanation:

according to Newton's second law, we are goven a relationship between force, mass and acceleration, with the formula:

F = m×a

F for force

m for mass

a for acceleration

we use the given data and get:

20 = 40×a

we find a=20/40=0.5m/s²

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2 years ago
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Answer:

<h2>135,000 J</h2>

Explanation:

The work done by an object can be found by using the formula

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From the question we have

workdone = 900 × 150

We have the final answer as

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