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madreJ [45]
3 years ago
11

F the radius of a sphere is increasing at the constant rate of 2 cm/min, find the rate of change of its surface area when the ra

dius is 100 cm
Physics
1 answer:
Mrac [35]3 years ago
5 0
The surface area of a sphere of radius r is
A(r) = 4πr²

The rate of change of the surface area with respect to time is
\frac{dA}{dt} = \frac{dA}{dr} \frac{dr}{dt}

The radius increases at the constant rate of 2 cm/min, therefore
\frac{dA}{dt} = 2 \frac{dA}{dr}=2*(8 \pi r) =16 \pi r

When r = 100 cm, the rate of change of the surface area is
16π(100) cm²/min
= 1600π cm²/min
= 5026.5 cm²/min

Answer: 1600π or 5026.5 cm²/min


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Provide an example of when momentum is conserved and explain your answer you can get 10 PTS if answered with a good explaination
dezoksy [38]

Answer:

m_1=8\ kg,\ m_2=6\ kg,\ v_1=12\ m/s, v_2=4\ m/s,\ v_1'=-6\ m/s,\ v_2'=28\ m/s

Explanation:

<u>Conservation of Momentum </u>

The total momentum of a system of two particles is

p=m_1v_1+m_2v_2

Where m1,m2,v1, and v2 are the respective masses and velocities of the particles at a given time. Then, the two particles collide and change their velocities to v1' and v2'. The final momentum is now

p'=m_1v_1'+m_2v_2'

The momentum is conserved if no external forces are acting on the system, thus

m_1v_1+m_2v_2=m_1v_1'+m_2v_2'

Let's put some numbers in the problem and say

m_1=8\ kg,\ m_2=6\ kg,\ v_1=12\ m/s, v_2=4\ m/s,\ v_1'=-6\ m/s,\ v_2'=28\ m/s

(8)(12)+(6)(4)=(8)(-6)+(6)(28)

96+24=-48+168

120=120

It means that when the particles collide, the first mass returns at 6 m/s and the second continues in the same direction at 28 m/s

4 0
3 years ago
Even when shut down after a period of normal use, a large commercial nuclear reactor transfers thermal energy at the rate of 150
Phoenix [80]

Answer:

The temperature of the core raises by 2.8^{o}C every second.

Explanation:

Since the average specific heat of the reactor core is 0.3349 kJ/kgC

It means that we require 0.3349 kJ of heat to raise the temperature of 1 kg of core material by 1 degree Celsius

Thus reactor core whose mass is 1.60\times 10^{5}kg will require

0.3349\times 1.60\times 10^{5}kJ\\\\=0.53584\times 10^{5}kJ

energy to raise it's temperature by 1 degree Celsius in 1 second

Hence by the concept of proportionately we can infer 150 MW of power will increase the temperature by

\frac{150\times 10^{6}}{0.53584\times 10^{8}}=2.8^{o}C/s

5 0
3 years ago
All of the orbitals in a given subshell have the same value of the __________ quantum number.
Gelneren [198K]
All of the orbitals in a given subshell have the same value of the "<span>magnetic and principal" quantum number

Hope this helps!</span>
3 0
3 years ago
a ball is thrown horizontally from the roof of a building 45m tall and lands 24m from the base what is the initial speed?
Irina-Kira [14]
Its initial speed is 7.92 m/s

6 0
3 years ago
A sphere of radius 5.00 cmcm carries charge 3.00 nCnC. Calculate the electric-field magnitude at a distance 4.00 cmcm from the c
kogti [31]

Answer:

a) E = 8628.23 N/C

b) E = 7489.785 N/C

Explanation:

a) Given

R = 5.00 cm = 0.05 m

Q = 3.00 nC = 3*10⁻⁹ C

ε₀ = 8.854*10⁻¹² C²/(N*m²)

r = 4.00 cm = 0.04 m

We can apply the equation

E = Qenc/(ε₀*A)  (i)

where

Qenc = (Vr/V)*Q

If    Vr = (4/3)*π*r³  and  V = (4/3)*π*R³

Vr/V = ((4/3)*π*r³)/((4/3)*π*R³) = r³/R³

then

Qenc = (r³/R³)*Q = ((0.04 m)³/(0.05 m)³)*3*10⁻⁹ C = 1.536*10⁻⁹ C

We get A as follows

A = 4*π*r² = 4*π*(0.04 m)² = 0.02 m²

Using the equation (i)

E = (1.536*10⁻⁹ C)/(8.854*10⁻¹² C²/(N*m²)*0.02 m²)

E = 8628.23 N/C

b) We apply the equation

E = Q/(ε₀*A)  (ii)

where

r = 0.06 m

A = 4*π*r² = 4*π*(0.06 m)² = 0.045 m²

Using the equation (ii)

E = (3*10⁻⁹ C)/(8.854*10⁻¹² C²/(N*m²)*0.045 m²)

E = 7489.785 N/C

6 0
2 years ago
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