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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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harina [27]

The term used is " WORK".

I'm really sorry it's not one of the choices.

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A juggler throws a bowling pin straight up with an initial speed of 8.20 m/s. How much time elapses until the bowling pin return
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Answer:

1.68 s

Explanation:

From newton's equation of motion,

a = (v-u)/t.................................. Equation 1

Making t the subject of the equation

t =(v-u)g............................. Equation 2

Where t = time taken for the bowling pin to reach the maximum height, v = final velocity bowling pin, u = initial velocity of the bowling pin, g = acceleration due to gravity.

Note: Taking upward to be negative and down ward to be positive,

Given: v = 0 m/s ( at the maximum height), u = 8.20 m/s, g = -9.8 m/s²

t = (0-8.20)/-9.8

t = -8.20/-9.8

t = 0.84 s.

But,

T = 2t

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7 0
3 years ago
A spring is hanging from the ceiling. When a 250 gram of mass is attached to the free end, the spring elongates by 5 cm. The spr
lord [1]

Answer:

k = 49 N/m

Explanation:

Given that,

Mass, m = 250 g = 0.25 kg

When the mass is attached to the end of the spring, it elongates 5 cm or 0.05 m. We need to find the spring constant. Let it is k.

The force due to mass is balanced by its weight as follows :

mg=kx

k=\dfrac{mg}{x}\\\\k=\dfrac{0.25\times 9.8}{0.05}\\\\k=49\ N/m

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Starting from rest, a 2-m-long pendulum swings from an angleof
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Answer:

D.) 1m/s

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L_1 = L*cos(12.8) = 2*0.975 = 1.95 m

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The vertical distance from the lowest point to the pivot point L_2 is the pendulum length 2m

this means the vertical distance from this initial point to the lowest point is simply:

L_3 = L_2 - L_1 = 2 - 1.95 = 0.05 m

As the pendulum travel (vertically) from the initial point to the bottom point, its potential energy is converted to kinetic energy:

E_p = E_k

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where m is the mass of the pendulum, g  = 10 m/s2 is the constant gravitational acceleration, h = 0.05 is the vertical it travels, v is the pendulum velocity at the bottom, which we are trying to solve for.

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Electromagnetic waves can travel through a vacuum, that is an empty space, whereas mechanical waves cannot. They need a medium to travel such as water or air. Ripples in a pond are an example of mechanical waves whereas electromagnetic waves include light and radio signals, which can travel through the vacuum of space.

Mechanical waves can be classed as elastic waves because their transmission depends on the medium's (water, air etc.) elastic properties.

Electromagnetic waves are caused because of the varying magnetic and electric fields. They are produced by the vibration of the charged particles.

Because of these differences, the speed of each type of wave varies significantly. Electromagnetic waves travel at the speed of light but mechanical waves are far slower.

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