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lisabon 2012
3 months ago
5

A Styrofoam slab has thickness h and density ρs. When a swimmer of mass m is resting on it, the slab floats in fresh water with

its top at the same level as the water surface. Find the area of the slab. (Use any variable or symbol stated above along with the following as necessary: ρw for the density of water.)
Physics
1 answer:
Ostrovityanka [3.2K]3 months ago
8 0
 <span>A = area of styrofoam 
M = mass of styrofoam = A*h*rho_s 
m = mass of swimmer 

The overall mass totals = m + M = m + A*h*rho_s 
The force acting downwards = g*(combined mass) = g*[m + A*h*rho_s] 

The slab is entirely submerged. 
The buoyant force = g*(weight of water displaced) = g*[A*h*rho_w] 

By setting these two equal
g*[m + A*h*rho_s] = g*[A*h*rho_w] 
This leads to m + A*h*rho_s = A*h*rho_w 
Rearranging gives A*h*[rho_w - rho_s] = m 
Thus, A = m/[h*(rho_w - rho_s)]</span>
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Answer:

a

The value at a point inside is Zero

b

The electric field is E = 2.7*10^{6} \ N/C

Explanation:

We know from the problem that

The charge magnitude is q = 3.0 \mu C = 3.0 *10^{-6} \ C

The radius of the spherical ball is r = 5.0 \ mm = 0.005 \ m

According to Gauss’s law, the enclosed charge within a conductor is zero which indicates that the electric field within the spherical ball is zero

On the outside, the electric field around the spherical ball is mathematically expressed as

E = \frac{kq}{ a^2}

Here a denotes a point outside the spherical ball with its value of a = 10 \ cm = \frac{10}{100} = 0.1 \ m

and k represents Coulomb's constant, valued at

k = 9*10^{9}\ kg\cdot m^3\cdot s^{-4} \cdot A^{-2}.

=> E = \frac{ 3 *10^{-6} * 9*10^9 }{ (0.1)^2}

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2 months ago
A helicopter starting on the ground is rising directly into the air at a rate of 25 ft/s. You are running on the ground starting
serg [3582]

Response:

The speed at which the distance from the helicopter to you is changing (in ft/s) after 5 seconds is \sqrt{725} ft/ sec

Clarification:

Provided:

h(t) = 25 ft/sec

x(t) = 10 ft/ sec

h(5) = 25 ft/sec. 5 = 125 ft

x(5) = 10 ft/sec. 5 = 50 ft

At this point, we can determine the distance between the individual and the helicopter utilizing the Pythagorean theorem

D(t) = \sqrt{h^2 + x^2}

Now, let's calculate the derivative of distance in relation to time

\frac{dD}{dt} (t) = \frac{2h \cdot \frac{dh}{dt} +2x \cdot\frac{dx}{dt}} {2\sqrt{h^2 + x^2}}

By plugging in the values for h(t) and x(t) and simplifying, we arrive at,

\frac{dD}{dt}(t) = \frac{50t \cdot \frac{dh}{dt} + 20 \cdot \frac{dx}dt}{2\sqrt{625\cdot t^2 + 100 \cdot t^2}}

\frac{dh}{dt} = 25ft/sec

\frac{dx}{dt} = 10 ft/sec

\frac{Dd}{dt} (t) = \frac{1250t +200t}{2\sqrt{725}t} = \frac{725}{\sqrt{725}} = \sqrt{725} ft / sec

5 0
1 month ago
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