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Olin [163]
4 years ago
7

A 5 kg bucket is lifted from the ground into the air by pulling in 10 meters of rope with linear density of 2 kg/m at a constant

speed. The bucket starts with 100 cm^3 of water and leaks at a constant rate. It finishes draining just as it reaches the 10 meter mark. How much work was spent lifting the bucket, rope, and water?
Physics
1 answer:
iren [92.7K]4 years ago
7 0

Answer:

Workdone W = 1465.1 J

Explanation:

The weight of the water = density × volume

weight of the water = 1000 kg/m³ × 100 cm³

weight of the water = 1000 kg/m³ × 0.0001 m³

weight of the water = 0.1 kg

weight of the bucket  = 5 kg

weight of the rope = 2*10- 2x\\\\

= 20- 2x

Leakage = \frac{0.1}{10}  * x

= 0.01 x

Total  weight = 5 + 20 - 2x - 0.01 x

= 25 - 2.01 x

Force = wg

Force = (25 - 2.01 x)g

Force = 9.8 (25 - 2.01 x)

Finally; the amount of work spent in lifting the bucket, rope, and water is calculated as follows:

W = \int\limits^{10}_0 {(25-2.01 x)} \, 9.8 dx \\\\W = 9.8 (25x - \frac{2.01x^2}{2}})^{10}__0\\\\

W = 9.8 (25*10-2.01*50)\\\\W = 1465.1 \ \ J

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3 years ago
Some fish have a density slightly less than that of water and must exert a force (swim) to stay submerged. What force must an 85
vichka [17]

The force require to keep grouper submerged is 8.207N.

According to Archimedes principle  buoyant force of any object must equal to weight of fluid it displaced.

The expression for the force exerted to stay submerged in salt water is

           F = F(b) - w(fish)

 where F(b) = buoyant force

              w(fish) = weight

      now substitute w(b) for F(b)

   →  F = Vρg - w(fish)

where  V = volume of sea water

             ρ = density of sea water

Now by Archimedes principle   V = m(fish)  / ρ(fish)

    →    F = (m(fish) / ρ (fish) ) ρg - m(fish)g

           F =   (85 kg/1015 kg-m^-3) (1.025× 10³ kg-m^-3) (9.8 m/s^2)

                                  -   (85kg)  × 9.8 m/s^2

           F = 841.207N - 833N

           F = 8.207 N

  Hence, the force require to keep grouper submerged is 8.207N.

    Learn more about Archimedes Principle here:

         brainly.com/question/15076878

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7 0
2 years ago
Two tiny, spherical water drops, with identical charges of −8.00 ✕ 10^(−17) C, have a center-to-center separation of 2.00 cm.
Damm [24]

Answer:

F=1.4384×10⁻¹⁹N

Explanation:

Given Data

Charge q= -8.00×10⁻¹⁷C

Distance r=2.00 cm=0.02 m

To find

Electrostatic force

Solution

The electrostatic force between between them can be calculated from Coulombs law as

F=\frac{kq^{2} }{r^{2} }

Substitute the given values we get

F=\frac{(8.99*10^{9} )*(-8.00*10^{-17} )^{2} }{(0.02)^{2} }\\ F=1.4384*10^{-19} N

7 0
3 years ago
How much does the gravitational force of attraction change between two asteroids if the two asteroids drift three times closer t
Katen [24]

Answer:

Increase 9 times

Explanation:

We have Newton formula for attraction force between 2 objects with mass and a distance between them:

F_G = G\frac{M_1M_2}{R^2}

where G =6.67408 \times 10^{-11} m^3/kgs^2 is the gravitational constant. M_1, M_2 is the masses of the 2 objects. and R is the distance between them.

Since the force is inversely proportional to the distance squared, if it is reduced by 3 times, the gravitational force between them would increase by 3^2 = 9 times

6 0
3 years ago
A particle with mass 1.81*10^-3kg and a charge of 1.22*10^-8C has, at a given instant, a velocity v= (3.0*10^4 m/s)j.
charle [14.2K]

Answer:

a = -0.33 m/s² k^

Direction: negative

Explanation:

From Newton's law of motion, we know that;

F = ma

Now, from magnetic fields, we know that;. F = qVB

Thus;

ma = qVB

Where;

m is mass

a is acceleration

q is charge

V is velocity

B is magnetic field

We are given;

m = 1.81 × 10^(−3) kg

q = 1.22 × 10 ^(−8) C

V = (3.00 × 10⁴ m/s) ȷ^.

B = (1.63T) ı^ + (0.980T) ȷ^

Thus, since we are looking for acceleration, from, ma = qVB; let's make a the subject;

a = qVB/m

a = [(1.22 × 10 ^(−8)) × (3.00 × 10⁴)ȷ^ × ((1.63T) ı^ + (0.980T) ȷ^)]/(1.81 × 10^(−3))

From vector multiplication, ȷ^ × ȷ^ = 0 and ȷ^ × i^ = -k^

Thus;

a = -0.33 m/s² k^

7 0
3 years ago
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