Ask question

Ask question

All categories

Ksenya-84 [330]

3 years ago

14

A leaky 10-kg bucket is lifted from the ground to a height of 11 m at a constant speed with a rope that weighs 0.9 kg/m. Initial

ly the bucket contains 33 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 11-m level. Find the work done. (Use 9.8 m/s2 for g.) Show how to approximate the required work by a Riemann sum. (Let x be the height in meters above the ground. Enter xi* as xi.)

1 answer:

nalin [4]3 years ago

8 0

Answer:

the work done to lift the bucket = 3491 Joules

Explanation:

Given:

Mass of bucket = 10kg

distance the bucket is lifted = height = 11m

Weight of rope= 0.9kg/m

g= 9.8m/s²

initial mass of water = 33kg

x = height in meters above the ground

Let W = work

Using riemann sum:

the work done to lift the bucket =∑(W done by bucket, W done by rope and W done by water)

= $\int\limits^a_b {(Mass of Bucket + Mass of Rope + Mass of water)*g*d} \, dx$

Work done in lifting the bucket (W) = force × distance

Force (F) = mass × acceleration due to gravity

Force = 9.8 * 10 = 98N

W done by bucket = 98×11 = 1078 Joules

Work done to lift the rope:

At Height of x meters (0≤x≤11)

Mass of rope = weight of rope × change in distance

= 0.8kg/m × (11-x)m

W done = integral of (mass×g ×distance) with upper 11 and lower limit 0

W done = $\int\limits^1 _0 {9.8*0.8(11-x)} \, dx$

Note : upper limit is 11 not 1, problem with math editor

W done = 7.84 (11x-x²/2)upper limit 11 to lower limit 0

W done = 7.84 [(11×11-(11²/2)) - (11×0-(0²/2))]

=7.84(60.5 -0) = 474.32 Joules

Work done in lifting the water

At Height of x meters (0≤x≤11)

Rate of water leakage = 36kg ÷ 11m = $\frac{36}{11}$ kg/m

Mass of rope = weight of rope × change in distance

= $\frac{36}{11}$ kg/m × (11-x)m = 3.27kg/m × (11-x)m

W done = integral of (mass×g ×distance) with upper 11 and lower limit 0

W done = $\int\limits^1 _0 {9.8*3.27(11-x)} \, dx$

Note : upper limit is 11 not 1, problem with math editor

W done = 32.046 (11x-x²/2)upper limit 11 to lower limit 0

W done = 32.046 [(11×11-(11²/2)) - (11×0-(0²/2))]

= 32.046(60.5 -0) = 1938.783 Joules

the work done to lift the bucket =W done by bucket+ W done by rope +W done by water)

the work done to lift the bucket = 1078 +474.32+1938.783 = 3491.103

the work done to lift the bucket = 3491 Joules

You might be interested in

You travel in a car 30 miles north to ava and home again. what is your distance? __________________________________________ what

Luden [163]

If you travel 30 miles somewhere and then come home again your distance is 60 miles. Your displacement is 0 because it is the ending position minus the beginning position, which are the same place (home). In other words, displacement is a vector and distance is a scalar.

4 0

3 years ago

What do you think we can learn about Earth's history by looking at the Grand Canyon?

viktelen [127]

We can look at all the ages of the earth since it’s a big crack is reveals many layers of the earth and we can know about chemicals and metals that were in earth and diffrent times

5 0

3 years ago

NASA developed a reflective foil barrier to help shield spacecraft from heat transfer in space. These reflective barriers are no

morpeh [17]

Answer: Radiation

Explanation: Radiation is the energy that comes from a source in form of electromagnetic waves, subatomic particles, light, or heat which travels through space.

Examples of radiation include the light, heat, and particles emitted from the Sun.

Using a foil barrier to prevent heat transfer is possible because foil has a silver color, and silver reflects light and heat instead of absorbing them. This is the opposite of black surfaces that absorb heat.

So in homes where these foil reflective barriers are used, the transfer of heat through Radiation is highly reduced.

3 0

3 years ago

FIGURE 1 shows part of a mass spectrometer. The whole arrangement is in a vacuum. Negative ions of mass 2.84 x 10-20 kg and char

yuradex [85]

Yes, the ions can exit slit P without being deflected, if the electric field strength is 170.6 N/C

Explanation:

When the ions are inside the container, they are subjected to two forces, with directions opposite to each other:

The force due to the electric field, whose magnitude is $F_E=qE$ , where q is the charge of the ion and E is the strength of the electric field
The force due to the magnetic field, whose magnitude is $F_B=qvB$ , where v is the speed of the ions and B is the strength of the magnetic field

The ions will move straight and undeflected if the two forces are equal and opposite. By using Fleming Left Hand rule, we notice that the magnetic force on the (negative) ions point upward: this means that the electric field must be also upward (so that the electric force on the ions is downward). Then, the two forces are balanced if

$F_E = F_B$

which translates into

$qE=qvB\\\rightarrow v = \frac{E}{B}$

Therefore, if the speed of the ions is equal to this ratio, the ions will go undeflected.

We can even calculate the value of E at which this occurs. In fact, we know that the ions are earlier accelerated by a potential difference $V=-3000 V$ , so we have that their kinetic energy is given by the change in electric potential energy:

$qV=\frac{1}{2}mv^2$

where

$q=-2.0\cdot 10^{-19}C\\m=2.84\cdot 10^{-20}kg$

Solving for v, the speed,

$v=\sqrt{\frac{2qV}{m}}=\sqrt{\frac{2(-2.0\cdot 10^{-19})(-3000)}{2.84\cdot 10^{-20}}}=205.6 m/s$

And since the magnetic field strength is

B = 0.83 T

The strength of the electric field must be

$E=vB=(205.6 m/s)(0.83 T)=170.6 N/C$

Learn more about electric and magnetic fields:

brainly.com/question/8960054

brainly.com/question/4273177

brainly.com/question/3874443

brainly.com/question/4240735

#LearnwithBrainly

7 0

3 years ago

How do earthquakes affect boulders

MaRussiya [10]

Weathering and rock slides

5 0

3 years ago