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pashok25 [27]
3 years ago
7

"The two equations below express conservation of energy and conservation of mass for water flowing from a circular hole of radiu

s 3 centimeters at the bottom of a cylindrical tank of radius 20 centimeters. In these equations, delta m is the mass that leaves the tank in time delta t, v is the velocity of the water flowing through the hole, and h is the height of the water in the tank at time t. g is the accelertion of gravity, which you should approximate as 1000 cm/s2
The first equation says that the gain in kinetic energy of the water leaving the tank equals the loss in potential energy of the water in the tank.
1/2 delta m v2 = delta m gh
The second equation says that the rate at which water leaves the tank equals the rate of decrease in the volume of water in the tank (which is conservation of mass because water has constant density)
pi 102^2 dh/dt = pi 3^2 v
Derive a differential equation for the height of water in the tank.
If the initial height of the water is 30 centimeters, find a formula or the solution.
According to the model, how long does it take to empty the tank?
Another way to solve this differential equation is to make the substitution w = underroot h. What is the differential equation that w satisfies?
Physics
1 answer:
Leno4ka [110]3 years ago
5 0

Answer:

The two equations below express conservation of energy and conservation of mass for water flowing from a circular hole of radius 3 centimeters at the bottom of a cylindrical tank of radius 10 centimeters. In these equations, delta m is the mass that leaves the tank in time delta t, v is the velocity of the water flowing through the hole, and h is the height of the water in the tank at time t. g is the acceleration of gravity, which you should approximate as 1000 cm/s2.

shdh

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The formula h = -16t squared + 64t squared gives the height, h, and time, t, of an object launched from the ground with a speed
padilas [110]

Answer:

<em>Details in the explanation</em>

Explanation:

<u>Vertical Launch</u>

When an object is thrown vertically in free air (no friction), it moves upwards at its maximum speed while the acceleration of gravity starts to brake it. At a given time and height, the object stops in mid-air and starts to fall back to the launching point until reaching it with the same speed it was launched.

We are given an expression for the height of an object in function of time t

h = -16t^2 + 64t

<em>Please note we have deleted the second 'squared' from the formula since it's incorrect and won't describe the motion of vertical launch.</em>

We now have to evaluate h for the following times, assuming h comes in feet

At t=1 sec

h = -16(1)^2 + 64(1)=64-16=48\ ft

The object is at a height of 48 feet

At t=2 sec

h = -16(2)^2 + 64(2)=128-64=64\ ft

The object is at a height of 64 feet. This is the maximum height the object will reach, as we'll see below

At t=3 sec

h = -16(3)^2 + 64(3)=192-144=48\ ft

The object is at a height of 48 feet. We can clearly see it's returning from the maximum height and is going down

At t=4 sec

h = -16(4)^2 + 64(4)=256-256=0\ ft

The object is at ground level and has returned to the launch point.

5 0
3 years ago
An asteroid of mass 5.7×104 kg carrying a negative charge of 14.0 μC is 190 m from a second asteroid of mass 5.5×104 kg carrying
Finger [1]

Answer:

repulsion force es  R = 5,224 10⁻³ N

Explanation:

We use Newton's second law to add forces, the elective force is repulsive because the asteroids have the same type of charge and gravitational force is always attractive.

Gravitational force

      Fg = G m1 m2 / r²

      Fg = 6,673 10⁻¹¹ 5.7 10⁴ 5.5 10⁴/190²

      Fg = 5,795 10⁻⁶ N

Electric force

     Fe = k q1 q2 / r²

     Fe = 8.99 10⁹ 14.0 10⁻⁶ 15.0 10⁻⁶ / 190²

     Fe = 5.2296 10⁻³ N

The resulting force is

     R = Fe - Fg

     R = 5.2296 10⁻³ - 5.795 10⁻⁶=  5229.6 10⁻⁶ - 5,795 10⁻⁶

     R = 5,224 10⁻³ N

this is a repulsive force and the asteroids move away from each other

7 0
3 years ago
a bowling ball has a mass of 6 kilograms. a tennis ball has a mass of 0.06 kilogram. how much inertia does the bowling ball have
Andreyy89

Answer:

100 times

Explanation:

Since inertia is directly proportional to the mass of an object, the higher the mass the higher the inertia. In this case, 6 Kg is 100 times heavier than 0.06 Kg to imply The bowling ball  has 100 times more inertia than the tennis  ball because it has 100 times more mass

5 0
3 years ago
A closed cylindrical tank of radius 3.5 m and height 2m is made from
Dahasolnce [82]

Explanation:

Total surface area of cylinder:

2\pi \times r(h + r) \\ 2 \times \pi \times 3.5(3.5 + 2) \\ 2\pi \times 19.25 = 120.951317 \\ 120.95  \: {cm}^{2}

sheet of metal required = 120.95 cm^2

3 0
3 years ago
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What challenges arise when trying to protect the environment? Check all that apply.
fenix001 [56]

Answer

The challenge when trying to protect the environment is expensive clean energy startup cost

Explanation

In attempts to protect the environment, energy users across the globe are shifting to new renewable energy resources which are faced by the challenge of high capital cost. Renewable energy technologies are cheap to operate but very expensive to build. The perception is that renewable energy resources are risky because they require higher construction costs.


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