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Svetllana [295]
3 years ago
15

A string under a tension of 36 N is used to whirl a rock in a horizontal circle of radius 3.6 m at a speed of 16.12 m/s. The str

ing is pulled in, and the speed of the rock increases. When the string is 0.468 m long and the speed of the rock is 75.1 m/s, the string breaks.
Physics
1 answer:
ExtremeBDS [4]3 years ago
3 0

Answer:

6010.457N

Explanation:

Centripetal acceleration = a= V²/R

At a radius of 3.6m and velocity of 16.12m/s,

Acceleration is

a = 16.12²/ 3.6 = 72.182 m/s²

Force = Mass (m) * Acceleration (a)

36 = m * 72.182

m = 36/72.182

At breaking point

Radius = 0.468 m and Velocity = 75.1 m/s

a = V²/R = 75.1²/0.468

a = 12051.3 m/s

F = Mass(m) * Acceleration (a)

F = m * 12051.3

m = F/ 12051.3

Settings the ratio of mass equal

m = m

=> 36/72.182 = F/12051.3

F = 12051.3 * 36/72.182

F = 6010.457N

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Rainbow [258]
It depends on how many hours!
1 hour = 40km
2 hours = 80km
8 0
3 years ago
A gasoline tank has the shape of an inverted right circular cone with base radius 4 meters and height 5 meters. Gasoline is bein
RSB [31]

Answer:

h'=0.25m/s

Explanation:

In order to solve this problem, we need to start by drawing a diagram of the given situation. (See attached image).

So, the problem talks about an inverted circular cone with a given height and radius. The problem also tells us that water is being pumped into the tank at a rate of 8m^{3}/s. As you  may see, the problem is talking about a rate of volume over time. So we need to relate the volume, with the height of the cone with its radius. This relation is found on the volume of a cone formula:

V_{cone}=\frac{1}{3} \pi r^{2}h

notie the volume formula has two unknowns or variables, so we need to relate the radius with the height with an equation we can use to rewrite our volume formula in terms of either the radius or the height. Since in this case the problem wants us to find the rate of change over time of the height of the gasoline tank, we will need to rewrite our formula in terms of the height h.

If we take a look at a cross section of the cone, we can see that we can use similar triangles to find the equation we are looking for. When using similar triangles we get:

\frac {r}{h}=\frac{4}{5}

When solving for r, we get:

r=\frac{4}{5}h

so we can substitute this into our volume of a cone formula:

V_{cone}=\frac{1}{3} \pi (\frac{4}{5}h)^{2}h

which simplifies to:

V_{cone}=\frac{1}{3} \pi (\frac{16}{25}h^{2})h

V_{cone}=\frac{16}{75} \pi h^{3}

So now we can proceed and find the partial derivative over time of each of the sides of the equation, so we get:

\frac{dV}{dt}= \frac{16}{75} \pi (3)h^{2} \frac{dh}{dt}

Which simplifies to:

\frac{dV}{dt}= \frac{16}{25} \pi h^{2} \frac{dh}{dt}

So now I can solve the equation for dh/dt (the rate of height over time, the velocity at which height is increasing)

So we get:

\frac{dh}{dt}= \frac{(dV/dt)(25)}{16 \pi h^{2}}

Now we can substitute the provided values into our equation. So we get:

\frac{dh}{dt}= \frac{(8m^{3}/s)(25)}{16 \pi (4m)^{2}}

so:

\frac{dh}{dt}=0.25m/s

3 0
2 years ago
What role does Nitrogen play for all living organisms?​
Y_Kistochka [10]

It is an important part of many cells and processes such as amino acids, proteins and even our DNA. It is also needed to make chlorophyll in plants, which is used in photosynthesis to make their food.

Hope this helps! ;)

5 0
3 years ago
4. How much work is done when you lift a 25 N box up to a 2 m shelf?
Semmy [17]

Answer:

<h2>50 J</h2>

Explanation:

The work done by an object can be found by using the formula

workdone = force × distance

From the question

force = 25 N

distance = 2 m

We have

workdone = 25 × 2 = 50

We have the final answer as

<h3>50 J</h3>

Hope this helps you

6 0
2 years ago
What is the volume of the cone?
dezoksy [38]

Answer:

42.417 cm³

Explanation:

The formula to find the volume of a cone is :

V = \frac{1}{3} × π r² h

Here,

r ⇒ radius ⇒ 3 cm

h ⇒ height ⇒ 4.5 cm

<u>Let us find it now.</u>

V = \frac{1}{3} × π r² h

V = \frac{1}{3} × π × 3 × 3 × 4.5

V = \frac{1}{3} × π × 9 × 4.5

V = \frac{1}{3} × π × 9 × 4.5

V = \frac{1}{3} × π × 40.5

V = \frac{1}{3} × 3.142 × 40.5

V = \frac{1}{3} × 127.251

V = <u>42.417 cm³</u>

4 0
2 years ago
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