In your own words explain why plants are so important to society.

Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a const

Dafna1 [17]

Answer:

$\frac{dA}{dt} = 188.5 m^2/s$

Explanation:

As we know that area of the circle at any instant of time is given as

$A = \pi r^2$

now in order to find the rate of change in area we will have

$\frac{dA}{dt} = 2\pi r\frac{dr}{dt}$

here we know that

rate of change of radius is given as

$\frac{dr}{dt}= 1 m/s$

radius of the circle is given as

$r = 30 m$

now we have

$\frac{dA}{dt} = 2\pi (30)(1)$

$\frac{dA}{dt} = 60\pi$

$\frac{dA}{dt} = 188.5 m^2/s$

8 0

4 years ago

A large crate with mass m rests on a horizontal floor. The static and kinetic coefficients of friction between the crate and the

Mariana [72]

a) $F=\frac{\mu_k mg}{cos \theta - \mu_k sin \theta}$

Here the crate is moving at constant velocity, so no acceleration:

a = 0

Let's analyze the forces acting along the horizontal and vertical direction.

- Vertical direction: the equation of the forces is

$R-Fsin \theta - mg = 0$ (1)

where

R is the normal reaction of the floor (upward)

$F sin \theta$ is the component of the force F in the vertical direction (downward)

mg is the weight of the crate (downward)

- Horizontal direction: the equation of the forces is

$F cos \theta - \mu_k R = 0$ (2)

where

$F cos \theta$ is the horizontal component of the force F (forward)

$\mu_k R$ is the force of friction (backward)

From (1) we get

$R=Fsin \theta +mg$

And substituting into (2)

$F cos \theta - \mu_k (Fsin \theta +mg) = 0\\F cos \theta -\mu _k F sin \theta = \mu_k mg\\F(cos \theta - \mu_k sin \theta) = \mu_k mg\\F=\frac{\mu_k mg}{cos \theta - \mu_k sin \theta}$

b) $\mu_s=cot(\theta)$

In this second case, the crate is still at rest, so we have to consider the static force of friction, not the kinetic one.

The equations of the forces will be:

$R-Fsin \theta - mg = 0$ (1)

$F cos \theta - \mu_s R = 0$ (2)

In this second case, we want to find the critical value of $\mu_s$ such that the woman cannot start the crate: this means that the force of friction must be at least equal to the component of the force pushing on the horizontal direction, $F cos \theta$ .

Therefore, using the same procedure as before,

$R=Fsin \theta +mg$

$F cos \theta - \mu_s (Fsin \theta +mg) = 0$

And solving for $\mu_s$ ,

$F cos \theta = \mu_s (Fsin \theta +mg) \\\mu_s = \frac{F cos \theta}{F sin \theta + mg}$

Now we analyze the expression that we found. We notice that if the force applied F is very large, $F sin \theta >> mg$ , therefore we can rewrite the expression as

$\mu_s \sim \frac{F cos \theta}{F sin \theta}\\\mu_s=cot(\theta)$

So, this is the critical value of the coefficient of static friction.

8 0

3 years ago

PERSONAL QUESTION <br> if a bird can fly why can't a fly just bird ?

Sergeeva-Olga [200]

Answer:

counter question if you get out the shower clean then how does your towel get dirty?

3 0

4 years ago

Read 2 more answers

A car's gas tank contains 58.7 kg

Bogdan [553]

Answer:

721 kg/m^3

Explanation:

Trust me bro

8 0

3 years ago

Which will increase the kinetic energy of an object more, increasing its mass or increasing its speed? Why?

agasfer [191]

Increasing its velocity will add to the kinetic energy more as the formula for kinetic energy is 0.5*m*v^2. (The speed will be squared making it greater)

4 0

4 years ago