Fill in the blank

Determine the angle of an incline that would yield a constant velocity, given the coefficient of kinetic friction is 0.10.

azamat

Answer:

$\theta=5.71^{o}$

Explanation:

In order to solve this problem, we mus start by drawing a free body diagram of the given situation (See attached picture).

From the free body diagram we can now do a sum of forces in the x and y direction. Let's start with the y-direction:

$\sum F_{y}=0$

$-W_{y}+N=0$

$N=W_{y}$

so:

$N=mgcos(\theta)$

now we can go ahead and do a sum of forces in the x-direction:

$\sum F_{x}=0$

the sum of forces in x is 0 because it's moving at a constant speed.

$-f+W_{x}=0$

$-\mu_{k}N+mg sen(\theta)=0$

$-\mu_{k}mg cos(\theta)+mg sen(\theta)=0$

so now we solve for theta. We can start by factoring mg so we get:

$mg(-\mu_{k} cos(\theta)+sen(\theta))=0$

we can divide both sides into mg so we get:

$-\mu_{k} cos(\theta)+sen(\theta)=0$

this tells us that the problem is independent of the mass of the object.

$\mu_{k} cos(\theta)=sen(\theta)$

we now divide both sides of the equation into $cos(\theta)$ so we get:

$\mu_{k}=\frac{sen(\theta)}{cos(\theta)}$

$\mu_{k}=tan(\theta)$

so we now take the inverse function of tan to get:

$\theta=tan^{-1}(\mu_{k})$

so now we can find our angle:

$\theta=tan^{-1}(0.10)$

so

$\theta=5.71^{o}$

8 0

3 years ago

Prove(show) ''T=2π√(l/g)''

Nonamiya [84]

Answer:

Time period for Simple pendulum, $T=2\pi\sqrt{\frac{l}{g}$

Explanation:

The Simple Pendulum

Consider a small bob of mass $m$ is tied to extensible string of length $l$ that is fixed to rigid support. The bob is oscillating in the plane about verticle.

Let $\theta$ is the angle made by string with vertical during oscillation.

Vertical component of the force on bob, $F=-mg\sin\theta$

Negative sign shows that its opposing the motion of bob.

Taking $\theta$ as very small angle then, $\sin\theta\sim\theta$

$F=-mg\theta$

Let $x$ is the displacement made by bob from its mean position ,

then, $\theta=\frac{x}{l}$

so, $F=-mg\frac{x}{l}$ ........(1)

Since, pendulum is in hormonic motion,

as we know, $F=-kx$

where $k$ is the constant and $k=m\omega^{2}$

$F=-m\omega^2x$ .........(2)

From equation (1) and (2)

$-m\omega^2x=-mg\frac{x}{l}$

$\omega=\sqrt{\frac{g}{l}}$

Since, $\omega=\frac{2\pi}{T}$

$\frac{2\pi}{T}=\sqrt{\frac{g}{l}$

$T=2\pi\sqrt{\frac{l}{g}}$

6 0

3 years ago

A cyclist is traveling 10 m/s with an acceleration of 6 m/s2. How fast is the cyclist traveling at the end of 20 seconds

krok68 [10]

Answer:

<em>The cyclist is traveling at 130 m/s</em>

Explanation:

<u>Constant Acceleration Motion </u>

It's a type of motion in which the velocity of an object changes by an equal amount in every equal period of time.

Being a the constant acceleration, vo the initial speed, vf the final speed, and t the time, the following relation applies:

$v_f=v_o+at$

The cyclist initially travels at 10 /s and it's accelerating at a=6m/s^2. We need to know the new speed when t= 20 seconds have passed.

Apply the above equation:

$v_f=10+6\cdot 20$

$v_f=10+120$

$v_f=130\ m/s$

The cyclist is traveling at 130 m/s

7 0

3 years ago

Two objects are made of the same material, but they have different masses and temperatures. If the objects are brought into ther

DIA [1.3K]

The smaller body will have greater temperature change.

<h3><u>Explanation</u>:</h3>

Temperature is defined as the degree of hotness or coldness of a body. The relationship of the temperature with heat is described as

Q =m c dT.

Where Q is the heat content

m is the mass of body

c is the specific heat of body

dT is the temperature change of body.

Here the bodies are made up of same substance, so specific heat is same. The mass of bigger body is M and smaller body is m.

So the temperature change of the body will be dependent on the mass of the body. Heat loss by one body will be equal to heat gained by the other.

So M dT1 = mdT2.

So, M/m = dT2 / dT1.

So the the smaller body will be suffering higher temperature change.

3 0

4 years ago

A _______ is a series of waves that come ashore at interval 10-45 mintues

Nostrana [21]

Answer:

tsunami

Explanation:

A tsunami is a series of waves that come ashore at interval 10-45 mintues

3 0

3 years ago