Preventing projects

"A uniform cylinder of mass M and radius R is rolling without slipping. The velocity of its center of mass is v. What is the cyl

Goshia [24]

Answer:

Explanation:

Given

mass of cylinder is M

radius R

velocity of center of mass is v

As there is no slipping therefore cylinder will rotate as well as translate

Moment of inertia of cylinder $I=\frac{MR^2}{2}$

Kinetic Energy of cylinder $K.E.=\frac{1}{2}Mv^2$

Rotational energy $R.E.=\frac{1}{2}I\omega ^2$

for rolling

$v=\omega \times r$

where $\omega =angular\ velocity\ of\ cylinder$

$R.E.=\frac{1}{2}\times \frac{MR^2}{2}\times (\frac{v}{R})^2=\frac{1}{4}Mv^2$

Total kinetic Energy $=\frac{1}{2}Mv^2+\frac{1}{4}Mv^2=\frac{3}{4}Mv^2$

6 0

3 years ago

Who was the first person to walk on the moon ?

liq [111]

Answer:

god correct correct

Explanation:

8 0

3 years ago

Read 2 more answers

Coulomb's law is expressed mathematically as

nataly862011 [7]

Force between two charges =

( 1/4πε₀ ) · (Charge #1) · (Charge #2) / (Distance between them)²

in the direction away from each other.

In other words, if the force is positive, the charges are repelling.
If the force is negative, the charges are attracting.

4 0

3 years ago

8. The fact that voltage can be created by exerting force on a crystal is used in which type of sensor?

AfilCa [17]

Option C

The fact that voltage can be created by exerting force on a crystal is used in Knock sensor

<u>Explanation:</u>

Any knock to an engine exhibits as a little shake that is distinguished by the knock sensor. This sensor acts by altering the fluctuation to an electrical sign, which is later transferred to the processor mastering the ignition system.

There the variation in quake to the voltage sign modifies the timing improvements on the kindling. The knock sensor is placed on the engine base, cylinder cap or consumption manifold. This is because its purpose is to sense fluctuations affected by engine knock or explosion.

5 0

3 years ago

A 4.87-kg ball of clay is thrown downward from a height of 3.21 m with a speed of 5.21 m/s onto a spring with k = 1570 N/m. The

Yuki888 [10]

Answer:

Approximately $0.560\; {\rm m}$ , assuming that:

the height of $3.21\; {\rm m}$ refers to the distance between the clay and the top of the uncompressed spring.
air resistance on the clay sphere is negligible,
the gravitational field strength is $g = 9.81\; {\rm m\cdot s^{-2}}$ , and
the clay sphere did not deform.

Explanation:

Notations:

Let $k$ denote the spring constant of the spring.
Let $m$ denote the mass of the clay sphere.
Let $v$ denote the initial speed of the spring.
Let $g$ denote the gravitational field strength.
Let $h$ denote the initial vertical distance between the clay and the top of the uncompressed spring.

Let $x$ denote the maximum compression of the spring- the only unknown quantity in this question.

After being compressed by a displacement of $x$ , the elastic potential energy $\text{PE}_{\text{spring}}$ in this spring would be:

$\displaystyle \text{PE}_{\text{spring}} = \frac{1}{2}\, k\, x^{2}$ .

The initial kinetic energy $\text{KE}$ of the clay sphere was:

$\displaystyle \text{KE} = \frac{1}{2}\, m \, v^{2}$ .

When the spring is at the maximum compression:

The clay sphere would be right on top of the spring.
The top of the spring would be below the original position (when the spring was uncompressed) by $x$ .
The initial position of the clay sphere, however, is above the original position of the top of the spring by $h = 3.21\; {\rm m}$ .

Thus, the initial position of the clay sphere ( $h = 3.21\; {\rm m}$ above the top of the uncompressed spring) would be above the max-compression position of the clay sphere by $(h + x)$ .

The gravitational potential energy involved would be:

$\text{GPE} = m\, g\, (h + x)$ .

No mechanical energy would be lost under the assumptions listed above. Thus:

$\text{PE}_\text{spring} = \text{KE} + \text{GPE}$ .

$\displaystyle \frac{1}{2}\, k\, x^{2} = \frac{1}{2}\, m\, v^{2} + m\, g\, (h + x)$ .

Rearrange this equation to obtain a quadratic equation about the only unknown, $x$ :

$\displaystyle \frac{1}{2}\, k\, x^{2} - m\, g\, x - \left[\left(\frac{1}{2}\, m\, v^{2}\right)+ (m\, g\, h)\right] = 0$ .

Substitute in $k = 1570\; {\rm N \cdot m^{-1}}$ , $m = 4.87\; {\rm kg}$ , $v = 5.21\; {\rm m\cdot s^{-1}}$ , $g = 9.81\; {\rm m \cdot s^{-2}}$ , and $h = 3.21\; {\rm m}$ . Let the unit of $x$ be meters.

$785\, x^{2} - 47.775\, x - 219.453 \approx 0$ (Rounded. The unit of both sides of this equation is joules.)

Solve using the quadratic formula given that $x \ge 0$ :

$\begin{aligned}x &\approx \frac{-(-47.775) + \sqrt{(-47.775)^{2} - 4 \times 785 \times (-219.453)}}{2 \times 785} \\ &\approx 0.560\; {\rm m}\end{aligned}$ .

(The other root is negative and is thus invalid.)

Hence, the maximum compression of this spring would be approximately $0.560\; {\rm m}$ .

5 0

3 years ago

Preventing projects​

Preventing projects