Ask question

Ask question

All categories

3 years ago

5

piston in a gasoline engine is in simple harmonic motion. The engine is running at the rate of 2 940 rev/min. Taking the extreme

s of its position relative to its center point as ±5.50 cm.(a) Find the magnitude of the maximum velocity of the piston. 16.93 Correct: Your answer is correct. m/s(b) Find the magnitude of the maximum acceleration of the piston

1 answer:

zhannawk [14.2K]3 years ago

3 0

Answer:

The the magnitude of the maximum velocity and acceleration are 16.93 m/s and $5.213\times10^{3}\ m/s^2$ .

Explanation:

Given that,

Rate = 2940 rev/min

Amplitude = ±5.50 cm

(a). We need to calculate the magnitude of the maximum velocity

Using formula of maximum velocity

$v=A\times\omega$

Where, A = amplitude

Put the value into the formula

$v=5.50\times10^{-2}\times2940\times\dfrac{2\pi}{60}$

$v=16.93\ m/s$

(b). We need to calculate the maximum acceleration

Using formula of maximum acceleration

$a=A\times\omega^2$

$a=5.50\times10^{-2}\times(2940\times\dfrac{2\pi}{60})^2$

$a=5.213\times10^{3}\ m/s^2$

Hence, The the magnitude of the maximum velocity and acceleration are 16.93 m/s and $5.213\times10^{3}\ m/s^2$ .

You might be interested in

Two floors in a building are separated by 4.1 m. People move between the two floors on a set of stairs. (a) Determine the change

Ket [755]

Answer:

a) The change in potential energy of a 3.0 kilograms backpack carried up the stairs.

b) The change in potential energy of a persona with weight 650 newtons that descends the stairs is -2665 joules.

Explanation:

Let consider the bottom of the first floor in a building as the zero reference ( $z = 0\,m$ ). The change in potential energy experimented by a particle ( $\Delta U_{g}$ ), measured in joules, is:

$\Delta U_{g} = m\cdot g\cdot (z_{f}-z_{o})$ (1)

Where:

$m$ - Mass, measured in kilograms.

$g$ - Gravitational acceleration, measured in meters per square second.

$z_{o}$ , $z_{f}$ - Initial and final height with respect to zero reference, measured in meters.

Please notice that $m\cdot g$ is the weight of the particle, measured in newtons.

a) If we know that $m = 3\,kg$ , $g = 9.807\,\frac{m}{s^{2}}$ , $z_{o} = 0\,m$ and $z_{f} = 4.1\,m$ , then the change in potential energy is:

$\Delta U_{g} = (3\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (4.1\,m-0\,m)$

$\Delta U_{g} = 120.626\,J$

The change in potential energy of a 3.0 kilograms backpack carried up the stairs.

b) If we know that $m\cdot g = 650\,N$ , $z_{o} = 4.1\,m$ and $z_{f} = 0\,m$ , then the change in potential energy is:

$\Delta U_{g} = (650\,N)\cdot (0\,m-4.1\,m)$

$\Delta U_{g} = -2665\,J$

The change in potential energy of a persona with weight 650 newtons that descends the stairs is -2665 joules.

5 0

3 years ago

Convection is a means of heat transfer that involves fluids, such as liquids or gasses. The process of convection is responsible

Grace [21]

Answer:

Correct answer is B.

Explanation:

6 0

3 years ago

Read 2 more answers

What is the fraction of the hydrogen atom's mass (11h) that is in the nucleus? the mass of proton is 1.007276 u, and the mass of

Alex_Xolod [135]

The mass fraction of the hydrogen atom is 0.9995 u.

<h3>Calculation:</h3>

We know that mass fraction can be determines as,

Mass fraction = Mass of proton/mass of H atom

Given,

Mass of proton = 1.007276 u

Mass of H atom = 1.007825 u

Put the values in the formula,

Mass fraction = Mass of proton/mass of H atom

Mass fraction = 1.007276/1.007825

= 0.9995 u

Hence, the mass fraction of the hydrogen atom is 0.9995 u.

Learn more about mass fraction here:

brainly.com/question/9639161

#SPJ4

3 0

2 years ago

Beginning 156 miles directly east of the city of Uniontown, a truck travels due south. If the truck is travelling at a speed of

timurjin [86]

Answer:

14.3

Explanation:

The distance s as a function of time can be written as:

$s(t) = \sqrt{156^{2} + (31t)^2}$

The rate of change is the derivative of d with respect to time:

$\frac{ds}{dt} =\frac{961t}{\sqrt{156^{2}+(31t)^{2}}}$

The time t when the track has been traveling for 81 miles is given by:

$81 = 31t\\ t = \frac{81}{31}$

Using t in the previous equation gives:

$\frac{ds}{dt}(\frac{81}{31} ) =\frac{2511}{\sqrt{156^{2}+81^{2}}}=14.3$

5 0

3 years ago

When a pendulum with a period of 2.00000 s is moved to a new location from one where the acceleration due to gravity was 9.80 m/

Ivahew [28]

Answer:

0.021 $m/s^2$

Explanation:

The period of a pendulum is dependent on the length of the string holding the pendulum, L, and acceleration due to gravity, g. It is given mathematically as:

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

Let us make L the subject of the formula:

$T^2 = 4\pi ^2(\frac{L}{g}) \\\\\\\frac{L}{g} = \frac{T^2}{4\pi ^{2}} \\\\\\L = \frac{gT^2}{4\pi ^{2}}$

We are not told that the length of the string changes, hence, we can conclude that it is constant in both locations.

When the period of the pendulum is 2 s and the acceleration due to gravity is 9.8 $m/s^2$ , the length L is:

$L = \frac{9.8 * 2^2}{4 \pi^{2}}\\ \\\\L = 0.9929 m$

When the pendulum is moved to a new location, the period becomes 1.99782 s.

We have concluded that length is constant, hence, we can find the new acceleration due to gravity, $g_n$ :

$0.9929 = \frac{g_n * 1.99782^2}{4\pi^{2}} \\\\\\0.9929 = 0.1011 g_n$

Therefore:

$g_n = 0.9929/0.1011\\\\\\g_n = 9.821 m/s^2$

The difference between the new acceleration due to gravity, $g_n$ and the former acceleration due to gravity, g, will be:

$g_n - g$ = $9.821 - 9.8$ = $0.021 m/s^2$

The acceleration due to gravity differs by a value of $0.021 m/s^2$ at the new location.

7 0

3 years ago

Read 2 more answers