A wheelbarrow is a complex machine that combines which simply marchines?

A sphere moves in simple harmonic motion with a frequency of 4.80 Hz and an amplitude of 3.40 cm. (a) Through what total distanc

geniusboy [140]

Answer:

a) the total distance traveled by the sphere during one cycle of its motion = 13.60 cm

b) The maximum speed is = 102.54 cm/s

The maximum speed occurs at maximum excursion from equilibrium.

c) The maximum magnitude of the acceleration of the sphere is = 30.93 $m/s^2$

The maximum acceleration occurs at maximum excursion from equilibrium.

Explanation:

Given that :

Frequency (f) = 4.80 Hz

Amplitude (A) = 3.40 cm

a)

The total distance traveled by the sphere during one cycle of simple harmonic motion is:

d = 4A (where A is the Amplitude)

d = 4(3.40 cm)

d = 13.60 cm

Hence, the total distance traveled by the sphere during one cycle of its motion = 13.60 cm

b)

As we all know that:

$x = Asin \omega t$

Differentiating the above expression with respect to x ; we have :

$\frac{d}{dt}(x) = \frac{d}{dt}(Asin \omega t)$

$v = A \omega cos \omega t$

Assuming the maximum value of the speed(v) takes place when cosine function is maximum and the maximum value for cosine function is 1 ;

Then:

$v_{max} = A \omega$

We can then say that the maximum speed therefore occurs at the mean (excursion) position where ; x = 0 i.e at maximum excursion from equilibrium

substituting $2 \pi f$ for $\omega$ in the above expression;

$v_{max} = A(2 \pi f)$

$v_{max} = 3.40 cm (2 \pi *4.80)$

$v_{max} = 102.54 \ cm/s$

Therefore, the maximum speed is = 102.54 cm/s

The maximum speed occurs at maximum excursion from equilibrium.

c) Again;

$v = A \omega cos \omega t$

By differentiation with respect to t;

$\frac{d}{dt}(v) = \frac{d}{dt}(A \omega cos \omega t)$

$a =- A \omega^2 sin \omega t$

The maximum acceleration of the sphere is;

$a_{max} =A \omega^2$

where;

$w = 2 \pi f$

$a_{max} = A(2 \pi f)^2$

where A= 3.40 cm = 0.034 m

$a_{max} = 0.034*(2 \pi *4.80)^2$

$a_{max} = 30.93 \ m/s^2$

The maximum magnitude of the acceleration of the sphere is = 30.93 $m/s^2$

The maximum acceleration occurs at maximum excursion from equilibrium where the oscillating sphere will have maximum acceleration at the turning points when the sphere has maximum displacement of $x = \pm A$

6 0

3 years ago

What is the relationship between force of gravity and mass

sweet [91]

Answer:

I hope the picture below help.

Explanation:

6 0

2 years ago

A sound wave traveling at 343 m/s is emitted by the foghorn of a tugboat. an echo is heard 2.80 s later. how far away is the ref

Nostrana [21]

The echo is heard 2.80 s later, this means this is the time the sound takes to travel to the reflecting object and then back to us. So, during this time, the sound wave has covered the distance L between us and the object twice:
$S=2L$
The speed of the sound wave is: $v=343 m/s$ , and since it is moving by uniform motion, we can find the distance covered by the wave using
$S=vt=(343 m/s)(2.80 s)=960 m$
And we said this corresponds to twice the distance between us and the reflecting object, so:
$L= \frac{S}{2} = \frac{960 m}{2} =480 m$
so, the object is 480 meters away.

3 0

3 years ago

The pressure and volume of a fixed mass of gas _ are related. if one decreases, the other ___ ___ this relationship is known as

mihalych1998 [28]

1) Inversely
2) increases
3) Boyle's
4) mass
5) Kelvin
6) Charles's
7) Gay-Lussac's
8) directly
9) combined
10) the amount

<span>The pressure and volume of a fixed mass of gas are inversely related. If one decreases, the other increases. This relationship is known as Boyle's law. The volume of a fixed mass of a gas is directly proportional to its kelvin temperature. This relationship is known as Charles's law. Gay-Lussac's law states that the pressure of a gas is directly proportional to the kelvin temperature if the volume remains constant. These three separate gas laws can be written as a single expression called the combined gas law. It can be used in situations in which only the amount of gas is constant. </span>

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3 years ago

If another vehicle is trying to pass your vehicle,

Vladimir [108]

Answer:

Reduce you're speed, and let the other vehicle pass you

8 0

3 years ago