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2 years ago

What is simple harmonic oscillation? express your answer verbally, mathematically, and visually.

1 answer:

3 0

Simple harmonic motion is the motion in objects where the restoring for d is directly proportional to the body displacement.

<h3>What is simple harmonic motion?</h3>

Simple harmonic motion a type of periodic motion where the force that restores moving object to it's right position is directly proportional to the magnitude of body's displacement and this normally acts towards the object's equilibrium position.

The formulate for simple harmonic motion are

,F = −kx, where F is the force, x is the displacement, and k is a constanst. An example of a simple harmonic oscillator is the vibration of a mass attached to a vertical spring.

Simple harmonic oscillator can be represented by the equation x ( t ) = A cos ⁡ ( 2 π f t ) x(t) = A\cos(2\pi f t) x(t)=Acos(2πft)x,

where t is period.

x is displacement

A is amplitude.

Learn more about simple harmonic motion here.

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Please help answer question

nika2105 [10]

Answer:

C = 1.01

Explanation:

Given that,

Mass, m = 75 kg

The terminal velocity of the mass, $v_t=60\ m/s$

Area of cross section, $A=0.33\ m^2$

We need to find the drag coefficient. At terminal velocity, the weight is balanced by the drag on the object. So,

R = W

$\dfrac{1}{2}\rho CAv_t^2=mg$

Where

$\rho$ is the density of air = 1.225 kg/m³

C is drag coefficient

So,

$C=\dfrac{2mg}{\rho Av_t^2}\\\\C=\dfrac{2\times 75\times 9.8}{1.225\times 0.33\times (60)^2}\\\\C=1.01$

So, the drag coefficient is 1.01.

4 0

3 years ago

A very long insulating cylinder has radius R and carries positive charge distributed throughout its volume. The charge distribut

blsea [12.9K]

Answer:

1. $E(r) = \frac{\alpha}{4\pi \epsilon_0}(2 - \frac{r}{R})$

2. $E(r) = \frac{1}{4\pi \epsilon_0}\frac{\alpha R}{r}$

3.The results from part 1 and 2 agree when r = R.

Explanation:

The volume charge density is given as

$\rho (r) = \alpha (1-\frac{r}{R})$

We will investigate this question in two parts. First r < R, then r > R. We will show that at r = R, the solutions to both parts are equal to each other.

1. Since the cylinder is very long, Gauss’ Law can be applied.

$\int {\vec{E}} \, d\vec{a} = \frac{Q_{enc}}{\epsilon_0}$

The enclosed charge can be found by integrating the volume charge density over the inner cylinder enclosed by the imaginary Gaussian surface with radius ‘r’. The integration of E-field in the left-hand side of the Gauss’ Law is not needed, since E is constant at the chosen imaginary Gaussian surface, and the area integral is

$\int\, da = 2\pi r h$

where ‘h’ is the length of the imaginary Gaussian surface.

$Q_{enc} = \int\limits^r_0 {\rho(r)h} \, dr = \alpha h \int\limits^r_0 {(1-r/R)} \, dr = \alpha h (r - \frac{r^2}{2R})\left \{ {{r=r} \atop {r=0}} \right. = \alpha h (\frac{2Rr - r^2}{2R})\\E2\pi rh = \alpha h \frac{2Rr - r^2}{2R\epsilon_0}\\E(r) = \alpha \frac{2R - r}{4\pi \epsilon_0 R}\\E(r) = \frac{\alpha}{4\pi \epsilon_0}(2 - \frac{r}{R})$

2. For r> R, the total charge of the enclosed cylinder is equal to the total charge of the cylinder. So,

$Q_{enc} = \int\limits^R_0 {\rho(r)h} \, dr = \alpha \int\limits^R_0 {(1-r/R)h} \, dr = \alpha h(r - \frac{r^2}{2R})\left \{ {{r=R} \atop {r=0}} \right. = \alpha h(R - \frac{R^2}{2R}) = \alpha h\frac{R}{2} \\E2\pi rh = \frac{\alpha Rh}{2\epsilon_0}\\E(r) = \frac{1}{4\pi \epsilon_0}\frac{\alpha R}{r}$

3. At the boundary where r = R:

$E(r=R) = \frac{\alpha}{4\pi \epsilon_0}(2 - \frac{r}{R}) = \frac{\alpha}{4\pi \epsilon_0}\\E(r=R) = \frac{1}{4\pi \epsilon_0}\frac{\alpha R}{r} = \frac{\alpha}{4\pi \epsilon_0}$

As can be seen from above, two E-field values are equal as predicted.

4 0

3 years ago

In a city grid, each block on the east-west streets is 100 meters long. Each block on the north-south streets is 20 meters long.

alex41 [277]

Answer:

72.1 m

Explanation:

Hello!

When the walker walks west, each block he walks will be of 100 m, so the walker walked 4*100m = 400 m west.

Similarly, when the walker walks south, he walks 20 meters per block, therefore, the walker walked 4*20 m = 80 m south.

Since the directions west and south are perpendicular, the distance between the start ad end point is:

d = √(400^2 + 80^2) m = 407.92 m

However the walker traveled 480 m

Therefore, the walker traveled 480 - 407.9 m = 72.1 m farther than the actual distance

8 0

4 years ago

A kayaker moves 26 meters southward, then 18 meters

Svetllana [295]

Total distance: 56 meters. Magnitude and direction of displacement: 20 meters South.

Explanation:

The term distance refers to space between one point and other, or the total space a body or object covered while moving. In the case presented, this can be calculated by adding the partial distances given. This means the total distance is 56 meters as 26 meters + 18 meters + 12 meters = 56 meters.

On the other hand, displacement considers the distance from the initial position to the final position, and the direction of movement. This means partial distances should not be added but each movement should be considered according to the direction. The process is shown below:

-The first movement was 26 meters southward; this means by the end of this movement the distance between the initial position was 26 meters south.

- The second movement was 18 northward; this means the kayaker moved 18 meters towards the position. This changes the displacement to 8 meters South as 26 meters south - 18 meters north = 8 meters to the South.

-The last movement was 12 meters sound; this means the kayaker increased the distance from the original position 8 meters to the South + 12 meters to the South = 20 meters South (total displacement.)

8 0

3 years ago

16) A man ran a 5 mile race. The race looped around a city park and back

finlep [7]

Answer:

The man's total displacement is equal to 0.

Explanation:

Given that,

A man ran a 5 mile race. The race looped around a city park and back to the starting line.

We need to find the total displacement of the man.

We know that,

Displacement = shortest path covered

Also,

Displacement = final position - initial position

As it reaches back to its starting line, it means, the displacement is equal to 0.

Hence, the man's total displacement is equal to 0.

3 0

3 years ago