If you are swimming upstream (i.e., against the current), at what speed does your friend on the shore see you moving?

The dial of a scale looks like this: 00.0kg. A physicist placed a spring on it. The dial read 00.6kg. He then placed a metal cha

saveliy_v [14]

Answer:

d. The scale's resolution is too low to read the change in mass

Explanation:

If we want to find the change in energy of the spring, we will have to use the Hooke's Law. Hooke's Law states that:

F = kx

since,

w = Fd

dw = Fdx

integrating and using value of F, we get:

ΔE = (0.5)kx²

where,

ΔE = Energy added to spring

k = spring constant

x = displacement

The spring constant is typically in range of 4900 to 29400 N/m.

So if we take the extreme case of 29400 N/m and lets say we assume an unusually, extreme case of 1 m compression, we get the value of energy added to be:

ΔE = (0.5)(29400 N/m)(1 m)²

ΔE = 1.47 x 10⁴ J

Now, if we convert this energy to mass from Einstein's equation, we get:

ΔE = Δmc²

Δm = ΔE/c²

Δm = (1.47 x 10⁴ J)/(3 x 10⁸ m/s)²

As, you can see from the answer that even for the most extreme cases the value of mass associated with the additional energy is of very low magnitude.

Since, the scale only gives the mass value upto 1 decimal place.

Thus, it can not determine such a small change. So, the correct option is:

<u>d. The scale's resolution is too low to read the change in mass</u>

8 0

2 years ago

Astronomical observatories have been available since ancient times, and many cultures set aside special sites for astronomical o

inysia [295]

Answer:

Telescope

Explanation:

Telescope is usually defined as an optical instrument that is commonly used to observe the objects in a magnified way that are located at a large distance from earth. These telescopes are comprised of lenses and curved mirrors that are needed to be arranged in a proper way in order to have a prominent look. It is commonly used by the astronomers.

This was first constructed by Hans Lippershey in the year 1608.

6 0

2 years ago

Chromatic aberration comes from the fact that different wavelengths of light travel at different speeds through the material of

gtnhenbr [62]

Answer:

y_red / y_blue = 1.11

Explanation:

Let's use the constructor equation to find the image for each wavelength

1 /f = 1 /o + 1 /i

Where f is the focal length, or the distance to the object and i the distance to the image

Red light

1 / i = 1 / f - 1 / o

1 / i_red = 1 / f_red - 1 / o

1 / i_red = 1 / 19.57 - 1/30

1 / i_red = 1,776 10-2

i_red = 56.29 cm

Blue light

1 / i_blue = 1 / f_blue - 1 / o

1 / i_blue = 1 / 18.87 - 1/30

1 / i_blue = 1,966 10-2

i_blue = 50.863 cm

Now let's use the magnification ratio

m = y ’/ h = - i / o

y ’= - h i / o

Red Light

y_red ’= - 5 56.29 / 30

y_red ’= - 9.3816 cm

Light blue

y_blue ’= 5 50,863 / 30

y_blue ’= - 8.47716 cm

The ratio of the height of the two images is

y_red ’/ y_blue’ = 9.3816 / 8.47716

y_red / y_blue = 1,107

y_red / y_blue = 1.11

5 0

2 years ago

One end of a string is fixed. An object attached to the other end moves on a horizontal plane with uniform circular motion of ra

sveticcg [70]

Answer:

If both the radius and frequency are doubled, then the tension is increased 8 times.

Explanation:

The radial acceleration ( $a_{r}$ ), measured in meters per square second, experimented by the moving end of the string is determined by the following kinematic formula:

$a_{r} = 4\pi^{2}\cdot f^{2}\cdot R$ (1)

Where:

$f$ - Frequency, measured in hertz.

$R$ - Radius of rotation, measured in meters.

From Second Newton's Law, the centripetal acceleration is due to the existence of tension ( $T$ ), measured in newtons, through the string, then we derive the following model:

$\Sigma F = T = m\cdot a_{r}$ (2)

Where $m$ is the mass of the object, measured in kilograms.

By applying (1) in (2), we have the following formula:

$T = 4\pi^{2}\cdot m\cdot f^{2}\cdot R$ (3)

From where we conclude that tension is directly proportional to the radius and the square of frequency. Then, if radius and frequency are doubled, then the ratio between tensions is:

$\frac{T_{2}}{T_{1}} = \left(\frac{f_{2}}{f_{1}} \right)^{2}\cdot \left(\frac{R_{2}}{R_{1}} \right)$ (4)

$\frac{T_{2}}{T_{1}} = 4\cdot 2$

$\frac{T_{2}}{T_{1}} = 8$

If both the radius and frequency are doubled, then the tension is increased 8 times.

5 0

2 years ago

You have been hired to check the technical correctness of an upcoming made-for-TV murder mystery that takes place in a space shu

AlladinOne [14]

Answer:

The astronaut who has a mass of 80 kg without the toolkit do survive with 40 seconds of remaining air

Explanation:

Due the astronaut throws the 10-kg tool kit away with a speed of 8 m/s, it gives a momentum equivalent but in the other direction, so $I=mv=(10Kg)(8m/s)=80kg*m/s$ , then we can find the speed that the astronaut reaches due to its weight we get, $v=\frac{I}{m} =\frac{80kg*m/s}{80Kg} =1m/s$ .

Finally, as the distance to the space shuttle is 200m, the time taken to the astronaut to reach it at the given speed will be $t=\frac{d}{v}=\frac{200m}{1m/s}=200s$ , as the remaining air time is 4 min or 240 seconds, The astronaut who has a mass of 80 kg without the toolkit do survive with 40 seconds of remaining air.

5 0

2 years ago