PHYSICS COLLEGE

Write down the DE of motion of a particle moving under the influence of gravity and experiencing a resistive force. .

Answers

Answer 1

Answer:

Answer:

The DE will be $(d^2x)/(dt^2)-(k)/(m)(dx)/(dt)-g=0$

Explanation:

We have to find differential equation under the influence of gravity and experiencing a resistive force

Let an object of mass m falling under the influence of gravity

So the force experience under gravity $=mg$

Le the a resistive force of magnitude kv opposes this gravity force, here k is constant and v is velocity.

So net force $F_(NET)=mg-kv$ -----eqn 1

$F_(NET)=ma$

So $ma=mg-kv$

We know that velocity is rate of change of position so $v=(dx)/(dt)$ , and acceleration is rate of change of velocity so $a=(d^2x)/(dt^2)$

Putting all these value in eqn 1

$m(d^2x)/(dt^2)=mg-k(dx)/(dt)$

$(d^2x)/(dt^2)-(k)/(m)(dx)/(dt)-g=0$

Related Questions

If a pressure gauge measure an increase in 3×10^(5)Pa on an area of 0.7 m^2, calculate the increase in the force applied to the area?
As a science project, you drop a watermelon off the top of the Empire State Building. 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a constant speed of 30 m/s. A) How much time passes before the watermelon has the same velocity? B) How fast is the watermelon going when it passes Superman?C) How fast is the watermelon traveling when it hits the ground?
The graphs display velocity data Velocity is on the y-axis (m/s), while time is on the x-axis (s). Based on the graphs, which data set represents constant acceleration?
A truck’s suspension spring each have a spring constant of 769 N/m. If the potential energy of the right front spring is 250 J, how far is the spring compressed?
Crude oil is a mixture of many different components. The extraction of crude oil from the Earth is important, but its refinement into different substances is a key piece to obtaining as many uses as possible from the crude oil. Using the diagram, justify the source of data used to develop the technology for refining the crude oil.

An electron is accelerated by a 5.9 kV potential difference. das (sd38882) – Homework #9 – yu – (44120) 3 The charge on an electron is 1.60218 × 10−19 C and its mass is 9.10939 × 10−31 kg. How strong a magnetic field must be experienced by the electron if its path is a circle of

Answers

Complete Question

Answer:

The magnetic field strength is $B= 0.0048 T$

Explanation:

The work done by the potential difference on the electron is related to the kinetic energy of the electron by this mathematical expression

$\Delta V q = (1)/(2)mv^2$

Making v the subject

$v = \sqrt{[(2 \Delta V * q )/(m)] }$

Where m is the mass of electron

v is the velocity of electron

q charge on electron

$\Delta V$ is the potential difference

Substituting values

$v = \sqrt{(2 * 5.9 *10^3 * 1.60218*10^(-19) )/(9.10939 *10^(-31]) )$ f

$= 4.5556 *10^ {7} m/s$

For the electron to move in a circular path the magnetic force[ $F = B q v$ ] must be equal to the centripetal force[ $(mv^2)/(r)$ ] and this is mathematically represented as

$Bqv = (mv^2)/(r)$

making B the subject

$B = (mv)/(rq)$

r is the radius with a value = 5.4cm = $= (5.4)/(100) = 5.4*10^(-2) m$

Substituting values

$B = (9.1039 *10^(-31) * 4.556 *10^7)/(5.4*10^-2 * 1.60218*10^(-19))$

$= 0.0048 T$

The asteroid 234 Ida has a mass of about 4 × 1016 kg and an average radius of about 16 km. What is the acceleration due to gravity on 234 Ida? Assume that the asteroid is spherical; use G = 6.67 × 10–11 Nm2/kg2.A. 1 cm/s2
B. 2 cm/s2
C. 5 cm/s2
D. 6 cm/s2

Answers

The asteroid 234 Ida has a mass of about 4×1016 kg and an average radius of about 16 km. The acceleration due to gravity will be 1.04 cm/s². Hence, option A is correct.

What is the acceleration due to gravity?

The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity. M/s² is its SI unit. Its vector nature—which includes both magnitude and direction—makes it a quantity. The unit g stands for gravitational acceleration. At sea level, the standard value of g on the earth's surface is 9.8 m/s².

The formula for the acceleration due to gravity is g=GM/r².

According to the question, the given values are :

Mass, M = 4 × 1016 kg or

M = 4 × 10¹⁶.

Radius, r = 16 km or,

r = 16000 meter.

G = 6.67 × 10⁻¹¹ Nm²/kg²

g = (6.67 × 10⁻¹¹ ) (4 × 10¹⁶) / 16000²

g = 0.0104 m/s² or,

g = 1.04 cm/s².

Hence, the acceleration due to gravity will be 1.04 m/s²

To get more information about Acceleration due to gravity :

brainly.com/question/13860566

#SPJ2

Answer:

1 cm/s²

Explanation:

I just took the quiz

Two children, Ferdinand and Isabella, are playing with a waterhose on a sunny summer day. Isabella is holding the hose in herhand 1.0 meters above the ground and is trying to spray Ferdinand,who is standing 10.0 meters away. I know so far that she cannotspray Ferdinand at the current position and with the curreentspeed of spray. I got stuck inthe following question:To increase the range of the water, Isabellaplaces her thumb on the hose hole and partially covers it. Assuming that the flow remains steady, what fraction f of the cross-sectional area of the hose hole does shehave to cover to be able to spray her friend?

Assume that the cross section of the hoseopening is circular with a radius of 1.5 centimeters.

Answers

Answer:

Explanation:

According to the formula below, with constant flow rate, the less cross-sectional area there is, the faster water would flow, and vice-versa

$\dot{V} = A*v$

where $\dot{V} m^3/s$ is the constant flow rate,

A m2 is the cross-sectional area

v m/s is the water speed.

So if the flow rate is constant, when A decreases, v must increase proportionally.

Since this problem is missing the water speed, here are the steps to solve it

Step 1: find the new spray speed that could reach Ferdinand

Step 2: find the ratio of this new spray speed to the old one, this will also be the ratio of the old cross-sectional area to the new one.

Step 3: find the fraction f of the cross-sectional area of the hose hole

Carol is farsighted ( presbyopia) and cannot see objects clearly that are closer to her eyes than about meter. She sees objects clearly with a relaxed eye when they are distant. What is the refractive power of reading glasses that would allow her to read a book 50 cm away with a relaxed eye

Answers

Answer:

1.0 dioptres

Explanation:

Farsightedness is an eye defect in which a person can see far objects clearly but not near objects. That implies that the patients' near point is farther than 25cm which is the normal least distance of distinct vision.

Farsightedness results from the eyeball being too long or the crystalline lens not being sufficiently converging.

Carol is farsighted with a near point of about a meter (100cm). We desire to make a lens to enable her near point be reduced to about 50cm. The focal length and power of this lens is calculated in the image attached.

The power of a lens is the inverse of its focal length in meters hence the 100 in the formula for power of the lens.

Answer:

+1.00 diopter

Explanation:

The power of a lens can be described simply as the reciprocal of the focal length of the lens measured in meters.

But f is unknown, hence we look for the focal length with the formula

1/f = 1/u + 1/v

where u is former near point = 100cm

v is the new intended near point = 50cm

1/f = 1/50 - 1/100

1/f = 1/100

f = 100 cm

Hence we get Power (D) = 1/f

where f = focal length of the lens in meter

From the question, the focal length of the lens = 100cm = 1m

Hence D = 1/1

D = +1.00

Hence the refractive power of the reading glasses that would allow Carol to read a book 50cm away from the relaxed eye will be +1.00 diopters.

Explain how the Doppler effect works for sound waves and give some familiar examples.

Answers

Answer and Explanation:

Doppler effect : According to Doppler effect whenever there is a relative motion between the source and observer then there is an increase or decrease in frequency of sound light or waves.

REASON OF DOPPLER EFFECT : Doppler effect is mainly due to the sudden change in pitch of the sound

EXAMPLE OF DOPPLER EFFECT : The best example of Doppler effect is when an ambulance passes and when it comes closer then the frequency of the siren increases and when it goes away its frequency decreases.

A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.72 x 10^4 rad/s to an angular speed of 5.42 x 10^4 rad/s. In the process, the bit turns through 1.72 x 10^4 rad. Assuming a constant angular acceleration, how long would it take the bit to reach its maximum speed of 8.42 x 10^4 rad/s, starting from rest?