1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kirill115 [55]
3 years ago
9

A marble slides along a frictionless track at a constant speed u before encountering a section of the track that is covered with

a thin layer of putty. The instantaneous velocity v of the marble as it slides past the putty, as a function of time t, is given byv(t)=u-bt+ct^3where t = 0 at the moment when the marble first comes into contact with the putty. As the marble exits the region covered in putty, the marble\'s instantaneous acceleration goes to zero. For u = 2.50 m/s, b = 3.55 m/s2, and c = 6.70 m/s4, calculate the length of the track that is covered with putty._______m
Physics
1 answer:
Yuki888 [10]3 years ago
6 0

Answer:

x = 78.9 cm

Explanation:

The instantaneous velocity v of the marble as it slides past the putty, as a function of time t, is given by

v(t)=u-bt+ct^3

u = 2.50 m/s, b = 3.55 m/s², and c = 6.70 m/s⁴

As the marble exits the region covered in putty, the marble\'s instantaneous acceleration goes to zero.

a=\dfrac{dv}{dt}\\\\a=\dfrac{d(u-bt+ct^3)}{dt}\\\\a=-b+3ct^2

or

0-3.55+3\times 6.7t^2\\\\0=-3.55+20.1t^2\\\\t=\sqrt{\dfrac{3.55}{20.1}} \\\\t=0.42\ s

Let x is the length of the track.

v=\dfrac{dx}{dt}\\\\\text{or}\\\\\int\limits_0^x {dx} =\int\limits^{4.2}_0 {vdt} \\\\x=\int\limits^{4.2}_0 {u-bt+ct^3} \, dt\\\\x=[ut-\dfrac{bt^2}{2}+\dfrac{ct^4}{4}]_0^ {0.42}\\\\\text{Putting limits}\\\\x=0.42u-\dfrac{b(0.42)^2}{2}+\dfrac{c(0.42)^4}{4}\\\\\text{Now, put values of u,b and c}\\\\x=0.42(2.5)-\dfrac{3.55\times (0.42)^2}{2}+\dfrac{6.7\times (0.42)^4}{4}\\\\x=0.789\ m\\\\x=78.9\ cm

So, the length of the track that is covered with putty is 78.9 cm.

You might be interested in
Unlike the idealized voltmeter, a real voltmeter has a resistance that is not infinitely large. part a a voltmeter with resistan
Margaret [11]
The EMF of the battery includes the force to to drive across its internal resistance. the total resistance:  
R = internal resistance r + resistance connected rv 
R = r + rv  
Now find the current:  
V 1= IR 
I = R / V1  
find the voltage at the battery terminal (which is net of internal resistance) using  
V 2= IR  
So the voltage at the terminal is:  
V = V2 - V1  
This is the potential difference vmeter measured by the voltmeter.
6 0
3 years ago
Read 2 more answers
1. Which statement about subatomic particles is not true?
igomit [66]

1. Protons and neutrons have the same charge.

Protons have positive charge, equal to e=+1.6\cdot 10^{-19} C, while neutrons have zero charge.

2. mass number

The mass number of an atom is equal to the sum of protons and neutrons inside its nucleus.

3. Atoms are made up of smaller particles.

According to Dalton's theory, atoms are the smallest particles that make matter, and they are indivisible and indestructible, so they are NOT made up of smaller particles.

4. a solid sphere

In Dalton's theory, atoms are not made of smaller particles, so we can think them as solid spheres.

5. J. J. Thomson

In his experiment with cathode ray tubes, JJ Thomson demonstrated the existance of the electrons, which are negatively charged particles inside the atom. In his model of the atom (plum-pudding model), Thomson thought the atom consists of a uniform positive charge and the electrons are located inside this positive charge.

6. An electron has the same amount of energy in all orbitals.

In fact, each orbital corresponds to a different energy level: the farther the orbital from the nucleus, the higher the energy of the electrons contained in that orbital.

7. A hydrogen atom in heavy water has an extra neutron.

Heavy water is a type of water that contains deuterium, which is an isotope of the hydrogen consisting of one proton and one neutron (so, one extra neutron).

8. The glowing beam was always deflected by charged plates

In his cathode's ray tube experiment, Thomson shows that the beam of unknown particles (= the electrons) were deflected by charge plates, so the particles had to be also electrically charged.

9. electrons move to a lower energy level

When electrons move from a higher energy level to a lower energy, they emit a photon (light) of energy equal to the difference in energy between the two energy levels.

10. orbital

In quantum mechanics, electrons in the atom are not precisely located, since we cannot determine their exact position and velocity at the same time. Therefore, we can only describe regions of space where the electrons have a certain probability to be found, and these regions of space are called orbitals.

11. 14

According to Dalton's theory, the proportions of the reactants must be respected in order to form the same compound. Therefore, we can write:

2 g: 4 g = X : 28 g\\X=\frac{2 g \cdot 28 g}{4 g}=14 g

12. negative charge, found outside the nucleus

Electrons are particles with negative charge of magnitude e=-1.6\cdot 10^{-19}C that orbit around the nucleus. The nucleus, instead, consists of protons (positively charged, with charge opposite to the electron) and neutrons (neutrally charged).

13. move from higher to lower energy levels

When electrons move from a higher energy level to a lower energy inside a neon atom, they emit a photon (which is light) whose energy is equal to the difference in energy between the two energy levels.

14. atomic number from its mass number

In fact:

- the atomic number of an atom (Z) is equal to the number of protons inside the nucleus

- the mass number of an atom (A) is equal to the sum of protons+neutrons inside the nucleus

Therefore, we can find the number of neutrons in the nucleus by calculating the difference between A and Z:

Number of neutrons = A - Z

15. None of them

None of these examples is a good analogy to describe the location of an electron in an atomic orbital: in fact, the position of an electron in an orbital cannot be precisely described, we can only describe the probability to find the electron in a certain position, and none of these example is an analogy of this model.

8 0
3 years ago
A single conservative force acts on a 5.30-kg particle within a system due to its interaction with the rest of the system. The e
cupoosta [38]

Answer:

Given that

m = 5.3 kg

Fx = 2x + 4

We know that work done by force F given as

w= ∫ F. dx

a)

Given that x=1.08 m to x=6.5 m

Fx = 2x + 4

w= ∫ F. dx

w=\int_{1.08}^{6.5}(2x+4) .dx

w=\left [x^2+4x \right ]_{1.08}^{6.5}

w=(6.5^2-1.08^2)+4(6.5-1.08)\ J

w=62.7 J

b)

We know that potential energy given as

F=-\dfrac{dU}{dx}

∫ dU =  -∫F.dx           ( w= ∫ F. dx)

ΔU= -62.7 J

c)

We know that form work power energy theorem

Net work = Change in kinetic energy

W= KE₂ - KE₁

62.7 =KE₂ - (1/2)x 5.3 x 3²

KE₂ = 86.55 J

This is the kinetic energy at 6.5m

8 0
3 years ago
A car accelerates at a rate of 4 m/s in 5 s. Calculate the change of velocity PLS HELP
garri49 [273]

Answer:

Explanation:

a=Δv/Δt

Δv=a*Δt

a=4 m/s2

t=5 s

Δv=4*5

Δv=20 m/s

6 0
3 years ago
Suppose that a car skids 15 meters if it is moving at 50 kilometers per hour Acceleration-Velocity-Position when the brakes are
julia-pushkina [17]

Explanation:

Below is an attachment containing the solution.

4 0
3 years ago
Other questions:
  • If your runnin at full speed for an average human, and lept over a 10 foot brook would you make it?
    14·2 answers
  • If the surface air pressure is 1000 mb and the pressure at the top of the atmosphere (75 km) is 0 mb, at what altitude would I f
    11·1 answer
  • It is observed that the time for the ball to strike the ground at b is 2.5 s. determine the speed at which the ball was thrown.
    8·1 answer
  • Which type of energy will definitely not be used in the lighting of a match?
    10·1 answer
  • Who pioneered the use of galvanoplastic compounds for preserving footprints and ballistics?
    11·2 answers
  • Oppositely charged objects attract each other. This attraction holds electrons in atoms and holds atoms to one another in many c
    7·2 answers
  • The charge of an electron is
    14·1 answer
  • 3 An un calibrated mercury in glass thermometer immersed in melting ice. The length of the mercury thread is 25 mm when the ther
    11·1 answer
  • Suppose a 4,000-kg elephant is hoisted 20 m above Earth’s surface. Use a calculator and follow the steps below to find the eleph
    6·1 answer
  • What is the SI (metric) unit of FORCE?<br><br> A. meter<br> B. newton
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!