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9966 [12]
2 years ago
7

A particle (charge = 5.0 μC) is released from rest at a point x = 10 cm on the x-axis. If a 5.0-μC charge is held fixed at the o

rigin, what is the kinetic energy of the particle after it has moved 90 cm?
Physics
1 answer:
victus00 [196]2 years ago
4 0

Answer:

Explanation:

Given

Two charges with charge Q=5\ \mu C

When the first charge is at x=10\ cm on the x-axis and another at x=0 (origin)

there is only Potential Energy

Total Energy(E)=Kinetic Energy(K)+Potential Energy(U)

U_i=\frac{kQ\cdot Q}{r}

U_i=\frac{9\times 10^9\times (5\times 10^{-6})^2}{0.1}

U_i=2.25\ J

E=2.25

When First charge is at x=90

There will be both Kinetic energy and potential Energy

U_f=\frac{kQ\cdot Q}{r}

U_f=\frac{9\times 10^9\times (5\times 10^{-6})^2}{0.9}

U_f=0.25\ J

As total Energy is constant therefore Kinetic Energy is

k=E-U_f

k=2.25-0.25=2\ J

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Two uniform, solid cylinders of radius R and total mass M are connected along their common axis by a short, light rod and rest o
sveta [45]

Explanation:

A) To prove the motion of the center of mass of the cylinders is simple harmonic:

System diagram for given situation is shown in attached Fig. 1

We can prove the motion of the center of mass of the cylinders is simple harmonic if

a_{x} = -\omega^{2}  x

where aₓ is acceleration when attached cylinders move in horizontal direction:

<h3>PROOF:</h3>

rotational inertia for cylinders  is given as:

                                  I=\frac{1}{2}MR^{2} -----(1)

Newton's second law for angular motion is:

                                             ∑τ = Iα ------(2)

For linear motion in horizontal direction it is:

                                             ∑Fₓ = Maₓ ------ (3)

By definition of torque:

                                               τ  = RF --------(4)        

Put (4) and (1) in (2)

                                       RF=\frac{1}{2}MR^{2}\alpha

                                       RF=\frac{1}{2}MR^{2}\alpha

from Fig 3 it can be seen that fs is force by which the cylinders roll without slipping as they oscillate

So above equation becomes

                                   f_{s}=\frac{1}{2}MR\alpha------ (5)

As angular acceleration is related to linear by:

                                          a= R\alpha

Eq (5) becomes

                                    f_{s}=\frac{1}{2}Ma_{x}---- (6)

aₓ shows displacement in horizontal direction

From (3)

                                              ∑Fₓ = Maₓ

Fₓ is sum of fs and restoring force that spring exerts:

                                  \sum F_{x} = f_{s} - kx ----(7)

Put (7) in (3)

                                  f_{s} - kx  = Ma_{x}[/tex] -----(8)

Using (6) in (8)

                               \frac{1}{2}Ma_{x} - kx =Ma_{x}

                                     a_{x} = \frac{2k}{3M} x --- (9)

For spring mass system

                                  a= -\omega^{2} x ----- (10)

Equating (9) and (10)

                                  \omega^{2} = \frac{2k}{3M}

\omega = \sqrt{ \frac{2k}{3M}}

then (9) becomes

                                a_{x} = - \omega^{2}x

(The minus sign says that x and  aₓ  have opposite directions as shown in fig 3)

This proves that the motion of the center of mass of the cylinders is simple harmonic.

<h3 /><h3>B) Time Period</h3>

Time period is related to angular frequency as:

                                   T=\frac{2\pi }{\omega}

                                  T = 2\pi \sqrt{\frac{3M}{2k}

                           

 

5 0
2 years ago
The magnetic field around a current-carrying wire is ________proportional to the current and _________proportional to the distan
PSYCHO15rus [73]

Answer:Thus, The magnetic field around a current-carrying wire is <u><em>directly</em></u>  proportional to the current and <u><em>inversely</em></u>  proportional to the distance from the wire.  If the current triples while the distance doubles, the strength of the magnetic field increases by <u><em>one and half (1.5)</em></u> times.

Explanation:

Magnetic field around a long current carrying wire is given by

B=\frac{\mu _o I}{2\pi r}

where B= magnetic field

           \mu _o= permeability of free space

           I= current in the long wire and

           r= distance from the current carrying wire

Thus, The magnetic field around a current-carrying wire is <u><em>directly</em></u>  proportional to the current and <u><em>inversely</em></u>  proportional to the distance from the wire.  

Now if I'=3I and r'=2r then magnetic field B' is given by

B'=\frac{\mu _oI'}{2\pi r'}=\frac{\mu _o3I}{2\pi 2r}=1.5B

Thus If the current triples while the distance doubles, the strength of the magnetic field increases by <u><em>one and half (1.5)</em></u> times.

   

7 0
2 years ago
Read 2 more answers
A hot (70°C) lump of metal has a mass of 250 g and a specific heat of 0.25 cal/g⋅°C. John drops the metal into a 500-g calorimet
Gnom [1K]

Answer:

d. 37 °C

Explanation:

m_{m} = mass of lump of metal = 250 g

c_{m} = specific heat of lump of metal  = 0.25 cal/g°C

T_{mi} = Initial temperature of lump of metal = 70 °C

m_{w} = mass of water = 75 g

c_{w} = specific heat of water = 1 cal/g°C

T_{wi} = Initial temperature of water = 20 °C

m_{c} = mass of calorimeter  = 500 g

c_{c} = specific heat of calorimeter = 0.10 cal/g°C

T_{ci} = Initial temperature of calorimeter = 20 °C

T_{f} = Final equilibrium temperature

Using conservation of heat

Heat lost by lump of metal = heat gained by water + heat gained by calorimeter

m_{m} c_{m} (T_{mi} - T_{f}) = m_{w} c_{w} (T_{f} - T_{wi}) +  m_{c} c_{c} (T_{f} - T_{ci}) \\(250) (0.25) (70 - T_{f} ) = (75) (1) (T_{f} - 20) + (500) (0.10) (T_{f} - 20)\\T_{f} = 37 C

6 0
2 years ago
An electron is released from rest at a distance of 9.00 cm from a proton. If the proton is held in place, how fast will the elec
inna [77]

Answer:

v = 61.09m/s

Explanation:

In order to calculate the speed of the electron when it is 3.00cm from the proton, you first calculate the acceleration of the electron, produced by the electric force between the electron and the proton. By using the second Newton law you have:

F=ma=k\frac{q^2}{r^2}     (1)

m: mass of the electron = 9.1*10^-31kg

q: charge of electron and proton = 1.6*10^-19C

r: distance between electron and proton = 9.00cm = 0.09m

k: Coulomb's constant = 8.98*10^9Nm2/C^2

You solve the equation (1) for a, and replace the values of the other parameters:

a=\frac{kq^2}{mr^2}=\frac{(8.98*10^9Nm^2/C^2)(1.6*10^{-19}C)^2}{(9.1*10^{-31}kg)(0.09m)^2}=3.11*10^4\frac{m}{s^2}

Next, you use the following formula to calculate the final speed of the electron:

v^2=v_o^2+2ax       (2)

vo: initial speed of the electron = 0m/s

a: acceleration = 3.11*10^4m/s^2

x: distance traveled by the electron

When the electron is at 3.00cm from the proton the electron has traveled a distance of 9.00cm - 3.00cm = 6.00cm = 0.06m = x

You replace the values of the parameters in the equation (2):

v=\sqrt{2ax}=\sqrt{2(3.11*10^4m/s)(0.06m)}=61.09\frac{m}{s}

The speed of the electron is 61.09m/s

8 0
2 years ago
From Gauss's law, the electric field set up by a uniform line of charge is given by the following expression where is a unit vec
Evgesh-ka [11]

Answer:

\Delta V=\lambda *ln(r_{2}/r_{1}) /\ (2\pi*\epsilon_{o})

Explanation:

Using the Gauss Law, we obtain the electric Field for a uniform large line of charge:

2\pi r L*E=\lambda *L/\epsilon_{o}

E=\lambda /\(2 \pi* r *\epsilon_{o})

We calculate the potential difference from the electric field:

\Delta V=-\int\limits^{r_{1}}_{r_{2}} E \, dr =-\int\limits^{r_{1}}_{r_{2}} \lambda dr/ (2\pi*r*\epsilon_{o})=\lambda *ln(r_{2}/r_{1}) /\ (2\pi*\epsilon_{o})

5 0
2 years ago
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