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An object of mass m swings in a horizontal circle on a string of length L that tilts downward at angle θ.Find an expression for the angular velocity ω in terms of g, L and angle θ.

Answers

Answer 1

Answer:

Answer:

The expression would be ω = $\sqrt{(g)/(L sin 0 ) }$

Explanation:

Given that ω is the angular velocity

g is the acceleration due to gravity

L is the length

θ is the angle of downward tilt

For an object we compare the horizontal and vertical component of the forces acting on the body;

For vertical component

T sinθ = mg............1

For the horizontal component

T cos θ = $(mv^(2) )/(R)$ .............2

R is our radius and is = L cos θ

v = ωR

substituting into equation 2 we have

T cos θ = m(ωR $)^(2)$ /R

T cos θ=m(ω $)^(2)$ R ..................3

Now comparing the vertical and the horizontal component we have;

equation 1 divided by equation 3 we have

T sin θ /T cos θ = mg / m(ω $)^(2)$ R

Tan θ = g / (ω $)^(2)$ R............4

Making ω the subject formula we have;

(ω $)^(2)$ = g/ R Tan θ

But R = L cos θ and Tan θ = sin θ/ cosθ

putting into equation 4 we have;

(ω $)^(2)$ = g /[( L cos θ) x( sin θ/ cosθ)]

(ω $)^(2)$ = g/ L sinθ

ω = $\sqrt{(g)/(L sin 0 ) }$

Therefor the expression for the angular velocity ω in terms of g, L and angle θ would be ω = $\sqrt{(g)/(L sin 0 ) }$

Answer 2

Answer: Let g, r, L and T are gravity, radius, length, and angle of string w/r/t vertical, respectively.
Then
ω²r = rg/Lcos T
ω² = g/L cos T
ω = √(g / L cos T)

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An object rests on a horizontal floor.the coefficient static friction is0.4 and acceleration of gravity is 9.8m/sdetermine the maximum force of the static friction and the minimum force of F

Answers

Answer:

first of all since the value of mass of the object and force F(horizontal) or the relation between them is not mentioned , so there can be multiple effects and let us study them in cases.

Let us consider that mass of the object is m and the coefficient of friction is the coefficient of static friction of the surface{since friction can be static as well as dynamic} whose value(μ) as is given in the question is 0.2. Since the surface and the force applied are both horizontal so there will be no vertical component of the force applied which means that the normal force is N=weight of the object=mg where g is the acceleration due to gravity(9.8 m/s^2 on average on surface of earth).

Case 1:

When F<=μN. This means that when the value of F is less than or equal to μN then the static friction is equal to F. So the body remains stationary.

Case 2:

When F>μN. This means that when the value of F is greater than μN then the static friction is less than F. So the body starts moving and if the force applied F is constant then the body will start accelerating because coefficient of kinetic friction is less than that of static friction.

Explanation:

When an object rests on a horizontal floor. the coefficient of static friction is 0.4 and the acceleration of gravity is 9.8m/s, then the maximum force of friction would be 1.962M and the minimum force of friction would be zero when no external force is applied, where M represents the mass of the object

What is friction?

Friction is a type of force that resists or prevents the relative motion of two physical objects when their surfaces come in contact.

When an object is beginning to move as a result of an external force, limiting friction is involved. This frictional force balances the external force until the object is in a condition where it remains stationary.

maximum Frictional force= μN

where μ is the coefficient of static friction

N is the normal reaction force having a value of mg

Thus, The maximum force of friction would be 1.962M, and the minimum force would be zero

Learn more about friction here

brainly.com/question/24186853

#SPJ5

Which describes one feature of the image formed by a convex mirror?????

Answers

Answer:

The image formed by a convex mirror will always have its smaller than the size of the object no matter what the position of the object.

Explanation:

The image formed by a convex mirror will always have its smaller than the size of the object no matter what the position of the object.

Also notice that convex mirror always makes virtual images.

Another feature of the convex mirror is that an upright image is always formed by the convex mirror.

An important mirror formula to remember which is applicable for both convex and mirrors

1/f= 1/u + 1/v

Here:

'u' is an object which gets placed in front of a spherical mirror of focal

length 'f' and image 'u' is formed by the mirror.

Answer:

right side up

Explanation:

An electron enters a region of uniform electric field with an initial velocity of 50 km/s in the same direction as the electric field, which has magnitude E = 50 N/C, (a) what is the speed of the electron 1.5 ns after entering this region? (b) How far does the electron travel during the 1.5 ns interval?

Answers

Answer:

(a). The speed of the electron is $3.68*10^(4)\ m/s$

(b). The distance traveled by the electron is $4.53*10^(-5)\ m$

Explanation:

Given that,

Initial velocity = 50 km/s

Electric field = 50 N/C

Time = 1.5 ns

(a). We need to calculate the speed of the electron 1.5 n s after entering this region

Using newton's second law

$F = ma$ .....(I)

Using formula of electric force

$F = qE$ .....(II)

from equation (I) and (II)

$-qE= ma$

$a = (-qE)/(m)$

(a). We need to calculate the speed of the electron

Using equation of motion

$v = u+at$

Put the value of a in the equation of motion

$v = 50*10^(3)-(1.6*10^(-19)*50)/(9.1*10^(-31))*1.5*10^(-9)$

$v=36813.18\ m/s$

$v =3.68*10^(4)\ m/s$

(b). We need to calculate the distance traveled by the electron

Using formula of distance

$s = ut+(1)/(2)at^2$

Put the value in the equation

$s = 3.68*10^(4)*1.5*10^(-9)-(1)/(2)*(1.6*10^(-19)*50)/(9.1*10^(-31))*(1.5*10^(-9))^2$

$s=0.0000453\ m$

$s=4.53*10^(-5)\ m$

Hence, (a). The speed of the electron is $3.68*10^(4)\ m/s$

(b). The distance traveled by the electron is $4.53*10^(-5)\ m$

The word acid comes from the Latin word

Answers

Hi :)

The word acid comes from the Latin word acere, which means sour

Hope this helps!

It is acere but for future reference you can search of definition press more and google tells you its origin

Monochromatic coherent light shines through a pair of slits. If the distance between these slits is decreased, which of the following statements are true of the resulting interference pattern?A) The distance between the maxima stays the same.B) The distance between the maxima decreases.
C) The distance between the minima stays the same.
D) The distance between the minima increases.
E) The distance between the maxima increases.

Answers

Answer:

The correct statements are D and E.

Explanation:

The fringe width is given by the following formula as :

$\beta =(\lambda D)/(d)$

Here,

$\lambda$ is wavelength of light

D is distance between slit and the screen

d is slit width.

If the between these slits is decreased, the fringe width increases. As a result, the distance between the minima increases and also the distance between the maxima increases.

A capacitor consists of two closely spaced metal conductors of large area, separated by a thin insulating foil. It has an electrical capacity of 3000.0 μF and is charged to a potential difference of 60.0 V. Calculate the amount of energy stored in the capacitor. Tries 0/20 Calculate the charge on this capacitor when the electrical energy stored in the capacitor is 6.53 J. Tries 0/20 If the two plates of the capacitor have their separation increased by a factor of 5 while the charge on the plates remains constant, by what factor is the energy stored in the capacitor increased?

Answers

Answer:

1 = 5.4 J

2 = 0.1979 C

3 = 5

Explanation:

Energy in a capacitor, E is

E = 1/2 * C * V²

E = 1/2 * 3000*10^-6 * 60²

E = 1/2 * 3000*10^-6 * 3600

E = 1/2 * 10.8

E = 5.4 J

E = Q²/2C = 6.53 J

E * 2C = Q²

Q² = 6.53 * 2 * 3000*10^-6

Q² = 13.06 * 3000*10^-6

Q² = 0.03918

Q = √0.03918

Q = 0.1979 C

The Capacitor, C is inversely proportional to the distance of separation, D. Thus, if D is increased by 5 to be 5D, then C would be C/5. And therefore, our energy stored in the capacitor is increased by a factor of 5.

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