PHYSICS COLLEGE

A wheel 2.45 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.30 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3° with the horizontal at this time. At t = 2.00 s, find the following.a. the angular speed of the wheel and, for point P
b. the tangential speed.
c. the total acceleration.
d. the angular position.

Answers

Answer 1

Answer:

(a) The angular speed of the wheel at point P is 8.6 rad/s.

(b) The tangential speed of the wheel is 10.54 m/s.

(d) The angular position of the wheel is 87 ⁰.

The given parameters;

diameter of the wheel, d = 2.45 m
radius of the wheel, r = 1.225 m
angular acceleration of the wheel, α = 4.3 rad/s²
angular displacement of the wheel, θ = 57.3⁰
time of motion, t = 2.0 s

The angular speed of the wheel at point P is calculated as follows;

$\omega_f = \omega _i + \alpha t\n\n\omega _f = 0 + 4.3 * 2\n\n\omega _f = 8.6 \ rad/s$

The tangential speed of the wheel is calculated as follows;

$v = \omega _f r\n\nv = 8.6 * 1.225 \n\nv = 10.54 \ m/s$

The centripetal acceleration of the wheel is calculated as follows;

$a_c = (v^2)/(r) \n\na_c = ((10.54)^2)/(1.225) \n\na_c = 90.69 \ m/s^2$

The total acceleration of the wheel is calculated as follows;

$a_t = √(a_c^2 + a_r^2) \n\na_t = √(90.69^2 + 4.3^2) \n\na_t = 90.8 \ m/s^2$

The angular position is calculated as follows;

$\theta = tan^(-1) ((a_c)/(a_r) )\n\n\theta = tan^(-1) ((90.69)/(4.3) )\n\n\theta = 87 \ ^0$

Learn more here: brainly.com/question/14508449

Answer 2

Answer:

Answer:

Explanation:

Radius of wheel R = 1.225 m

For angular motion of wheel

ω = ω ₀ + α t

= 0 + 4.3 x 2

= 8.6 rad / s

This is angular speed of wheel and point P .

b )

Tangential speed = ωR

8.6 x 1.225

= 10.535 m / s

c )

radial acceleration

a_r = v² / r

= 10.535² / 1.225

= 90.6 m / s²

tangential acceleration = radius x angular acceleration

a_t = 4.3 x 1.225

= 5.2675

Total acceleration = √ 90.6² + 5.2675²

= √ 8208.36 + 27.7465

= 90.75 m/s²

d ) angle of rotation

= 1/2 α t²

= .5 x 4.3 x 4

= 8.6 radian

= (8.6/3.14) x 180

= 499 degree

= 499 + 57.3

= 556.3

556.3 - 360

= 196.3 degree

Point p will rotate by 196.3 degree

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Fuel cells have been developed that can generate a large amount of energy. For example, a hydrogen fuel cell works by combining hydrogen and oxygen gas to produce water and electrical energy. If a fuel cell can generate 10.0 kilowatts of power and the current is 15.8 amps, what is the voltage of the electricity?A.
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B.
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C.
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D.
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E.
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Answers

The voltage of the electricity will be 632.9 V. Electric power is found as the multiplication of the voltage and current. Option B is correct.

What is electric power?

Electric power is the product of the voltage and current. Its unit is the watt. It is the rate of the electric work done.

The given data in the problem is;

V is the voltage = ? Volt (V)

Electric current (I)= 15.8 amps (A)

P is the power =10.0 kilowatts =10⁴ watt

The formula for the power is given as;

$\rm P= V I \n\n\ 10^4= V * 15.8 \n\n V=632.9 \ V$

The voltage of the electricity will be 63.29 V.

Hence, option B is correct.

To learn more about the electric power, refer to the link;

brainly.com/question/12316834

#SPJ2

Hmmm. Kilowatts should be converted to watts. Simply just move the decimal place to the right three times.

10,000 W / 15.8 A = V

632.9, or 633.

7: A 2 mA current passes through a 1.4 cm long solenoid producing a magnetic field of .162 G. How many turns are in the solenoid

Answers

Answer:

The number of turns is 64449395

Explanation:

The expression for the solenoid formula is stated below, and it is what we are going to use to solve for the number of turns

B= μ₀nl

where B= magnetic field

μ₀= permeability , 4π × 10⁻⁷ Henry

n= number of turns

l= length of coil

Given data

current I= 2 mA

length L= 1.4 cm to meter we have 0.014

magnetic field B= 0.162 T

From the expression we can make n subject of formula we have

n=B/μ₀l

Substituting we have

n= 0.162/4π × 10⁻⁷*2*10^-3

n= 0.162/8π × 10^⁻10

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QuestIuI(2 PUMILS)
How much power is needed to lift a 750 kg elephant 14.3 m in 30.0 seconds?

Answers

Given Information:

Mass of elephant = m = 750 kg

Height = h = 14.3 m

time = t = 30 seconds

Required Information:

Power needed to lift elephant = P = ?

Answer:

Power needed to lift elephant ≈ 3507 watts

Explanation:

As we know power is given by

P = PE/t

Where PE is the potential energy and t is the time

Potential energy is given by

PE = mgh

Where m is the mass of elephant, g is the gravitational acceleration and h is the height to lift the elephant.

PE = 750*9.81*14.3

PE = 105212.25 Joules

Therefore, the required power to lift the elephant is

P = PE/t

P = 105212.25/30

P ≈ 3507 watts

In a charging process, 4 × 1013 electrons are removed from one small metal sphere and placed on a second identical sphere. Initially, both metal spheres were neutral. After the charging process, the electrical potential energy associated with the two spheres is found to be −0.063 J. What is the distance between the two spheres?

Answers

Answer:

The distance between the two spheres is 914.41 X 10³ m

Explanation:

Given;

4 X 10¹³ electrons, and its equivalent in coulomb's is calculated as follows;

1 e = 1.602 X 10⁻¹⁹ C

4 X 10¹³ e = 4 X 10¹³ X 1.602 X 10⁻¹⁹ C = 6.408 X 10⁻⁶ C

V = Ed

where;

V is the electrical potential energy between two spheres, J

E is the electric field potential between the two spheres N/C

d is the distance between two charged bodies, m

$V = (K*q)/(d^2)*d = (K*q)/(d)$

$d = (K*q)/(V)$

where;

K is coulomb's constant = 8.99 X 10⁹ Nm²/C²

d = (8.99 X 10⁹ X 6.408 X 10⁻⁶)/0.063

d = 914.41 X 10³ m

Therefore, the distance between the two spheres is 914.41 X 10³ m

a mass of .4 kg is raised by a vertical distance of .450 m in the earth's gravitational field. what is the change in its gravitational potential energy

Answers

Answer:

E = 1.76 J

Explanation:

Given that,

Mass of an object, m = 0.4 kg

It moves by a vertical distance of 0.45 m in the Earth's gravitational field.

We need to find the change in its gravitational potential energy. It can be given by the formula as follow :

$E=mgh\n\nE=0.4* 9.8* 0.45\n\nE=1.76\ J$

So, the change in its gravitational potential energy is 1.76 J.

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