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Two disks of identical mass but different radii (r and 2r) are spinning on frictionless bearings at the same angular speed ?0, b

cestrela7 [59]

Answer:

Explanation:

Moment of inertia of a disc = 1/2 M R²

Since mass is same for both and radius are r and 2r, their moment of inertia can be in the ratio of 1: 4 . Let them be I and 4I . Angular speed are ω₀ and - ω₀ .

We shall apply law of conservation of angular momentum .

initial total angular momentum

I x ω₀ - 4I x ω₀ = - 3Iω₀

Let final common angular momentum be ω

total final angular momentum = ( I + 4I ) ω

Applying law of conservation of angular momentum

( I + 4I ) ω = - 3Iω₀

ω = - 3 / 5 ω₀ .

b )

Initial total rotational K E

= 1/2 I ω₀² + 1/2 4I ω₀²

= 1/2 x5I ω₀²

Final total rotational K E

= 1/2 ( I + 4I ) ( - 3 / 5 ω₀ )²

= 1/2 x 9 / 5 I ω₀²

= 9 / 10I ω₀²

change in rotational kinetic energy = 9 / 10I ω₀² - 1/2 x5I ω₀²

(9/10 - 5/2) xI ω₀²

=( .9 - 2.5 )I ω₀²

= - 1.6 I ω₀² Ans

8 0

3 years ago

If a machine is doing 500 J of work with 75 watts of power, how long did it take to complete its task?

kompoz [17]

Answer:

time = 6.67secs

Explanation:

power = workdone( energy) / time

therefore :

Time = workdone / power

time = 500 / 75

time = 6.67secs

3 0

3 years ago

Two balls of mass m1 and m2, with velocities v1 and v2 collide head on. Is there any way for both balls to have zero velocity af

nordsb [41]

Answer:

Explanation:

As the final Kinetic energy is zero or less than initial kinetic energy, the collision must be inelastic.

In Inelastic collision both the bodies must stick together as final velocity is zero for both the bodies.

To conserve the momentum, momentum associated before the collision of first must be equal and opposite to the momentum associated with the second ball.

i.e.

$m_1v_1=m_2v_2$

8 0

3 years ago

A two-stage rocket is traveling at 1200 mis with respect to the earth when the first stage runs out of fuel. Explosive bolts rel

Aloiza [94]

Answer:

The speed of the second stage after separation is 4905 m/s

Explanation:

Hi there!

Due to conservation of momentum, the momentum of the system first stage - second stage must remain constant before and after the separation. The momentum of the system is calculated by adding the momentums of each object:

initial momentum = final momentum

m₁₊₂ · v = m1 · v1 + m2 · v2

Where:

m₁₊₂ = mass of the two stage rocket

v = velocity of the rocket

m1 = mass of stage 1

v1 = velocity of stage 1

m2 = mass of stage 2

v2 = velocity of stage 2

We have the following data:

m1 = 3 · m2

m₁₊₂ = m1 + m2 = 3 · m2 + m2 = 4 · m2

v = 1200 m/s

v1 = -35 m/s (let´s consider the backward direction as negative)

v2 = ?

Then, replacing these data in the equation of momentum of the system:

m₁₊₂ · v = m1 · v1 + m2 · v2

4 m2 · 1200 m/s = 3 m2 · (-35 m/s) + m2 · v2

Let´s solve the equation for v2:

divide both sides of the equation by m2:

4 · 1200 m/s = 3 · (-35 m/s) + v2

4800 m/s = -105 m/s + v2

v2 = 4800 m/s + 105 m/s = 4905 m/s

The speed of the second stage after separation is 4905 m/s

6 0

3 years ago

Read 2 more answers

6. The petrol in a petrol can weighs 2000g. The density of petrol is 0.8g/cm3.

frez [133]

Answer:

a. 2500 cm³.

b. 2.5 litres.

Explanation:

Given the following data:

Density = 0.8g/cm³

Mass = 2000g

To find the volume of the petrol;

Density can be defined as mass all over the volume of an object.

Simply stated, density is mass per unit volume of an object.

Mathematically, density is given by the equation;

$Density = \frac{mass}{volume}$

Making volume the subject of formula, we have;

$Volume = \frac{mass}{density}$

Substituting into the equation, we have:

$Volume = \frac{2000}{0.8}$

Volume = 2500 cm³

a. The volume of the petrol in the can in cubic centimeters (cm³) is 2000.

b. The volume of the petrol in the can in litres;

1000 cm³ = 1 litre

2500 cm³ = x litres

Cross-multiplying, we have;

1000x = 2500

x = 2500/1000

x = 2.5 litres.

Therefore, the volume of the petrol in the can in litres is 2.5.

7 0

3 years ago