Answer:
Explanation:
a ) Time period T = 2 s
Angular velocity ω = 2π / T
= 2π / 2 = 3.14 rad /s
Initial moment of inertia I₁ = 200 + mr²
= 200 + 25 x 2.5²
=356.25
Final moment of inertia
I₂ = 200 + 25 X 1.5 X 1.5
= 256.25
b ) We apply law of conservation of momentum
I₁ X ω₁ = I₂ X ω₂
ω₂ = I₁ X ω₁ / I₂
Putting the values
ω₂ = 4.365 rad s⁻¹
c ) Increase in rotational kinetic energy
=1/2 I₂ X ω₂² - 1/2 I₁ X ω₁²
.5 X 256.25 X 4.365² - .5 X 356.25 X 3.14²
= 684.95 J
This energy comes from work done against the centripetal pseudo -force.
The product of (wavelength) x (frequency) is always the same number ... the wave's speed.
So if the wavelength is somehow reduced to 1/4 its original length, the <em>frequency is immediately multiplied by 4</em> . That's the only way their product can remain the same.
Answer:
174.85 W
Explanation:
Area of plate = 3.14 x (15x 10⁻²)²
= 706.5 x 10⁻⁴ m²
heat being radiated by convection = 12 x 706.5 x 10⁻⁴ ( 180 - 15 )
= 139.88 W. This energy needs to be fed by heat source to maintain a constant temperature of 180 degree.
If power of electric source is P
P x .8 = 139.88
P = 139.88 / .8
= 174.85 W
D = vo t - at²/2
v = vo - at
40 m = vo · 7.10 - a · ( 7.10 )²/2
40 m = 7.10 vo - a· 50.41/2
40 m = 7.10 vo - 25.205 a
2.75 m/s = vo - 7.10 a ⇒ a = ( vo - 2.75 )/ 7.10
40 = 7.10 vo - 25.205 · ( vo - 2.75 ) / 7.10
40 = 7.1 vo - 3.55 vo + 9.7625
3.55 vo = 30.2375
vo = 30.2375 : 3.55 = 8.5176 m/s
Answer: the truck`s original speed is 8.5176 m/s.
Attached a diagram of the scheme described in the problem ..
To solve the problem we need to know the relationship between kinetic and normal force, so
Where
coefficient of kinetic
Normal force
We perform the sum of forces as well,
(2)
For Normal Force in Y,
(3)
The force in X,
(4)
Replacing in (4)
In this way, it does not matter which object is chosen.
