1) 0.0011 rad/s
2) 7667 m/s
Explanation:
1)
The angular velocity of an object in circular motion is equal to the rate of change of its angular position. Mathematically:
where
is the angular displacement of the object
t is the time elapsed
is the angular velocity
In this problem, the Hubble telescope completes an entire orbit in 95 minutes. The angle covered in one entire orbit is
rad
And the time taken is
Therefore, the angular velocity of the telescope is
2)
For an object in circular motion, the relationship between angular velocity and linear velocity is given by the equation
where
v is the linear velocity
is the angular velocity
r is the radius of the circular orbit
In this problem:
is the angular velocity of the Hubble telescope
The telescope is at an altitude of
h = 600 km
over the Earth's surface, which has a radius of
R = 6370 km
So the actual radius of the Hubble's orbit is
Therefore, the linear velocity of the telescope is:
Answer:
1838216 J
Explanation:
95 km/h = 26.39 m/s
40 km/h = 11.11 m/s
Initial kinetic energy
= .5 x 1600 x(26.39)²
= 557145.67 J
Final kinetic energy
= .5 x 1600 x ( 11.11)²
= 98745.68 J
Loss of kinetic energy
= 458400 J
Loss of potential energy
= mg x loss of height
= 1600 x 9.8 x 340 sin 15
= 1379816 J
Sum of Loss of potential energy and Loss of kinetic energy
= 1379816 + 458400
= 1838216 J
This is the work done by the friction . So this is heat generated.
Explanation:
1. Phases of Venus: Galileo was the first astronomer to use a telescope to observe the celestial objects. Through a telescope he observed that Venus shows the phases just like the Moon. This proved the Heliocentric theory correct against the then prevalent Geocentric theory.
2. Law of Falling bodies: The acceleration due to gravity is independent of weight of the objects that means two bodies of different mass will hit the ground at the same time if dropped from the same height.
3. The uneven surface of the Moon: He observed that the surface of the Moon is uneven and rough.
4. Discovery of the 4 Moons of Jupiter
The gravitational force <em>F</em> between two masses <em>M</em> and <em>m</em> a distance <em>r</em> apart is
<em>F</em> = <em>G M m</em> / <em>r</em> ²
Decrease the distance by a factor of 7 by replacing <em>r</em> with <em>r</em> / 7, and decrease both masses by a factor of 8 by replacing <em>M</em> and <em>m</em> with <em>M</em> / 8 and <em>m</em> / 8, respectively. Then the new force <em>F*</em> is
<em>F*</em> = <em>G </em>(<em>M</em> / 8) (<em>m</em> / 8) / (<em>r</em> / 7)²
<em>F*</em> = (1/64 × <em>G M m</em>) / (1/49 × <em>r</em> ²)
<em>F*</em> = 49/64 × <em>G M m</em> / <em>r</em> ²
In other words, the new force is scaled down by a factor of 49/64 ≈ 0.7656, so the new force has magnitude approx. 76.56 N.
