Use the law of universal gravitation, which says the force of gravitation between two bodies of mass <em>m</em>₁ and <em>m</em>₂ a distance <em>r</em> apart is
<em>F</em> = <em>G m</em>₁ <em>m</em>₂ / <em>r</em>²
where <em>G</em> = 6.67 x 10⁻¹¹ N m²/kg².
The Earth has a radius of about 6371 km = 6.371 x 10⁶ m (large enough for a pineapple on the surface of the earth to have an effective distance from the center of the Earth to be equal to this radius), and a mass of about 5.97 x 10²⁴ kg, so the force of gravitation between the pineapple and the Earth is
<em>F</em> = (6.67 x 10⁻¹¹ N m²/kg²) (1 kg) (5.97 x 10²⁴ kg) / (6.371 x 10⁶ m)²
<em>F</em> ≈ 9.81 N
Notice that this is roughly equal to the weight of the pineapple on Earth, (1 kg)<em>g</em>, where <em>g</em> = 9.80 m/s² is the magnitude of the acceleration due to gravity, so that [force of gravity] = [weight] on any given planet.
This means that on this new planet with twice the radius of Earth, the pineapple would have a weight of
<em>F</em> = <em>G m</em>₁ <em>m</em>₂ / (2<em>r</em>)² = 1/4 <em>G m</em>₁ <em>m</em>₂ / <em>r</em>²
i.e. 1/4 of the weight on Earth, which would be about 2.45 N.
Here is the energy that is left after the quantity of energy is transformed: 750 j of electrical energy is changed into 400 j of kinetic or mechanical energy, which is then turned into 0.32 j of efficient energy.
To run the fan, electrical energy is utilized.
Here, under the specified circumstances, 750 J of electrical energy is utilized to operate the fan, which is transformed into 400 J of kinetic energy. As a result, 350 J of energy is wasted due to various frictional and resistive losses.
Therefore, we may conclude that only 400 J of the 750 J available energy is used to power the fan, with the remaining energy being wasted as a result of friction.
Additionally, we can state that this fan's effectiveness will be
n = Useful ÷ Total
n = 400 ÷ 750
n = 8 ÷ 25
n = 0.32
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Answer:
<em>His angular velocity will increase.</em>
Explanation:
According to the conservation of rotational momentum, the initial angular momentum of a system must be equal to the final angular momentum of the system.
The angular momentum of a system = 
'ω'
where
' is the initial rotational inertia
ω' is the initial angular velocity
the rotational inertia = 
where m is the mass of the system
and r' is the initial radius of rotation
Note that the professor does not change his position about the axis of rotation, so we are working relative to the dumbbells.
we can see that with the mass of the dumbbells remaining constant, if we reduce the radius of rotation of the dumbbells to r, the rotational inertia will reduce to .
From
'ω' = ω
since is now reduced, ω will be greater than ω'
therefore, the angular velocity increases.
Answer: 12 N to the right
Explanation:
If we calculate the net force acting on the box, we will have:
<u>In y-component:</u>
(1)
Where 
is the Normal force, directed upwards and 
is the weight of the box (gravity force), directed downwards.
(2)
(3) Hence the net force in the vertical component is zero
<u>In x-component:</u>
(4)
Where 
and 
(5)
(6) This is the net force in the horizontal component
Therefore, the total net force acting on the box is 12 N directed to the right
Answer:
Towards the west
Explanation:
Magnetic force is the interaction between a moving charged particle and a magnetic field.
Magnetic force is given as
F = q (V × B)
Where F is the magnetic force
q is the charge
V is the velocity
B is the magnetic field
V×B means the cross product of the velocity and the magnetic field
NOTE:
i×i=j×j×k×k=0
i×j=k. j×i=-k
j×k=i. k×j=-i
k×i=j. i×k=-j
So, if the electron is moving southward, then, it implies that the velocity of it motion is southward, so the electron is in the positive z-direction
Also, the electron is curved upward due to the magnetic field, this implies that the force field is directed up in the positive y direction.
Then,
V = V•k
F = F•j
Then, apply the theorem
F •j = q ( V•k × B•x)
Let x be the unknown
From vector k×i =j.
This shows that x = i
Then, the magnetic field point in the direction of positive x axis, which is towards the west
You can as well use the Fleming right hand rule
The thumb represent force
The index finger represent velocity
The middle finger represent field
