What is the correct order of a signal being transmitted across a neuromuscular junction?
2 answers:
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Answer:
a. The force of gravity on the droplet is approximately 4.606 × 10⁻¹⁴ Newtons
b. The electric force that balances the force of gravity is approximately -4.606 × 10⁻¹⁴ Newtons
c. The excess charge is approximately -1.439375 × 10⁻¹⁸ C
d. There are approximately 9 excess electrons on the droplet
Explanation:
The parameters of the Millikan experiment are;
The mass of the droplet, m = 4.7 × 10⁻¹⁵ kg
The electric field in which the droplet floats, E = 3.20 × 10⁴ N/C
a. The force of gravity on the droplet, F = The weight of the droplet, W = m × g
Where;
g = The acceleration due to gravity ≈ 9.8 m/s²
W = 4.7 × 10⁻¹⁵ kg × 9.8 m/s² = 4.606 × 10⁻¹⁴ Newtons
∴ The force of gravity on the droplet = W = 4.606 × 10⁻¹⁴ Newtons
b. The electric force that balances the force of gravity, = -W = -4.606 × 10⁻¹⁴ Newtons
c. The excess charge is given as follows;
= q·E
∴ The electric force that balances the force of gravity, = q·E = -4.606 × 10⁻¹⁴ N
q·E = -4.606 × 10⁻¹⁴ N
q = -4.606 × 10⁻¹⁴ N/E
∴ q = -4.606 × 10⁻¹⁴ N/(3.20 × 10⁴ N/C) ≈ -1.439375 × 10⁻¹⁸ C
The excess charge, q ≈ -1.439375 × 10⁻¹⁸ C
d. The charge of one electron, e = 1.602176634 × 10⁻¹⁹C
The number of excess electrons in the droplet, n, is given as follows;
n = 1.439375 × 10⁻¹⁸ C/(1.602176634 × 10⁻¹⁹C) = 8.98387212405 electrons
∴ n ≈ 9 electrons.
(a) See figure in attachment (please note that the image should be rotated by 90 degrees clockwise)
There are only two forces acting on the balloon, if we neglect air resistance:
- The weight of the balloon, labelled with W, whose magnitude is
where m is the mass of the balloon+the helium gas inside and g is the acceleration due to gravity, and whose direction is downward
- The Buoyant force, labelled with B, whose magnitude is
where is the air density, V is the volume of the balloon and g the acceleration due to gravity, and where the direction is upward
(b) 4159 N
The buoyant force is given by
where is the air density, V is the volume of the balloon and g the acceleration due to gravity.
In this case we have
is the air density
is the volume of the balloon
g = 9.8 m/s^2 is the acceleration due to gravity
So the buoyant force is
(c) 1524 N
The mass of the helium gas inside the balloon is
where is the helium density; so we the total mass of the balloon+helium gas inside is
So now we can find the weight of the balloon:
And so, the net force on the balloon is
(d) The balloon will rise
Explanation: we said that there are only two forces acting on the balloon: the buoyant force, upward, and the weight, downward. Since the magnitude of the buoyant force is larger than the magnitude of the weigth, this means that the net force on the balloon points upward, so according to Newton's second law, the balloon will have an acceleration pointing upward, so it will rise.
(e) 155 kg
The maximum additional mass that the balloon can support in equilibrium can be found by requiring that the buoyant force is equal to the new weight of the balloon:
where m' is the additional mass. Re-arranging the equation for m', we find
(f) The balloon and its load will accelerate upward.
If the mass of the load is less than the value calculated in the previous part (155 kg), the balloon will accelerate upward, because the buoyant force will still be larger than the weight of the balloon, so the net force will still be pointing upward.
(g) The decrease in air density as the altitude increases
As the balloon rises and goes higher, the density of the air in the atmosphere decreases. As a result, the buoyant force that pushes the balloon upward will decrease, according to the formula
So, at a certain altitude h, the buoyant force will be no longer greater than the weight of the balloon, therefore the net force will become zero and the balloon will no longer rise.
