I'm assuming we're applying the standard Integral form of the calculation of work. The solution is provided in the image.
A force of 43.8 N is required to stretch the spring a distance of 15.5 cm = 0.155 m, so the spring constant <em>k</em> is
43.8 N = <em>k</em> (0.155 m) ==> <em>k</em> = (43.8 N) / (0.155 m) ≈ 283 N/m
The total work done on the spring to stretch it to 15.5 cm from equilibrium is
1/2 (283 N/m) (0.155 m)² ≈ 3.39 J
The total work needed to stretch the spring to 15.5 cm + 10.4 cm = 25.9 cm = 0.259 m from equilibrium would be
1/2 (283 N/m) (0.259 m)² ≈ 9.48 J
Then the additional work needed to stretch the spring 10.4 cm further is the difference, about 6.08 J.
Let V = the volume of the balloon
Force of gravity = V * ?hot * g downward
Buoyant force = V * ?cool * g upward
Net upward force F = V * ?cool * g - V * ?hot * g
F = V g (?cool - ?hot)
Mass of the balloon m = V ?hot
a = F/m = V g (?cool - ?hot)/(V ?hot)
a = g(?cool/?hot - 1)
a = 9.8(1.29/0.93 - 1)
a = 3.79 m/s^2
<span>Answer is 3.79 m/s^2</span>
In order to calculate the gravitational force of the two bodies we use the formula which is expressed as:
F = GMm/R²
where <span>G = 6.67 x 10^-11 in SI unit, M and m are the mass of the two bodies and R is the distance between them.
F = </span>6.67 x 10^-11 (1.99×10^30) (6×10^24) / (1.50×10^11)²
F = 3.53×10^22<span>N</span>
I would choose the vinegar before baking soda because the baking soda is what is making the chemical reaction with the vinegar. Both need eachother but the vinegar is a less powerful reactant than the baking soda.
