1) Vf = Vo - gt; Setting Vf = 0 gives Vo = gt, resulting in Vo = 9.8 m/s^2 * 1.5 s = 14.7 m/s. 2) The displacement is calculated as d = Vo*t - gt^2 / 2 = 14.7 m/s * 1.5 - 9.8 m/s^2 * (1.5 s)^2 / 2 = 11.02 m.
When Sonia rubs the balloon with a wool cloth, electrons from the balloon move to the wool because of the friction. This process causes the balloon to become positively charged. Since both balloons are treated similarly, they acquire positive charges. It’s a known principle of physics that like charges repel one another, so the two balloons will push away from each other after being rubbed with the wool.
The total mechanical energy of the rider at any height amounts to 6.34 × 10⁴ J.
The rider's mechanical energy is computed as the total of gravitational potential energy and kinetic energy. Assuming no forces are lost (like friction), this mechanical energy remains constant at different heights, as potential energy lost translates into kinetic energy gained, in accordance with the conservation of energy principle.
Calculating both potential and kinetic energy at 55.0 m and 19 m/s allows us to derive the consistent mechanical energy:
Mechanical energy = PE + KE
Where:
PE = potential energy,
KE = kinetic energy.
The potential energy calculation goes as follows:
PE = m · g · h,
Where:
m is the mass,
g is the gravitational acceleration,
h represents the height.
The calculation of the rider's potential energy yields:
PE = 88.0 kg · 9.81 m/s² · 55.0 m = 4.75 × 10⁴ J.
The kinetic energy is derived from:
KE = 1/2 · m · v²,
Here "m" refers to the mass and "v" stands for velocity. Thus,
KE = 1/2 · 88.0 kg · (19.0 m/s)² = 1.59 × 10⁴ J.
Consequently, the rider's mechanical energy calculates as:
Mechanical energy = PE + KE = 4.75 × 10⁴ J + 1.59 × 10⁴ J = 6.34 × 10⁴ J.
This mechanical energy remains unchanged since when the rider descends, potential energy is converted into kinetic energy, keeping the total sum of these energies constant.
