Question
Show the calculations and a clearly labelled diagram to determine what will happen to each of the droplets described in questions 5-7 (accel up, down or freeze mid-air). 5. A 1.88times 10^-16 g droplet has gained 45 electrons and is released in a 375N/C[D] electric field. 6. A 2.525times 10^-15 xg droplet has lost 216 electrons and is released in a 715.3N/C[U] electric field. 7. A 7.13times 10^-15 g droplet has lost 173 electrons and is released in an electric field that has a strength of 1686N/C [U].
Solution
4
(303 Votes)
Milo
Professional · Tutor for 6 years
Answer
Here's the breakdown for each droplet, including calculations and diagrams:**Understanding the Concepts*** **Forces at Play:** The droplet experiences two main forces: gravity (downwards) and the electric force (upwards or downwards depending on the field direction and charge).* **Equilibrium:** If the forces are balanced, the droplet will "freeze" mid-air. If gravity is stronger, it will accelerate downwards. If the electric force is stronger, it will accelerate upwards.* **Electric Force:** The electric force (FE) on a charged object in an electric field is given by FE = qE, where q is the charge and E is the electric field strength.* **Gravitational Force:** The gravitational force (Fg) is given by Fg = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s²).* **Electron Charge:** The elementary charge (e) is approximately 1.6 x 10-19 C.**5. Droplet 1*** **Mass (m):** 1.88 x 10-19 kg (converted from grams)* **Charge (q):** 45 * -1.6 x 10-19 C = -7.2 x 10-18 C (negative since it gained electrons)* **Electric Field (E):** 375 N/C [Down]* **Fg:** (1.88 x 10-19 kg) * (9.8 m/s²) = 1.84 x 10-18 N [Down]* **FE:** (-7.2 x 10-18 C) * (375 N/C) = -2.7 x 10-15 N The negative sign indicates the force is upwards (opposite to the field direction since the charge is negative).**Diagram 1:**``` ↑ FE o (Droplet) ↓ Fg E ↓```**Result:** Since FE > Fg, the droplet will accelerate **upwards**.**6. Droplet 2*** **Mass (m):** 2.525 x 10-18 kg* **Charge (q):** 216 * 1.6 x 10-19 C = 3.456 x 10-17 C (positive since it lost electrons)* **Electric Field (E):** 715.3 N/C [Up]* **Fg:** (2.525 x 10-18 kg) * (9.8 m/s²) = 2.47 x 10-17 N [Down]* **FE:** (3.456 x 10-17 C) * (715.3 N/C) = 2.47 x 10-14 N [Up] (Force is in the same direction as the field since the charge is positive)**Diagram 2:**``` ↑ E ↑ FE o (Droplet) ↓ Fg```**Result:** Since FE > Fg, the droplet will accelerate **upwards**.**7. Droplet 3*** **Mass (m):** 7.13 x 10-18 kg* **Charge (q):** 173 * 1.6 x 10-19 C = 2.768 x 10-17 C (positive since it lost electrons)* **Electric Field (E):** 1686 N/C [Up]* **Fg:** (7.13 x 10-18 kg) * (9.8 m/s²) = 7.0 x 10-17 N [Down]* **FE:** (2.768 x 10-17 C) * (1686 N/C) = 4.67 x 10-14 N [Up]**Diagram 3:**``` ↑ E ↑ FE o (Droplet) ↓ Fg```**Result:** Since FE > Fg, the droplet will accelerate **upwards**.