If you accidentally touch the "hot" wire connected to the 120 V line, how much current will pass through your body?

Stopping distance.

(6-16)/4.0=-2.5 m/s²
The car's acceleration is -2.5 m/s²

Part 1) Which metal will cool the fastest?
To determine this, we need to consider the heat flow rate formula, which indicates the speed at which a substance can gain or lose heat:

where:
denotes the heat exchanged
indicates the duration
k represents the thermal conductivity of the material
A is the area over which heat transfer takes place
shows the change in temperature
x is the thickness of the substance
It is evident that the heat flow rate is directly related to k, the thermal conductivity. Thus, a higher value of k means that the metal will cool more quickly.
Upon examining the thermal conductivity values for each metal, we observe:
- Aluminium: 237 W/(mK)
- Copper: 401 W/(mK)
- Gold: 314 W/(mK)
- Platinum: 69 W/(mK)
Consequently, copper has the highest heat flow rate, making it the metal that cools the fastest.

Part 2) Which sample of copper demonstrates the greatest increase in temperature
To address this part, we can examine how the heat exchanged Q correlates with temperature increase :

where m indicates the mass and Cs represents the specific heat capacity of the material. By rearranging the equation, we derive

As a result, it becomes clear that the temperature increase is inversely related to the mass m. Thus, the block exhibiting the highest temperature rise will be the one with the least mass, hence the right choice is A) 0.5 kg.

Answer:

  = 1,386 m / s

Explanation:

The mechanism behind rocket propulsion is defined by the formula

        - v₀ =   ln (M₀ / Mf)

Here, v refers to the initial, final, and relative velocities, while M indicates the masses

The provided values include the relative velocity (see = 2000 m / s) and the initial mass, where the mass of the rocket when loaded is represented as (M₀ = 5Mf)

For our analysis, we assume the rocket begins at rest (v₀ = 0)

Once half of the fuel has burnt, the mass ratio indicates that the current mass is    

       M = 2.5 Mf

        - 0 = 2000 ln (5Mf / 2.5 Mf) = 2000 ln 2

        = 1,386 m / s

Answer:

Part A) Electric fields at the designated point due to charges q₁ and q₂:

E₁ = 33.75 * 10³ N/C (-j), E₂ = (6.48 (-i) + 8.64 (+j)) * 10³ N/C

Part B) The overall electric field at P (Ep)

Ep = (6.48 * 10³ (-i) + 25.11 * 10³ (-j)) N/C

Explanation:

Conceptual analysis

The electric field at point P caused by a point charge is calculated as:

E = k*q/d²

E: Electric field measured in N/C

q: charge magnitude in Newtons (N)

k: electric constant measured in N*m²/C²

d: distance from the charge q to point P in meters (m)

Equivalence:

1 nC = 10⁻⁹ C

1 cm = 10⁻² m

Data:

k = 9 * 10⁹ N*m²/C²

q₁ = -6.00 nC = -6 * 10⁻⁹ C

q₂ = +3.00 nC = +3 * 10⁻⁹ C

d₁ = 4 cm = 4 * 10⁻² m

d₂ = 5 * 10⁻² m

Part A) Calculation for electric fields at point from q₁ and q₂:

Refer to the attached illustration:

E₁: Electric Field at point P(0,4) cm due to charge q₁. Since q₁ is negative (q₁-), the electric field approaches the charge.

E₂: Electric Field at point P(0,4) cm due to charge q₂. Since q₂ is positive (q₂+), the electric field emanates from the charge.

E₁ = k*q₁/d₁² = 9 * 10⁹ * 6 * 10⁻⁹ / (4 * 10⁻²)² = 33.75 * 10³ N/C

E₂ = k*q₂/d₂²= 9 * 10⁹ * 3 * 10⁻⁹ / (5 * 10⁻²)² = 10.8 * 10³ N/C

E₁ = 33.75 * 10³ N/C (-j)

E₂x = E₂cosβ = 10.8 * (3/5) = 6.48 * 10³ N/C

E₂y = E₂sinβ = 10.8 * (4/5) = 8.64 * 10³ N/C

E₂ = (6.48 (-i) + 8.64 (+j)) * 10³ N/C

Part B) Calculation for net electric field at P (Ep)

The electric field at point P from multiple point charges is the vector sum of the individual electric fields.

Ep = Epx (i) + Epy (j)

Epx = E₂x = 6.48 * 10³ N/C (-i)

Epy = E₁y + E₂y = (33.75 * 10³ (-j) + 8.64 * 10³ (+j)) N/C = 25.11 * 10³ (-j) N/C

Ep = (6.48 * 10³ (-i) + 25.11 * 10³ (-j)) N/C

Ep = (6.48 * 10³ (-i) + 25.11 * 10³ (-j)) N/C