2. A 14.8-kg child sits in a 1.30-kg swing. You pull the swing back, lifting it 52.1 cm vertically, and then let go. Determine t

Answer:

a, 71.8° C, 51° C

b, 191.8° C

Explanation:

Given the data:

D(i) = 200 mm

D(o) = 400 mm

q' = 24000 W/m³

k(r) = 0.5 W/m.K

k(s) = 4 W/m.K

k(h) = 25 W/m².K

The heat generation formula can be articulated as follows:

q = πr²Lq'

q = π. 0.1². L. 24000

q = 754L W/m

Thermal conduction resistance, R(cond) = 0.0276/L

Thermal conduction resistance, R(conv) = 0.0318/L

Applying the energy balance equation,

Energy In = Energy Out

This equates to q, which is 754L

From the initial analysis, the temperature at the interface between the rod and sleeve is found to be 71.8° C

Additionally, the outer surface temperature records as 51° C

Furthermore, based on the second analysis, the calculated temperature at the center of the rod is determined to be 191.8° C

Explanation:

The formula for force is mass multiplied by acceleration:

F = ma

Acceleration is defined as the change in velocity over the change in time:

F = m Δv / Δt

Since there is no rebound effect, Δv is equal to v.

F = m v / Δt

Mass can be calculated as density multiplied by volume:

F = ρ V v / Δt

Flow rate describes the volume per time:

F = ρ Q v

Flow rate is determined by velocity multiplied by the cross-sectional area:

F = ρ (v A) v

This simplifies to F = ρ A v²

The area of a circle is calculated as pi times the square of the radius, or as pi/4 times the diameter squared:

F = ρ (π/4 d²) v²

Hence, F = π/4 ρ d² v²