Answer:
Correct answer: m = 1,160 kg
Step-by-step explanation:
Given:
P = 104 hp = 77.48 kW = 77.48 · 10³ W
V₁ = 21 m/s Initial speed (velocity)
V₂ = 29 m/s Final speed (velocity)
t = 3 seconds The time interval during which the work was performed
m = ?
The formula for calculating power is:
P = A / Δt
Since work is a measure of energy change in this case kinetic:
P = ΔEk / Δt = (Ek₂ - Ek₁) / Δt = (m V₂²/ 2 - m V₁²/ 2) / Δt
P = m · (V₂² - V₁²) / 2 · Δt ⇒ m = (2 · P · Δt) / (V₂² - V₁²)
m = (2 · 77.48 · 10³ · 3) / (29² - 21²) = 464.88 · 10³ / (841 - 441)
m = 464.88 · 10³ / 400 = 1.16 · 10³ = 1,160 kg
m = 1,160 kg
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