Question

PLEASE explain why and show work so I can try to follow and understand!! Thank you!!

Answer 1

a)

Ep = m×g×h

∆Ep = m×g×h₂ - m×g×h₁
∆Ep = m×g × (h₂ - h₁)

-> from 15 cm to 25 cm
∆Ep = 0.5×9.8 × (0.25 - 0.15) = 0.49 J

-> from 25 cm to 35 cm
∆Ep = 0.5×9.8 × (0.35 - 0.25) = 0.49 J

=> same amount of additional energy in both cases

b)
Ek = m×v²/2

∆Ek = m×v₂²/2 - m×v₁²/2
∆Ek = (v₂² - v₁²) × m/2

-> from 15 m/s to 25 m/s
∆Ek = (25² - 15²) × 1000/2 = 200000 J

-> from 25 m/s to 35 m/s
∆Ek = (35² - 25²) × 1000/2 = 300000 J

=> the second case needs more additional energy

c)
Ep = k×x²/2

∆Ep = m×x₂²/2 - m×x₁²/2
∆Ep = (x₂² - x₁²) × m/2

-> from 15 cm to 25 cm
∆Ep = (0.25² - 0.15²) × 10/2 = 0.2000 J

-> from 25 cm to 35 cm
∆Ep = (0.35² - 0.25²) × 10/2 = 0.3000 J

=> the second case needs more additional energy