Two frisky grasshoppers collide in midair at the top of their respective trajectories and grab onto each other, holding tight thereafter. On

Question

Two frisky grasshoppers collide in midair at the top of their respective trajectories and grab onto each other, holding tight thereafter. One is a robust 250 g beast initially moving south at 15.0 cm/s, while the other is a svelte 130 g creature initially moving north at 65.0 cm/s.

Calculate the decrease in kinetic energy that results from the collision in J

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Diễm Kiều 4 years 2021-07-25T18:27:11+00:00 1 Answers 42 views 0

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  1. Gerda
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    2021-07-25T18:28:36+00:00
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    Answer:

    The decrease in Kinetic energy is 0.0107 Joules

    Explanation:

    Given

    Mass of grasshoppers

    Let m1 = Mass of grasshopper 1

    Let m2 = Mass of grasshopper 2

    Let u1 = initial speed of grasshopper 1

    Let u2 = initial speed of grasshopper 2

    m1 = 250g = 0.25kg

    m2 = 130g = 0.13kg

    u1 = 15cm/s = 0.15m/s

    u2 = 65cm/s = 0.65m/s

    First, we calculate the final velocity of the grasshoppers after collision using conservation of momentum.

    Using

    m1u1 + m2u2 = (m1 + m2) * v

    Where v = final velocity

    By substituton

    0.25 * 0.15 + 0.13 * 0.65 = (0.25 + 0.13) * v

    0.0375 + 0.0845 = 380v

    0.122 = 0.38v

    Make v the subject of formula

    v = 0.122/0.38

    v = 0.321 m/s

    Calculating the Kinetic energies before and after impact.

    Before collision;

    KE = ½m1u1²+ ½m2u2²

    KE = ½(m1u1² + m2u2²)

    By substituton;

    KE = ½(0.25 * 0.15² + 0.13 * 0.65²)

    KE = 0.030275J

    After collision:

    KE = ½(m1+m2)v²

    KE = ½(0.25 + 0.13) * 0.321²

    KE = 0.01957779 J

    Change in kinetic energy = ∆KE

    ∆KE = 0.030275J – 0.01957779J

    ∆KE = 0.01069721J

    ∆KE = 0.0107 J — Approximately

    Hence the decrease in Kinetic energy is 0.0107 Joules

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