Julia asked in Science & MathematicsPhysics · 3 months ago

A crate is given an initial speed of 5.0 m/s up the 22.5 ∘ plane shown in (Figure 1). Assume μk = 0.12.?

How much time elapses before it returns to its starting point? (in seconds)

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  • Whome
    Lv 7
    3 months ago
    Favorite Answer

    Let's say the crate has a mass m

    Upslope is the positive direction 

    g = -9.81 m/s

    θ = 22.5° from horizontal

    Going up-slope

    F = ma

    mgsinθ + μmgcosθ = ma

    a = g(sinθ + μcosθ)

    a = -9.81(sin22.5 + 0.12cos22.5)

    a = -4.8417 m/s²

    v² = u² + 2as

    s = (v² - u²) / 2a 

    Going upslope, v = 0 and u = 5.0 m/s

    s = - 5.0² / 2(-4.8417 m/s²)

    The mass travels up-slope a distance of

    s = 2.5817 m

    s = ½at²

    t₁ = √(2s/a)

    t₁ = √(2(2.5817) / 4.8417

    t₁ = 1.033  s

    Using the same logic going downslope

    a = -9.81(sin22.5 - 0.12cos22.5) 

    a = - 0.2718 m/s²

    t₂ = √(2(2.5817) / 0.2718 

    t₂ = 4.358 s

    total time is t₁ + t₂

    t = 1.033 + 4.358

    t = 5.391... ≈ 5.4 s

  • 3 months ago

    shown in (Figure 1) ???

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