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16 March, 05:07

If the motor exerts a force of F = (600 + 2s2) N on the cable, determine the speed of the 100-kg crate when it rises to s = 15 m. The crate is initially at rest on the ground.

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  1. 16 March, 06:03
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    The motor that exerts force is F = 600+2s²

    Mass of crate is m = 100kg

    Distance raises is s = 15m

    Crate at rest is V₁ = 0

    We will solve this using principle of energy and work because involves displacement, velocity, and force

    Work energy is

    T₁ + ΣU₁₋₂ = T₂

    Whereby T₁ = initial Kinetic energy

    = 1/2mw₁² = 1/2m (o) ₁² = 0 Because initial is at rest.

    Motor exerts the force on the cable forces acting in the cable at C are two times motor exerts force cable M work done by the exerted motor is

    U₁₋₂ = 2∫s²Fds

    U₁₋₂ = 2∫s² (600+2S²) ds

    =2 (600*s + 2s³/3) ¹⁵

    = 2 (600 * 15 + 2 * 15³/3)

    =22500N

    Work done by crate is the crates' weight acts downward to take the negative sign

    U₁₋₂ = - (m * g * s)

    U₁₋₂ = - (100 * 9.81 * 15)

    = - 14715N

    T₂ = Final kinetic energy = 1/2mw²₂

    T₁ + ∑U₁₋₂ = T₂

    0 + (22500 + (-14715)) = 1/2 (100) V²₂

    V₂ = 12.47m/s
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