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(II) A large crate of mass 1500 kg starts sliding from rest along a frictionless ramp, whose length is ℓ and whose inclination with the horizontal is θ. (a) Determine as a function of θ: (i) the acceleration a of the crate as it goes downhill, (ii) the time t to reach the bottom of the incline, (iii) the final velocity v of the crate when it reaches the bottom of the ramp, and (iv) the normal force FN on the crate. (b) Now assume ℓ = 100 m. Use a spreadsheet to calculate and graph a, t, v, and FN as functions of θ from θ = 0° to 90° in 1° steps. Are your results consistent with the known result for the limiting cases θ = 0° and θ = 90°?
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