a large crate of mass 1500 kg starts sliding from rest along a frictionless ramp

Question

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 . (a) Determine as a function of :(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=100m. Use a spreadsheet to calculate and graph a,t,v and Fn as function of =0° to 90° in 1° steps. Are your results consistent withe the know result for the limiting cases =0° and =90°

Explanation / Answer

a)

acceleration along the incline = g * sin(theta)

ii)

Using seocond equation of motion

d = u*t + 0.5 at^2

L = 0.5 * g *sin(theta) * t^2

t = sqrt(2*L/(g * sin(theta)))

iii)

using first equation of motion

v = a * t

v = g * sin(theta) * sqrt(2*L/(g * sin(theta)))

v = sqrt(2*L * g * sin(theta))

iv)

Normal force , FN = mg * cos(theta)

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