Question

Computer calculations: sledge sliding down ramp

A large sledge of mass 1000 kg slides down a frictionless ice ramp that has length ` and an angle of incline θ.

(a) Write expressions as functions of θ for

i. the acceleration a of the sledge while it is on the ramp

ii. the time t for the sled to reach the bottom of the ramp

iii. the final speed v of the sled at the bottom of the ramp

(b) Assuming the ramp length is ` = 100 m, calculate and plot a, v, and t for values of θ from 0^◦ to 90^◦ in 1^◦ steps.

(c) Check: are the results consistent with your previous experience with θ = 0^◦ and θ = 90^◦? Explain.

Answer 1

a] Since the ramp is frictionless, the net force on the sledge is,

=> i]

ii] Let L be the length of the ramp and let the initial velocity of the sledge be u = 0 m/s

so, L = ut + (1/2)at²

=>

=>

iii) v = u + at

=>

b] Below is the script for MATLAB:

theta = [0:1:pi/2] ;

L = 100;

a = 9.8sin(theta) ;

t = sqrt{L/(4.9sin(theta))} ;

v = sqrt{19.6 Lsin(theta) } ;

c) Check for the case where theta = 0^o (horizontal case; v = u) and 90^o (free-fall; a = g).