Question

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

14 mgsing geos ci acceleration is masinga gginia I a=gsino (ii) using lahat² stape TV Gilj using v²u²_zas v=Jag sinol = Tage Tsina (b) la loom. , Q= 9.81 sing 9.81+ - o't- 4 Todos T= √2x100 Jaho - 452 sec 2xis 61 J fino Isina 4.52sec - 4.52sect 8 /

CW) ve Jäge Jaingo = 32x9.8 xlvojsino V= 44.27 jsino mlec 44-27 dec --- ce) for 8=0°, azo, so it will talce Tyas to reach bottom and u= atzo are consistent Гuj+, 9тар. for o=90, It is like the free fall under gravity, aag, and T= 24 = 4.52 sec and v= Jagn. = 44.27. m / see consistent. are

Answer 2

S&efn N a Ne my cass fule sind d F: ma-mgsin 0 sing ij S=2 time Ruach bottomh e SE ut +Lat sine sing 1 V 9-12 O=M12 (t40) (a 40 10p1) (V&o) For 0=0, a-0 V=O t = 00= sino o V-VAge t = for O=90° Sin goz