Questions
1- Three toy cars weighing 55g, 45g, and 35g, are set on top of a ramp 4m high. the ramp is inclined at 50 degrees to the leveled ground. After each car reaches the bottom of the ramp, they will then travel 2m horizontally to a finish line. Which car, Car A (55g), Car B (45g), or Car C (35g), will cross the finish the line the quickest?
2- Solve for an expression, in variable form, for the horizontal sideways displacement d of a light ray passing through a sliver of glass, as shown in the diagram below. The thickness of the glass is h, its index of refraction is n, and the angle of incidence is θ
3- F1 = 153 lb @ 25° CCW from +x, applied at [ 21, 32 ] ft F2 = 146 lb @ 14° CV from-y, applied at [ 60, 87 ] ft Point A: [-9, 3 ]ft
A.) What is F2 in component vector form?
B.) What is the torque from F2 about point A
C.) What is the net torque of F1+F2about point A? (+CCW)
(include units with answer)
4 A surface ski lift is installed in a ski resort to pull skiers up a slope. The slope has an almost constant inclination of α = 10°, a length L = 1,030 m and the friction coefficient between the snow and the skis is μ = 0.04. when lifting a skier, the bar connecting the skier to the aerial steel rope remains inclined by β = 25° with respect to the normal to the slope and is subject to a time-varying tension T. For this exercise consider a skier of mass m 80 kg Aerial rope Bar Skier Slope α= 10° Surface ski lift schematics (not to scale)
i. Draw the free body diagram of the skier during the lifting and draw your selected coordinate system
ii. Obtain the equation of motion of the skier as a function of the only unknowns x (and/or its derivatives) and T (i.e. express all other quantities numerically) 1. 2. 3.
iii. Given that the skier position x(t) at time t is x(t) = Lsin(pi/2 t/ t end).
obtain the analytical expression of the tension in time and compute its maximum value Note that the total time that is taken to lift the skier along the slope from x = 0 to x = L is tend = 214 s and that the coordinate x is here intended parallel to the slope and directed in the same direction of motion of the skier.