Sm2 16thru2 17

Master Typing Sheet 8.5” x 11” 1/8 in size PROBLEM 2.16 KNOWN: Beginning from rest, and object of known mass slides down an inclined plane. The length of the ramp is given. FIND: Determine the velocity of the object at the bottom of the ramp. SCHEMATIC & GIVEN DATA: z_i m = 200 kg g = 9.81 m/s2 V_i = 0 z_f 10 m 40° V_2 ENGR MODEL: (1) The mass is a closed system. (2) There is no friction between the mass and the ramp, and air resistance is negligible. (3) The acceleration of gravity is constant. ANALYSIS: By assumption (2), the only force acting on the system is the force of gravity. Thus, Eq. 2.11 applies 1/2 m(V_f^2 - V_i^2) + mg(z_f - z_i) = 0 solving for V_f V_2 = √(2g(z_f - z_i)) From trigonometric relationships z_f - z_i = (10 m) sin 40° Thus V_2 = √[2(9.81 m/s^2)(10 m) sin 40°] = 11.23 m/s V_2 1. Even though the object travels along an inclined path, the vertical distance appears in this expression. PROBLEM 2.17 Fig. P2.17 Exercise Value = 620 kcal Caloric Value, 1 cup of vanilla ice cream = 264 kcal (Internet) To break even calorie-wise, Jack may have 620 kcal / 264 kcal/cup = 2.35 cups