Question

340-lb carriage has an initial velocity of 6.3 ft/sec down the incline at A, when a constant force of 120 lb is applied to the hoisting cable as shown. Calculate the velocity of the carriage when it reaches B. Show that in the absence of friction this velocity is independent of whether the initial velocity of the carriage at A was up or down the incline.

Answer 1

By force Balance,

2T - mgsin20 = ma

T = 120*32.17 = 3860.4

a = (2*3869.4 - 340*32.17*sin20)/340

a = (7738.8-3740.72)/340 = 11.75 lbf/s²

^Using

V² = U² + 2aS = 6.3² + 2*20*11.75 = 509.69

V = $\sqrt{509.69}$ = 22.57 ft/s

Now,

Velocity of B is indipendent of direction as kinetic energy is independent of direction of velocity. So, By conservation of energy change in kinetic energy still the same and will give same result.