The snowmobile has a weight of 240 lb centered at G1 while t

The snowmobile has a weight of 240 lb, centered at G_1, while the rider has a weight of 180 lb, centered at G_2. If h = 4ft, determine the snowmobile\'s maximum permissible acceleration a so that its front skid does not lift off the ground. (Figure 1) Part B Find the traction (horizontal) force under the rear track at A. Part C Find the normal reaction under the rear track at A.

Solution

m₁G₁ = m₂G₂

Given m₁ = 240 lb

m₂ = 180 lb

G₁ = 1 ft

G₂ = 4ft

the acceleration of the system (a) is given by

a = [(m₂ - m₁) / (m₂ + m₁)]g

a = -4.60 ft/sec²  

also acceleration at the centre of mass is given by a_c

a_c = (m₁ a₁ + m₂ a₂) / (m₁ + m₂ )

a_c = [240(a) + 180(-a)] / [240+180]

a_c = -0.66 ft/sec²

The tractive effort or force between a BIKE wheel and the surface can be expressed as

F = _t W

   = _t m a_g   (1)

where

F = traction effort or force acting on the wheel from the surface (N, lb_f)

_t = adhesion coefficient between the wheel and the surface

W = weight or vertical force between wheel and surface (N, lb_f))

m = mass on the wheel (kg, slugs)

a_g = acceleration of gravity (9.81 m/s², 32.17405 ft/s²)

For wet ice _t = 0.1