Question

9.) The 17 kg shopping cart carries a 73 kg child. The shopping cart wheel base b = 480 mm and its vertical CG is symmetrically located 580 mm above the floor surface. The child remains centered symmetrically between the cart wheels with her vertical CG located 750 mm above the floor surface. Determine (a) location above the floor of the vertical CG of the cart + child in mm and (b) the tipping angle in degrees.

Answer 1

Given,

mass of the shopping cart, m = 17 kg

mass of the the child, M = 73 kg

Wheel base, b = 480 mm

Vertical CG of cart above the floor surface, y₁ = 580 mm

Vertical CG of the child above the floor surface, y₂ = 750 mm

a)

Location of CG of cart + child, Y = ( my₁ + My₂) / ( m + M)

                                                     = ( 17*580 + 73*750) / ( 17 + 73)

                                                      = ( 9860 + 54750) / 90

                                                      = 64610 / 90 = 717.89 mm

thus, location of CG of cart + child is 717.89 mm above floor surface.

b)

As it is given, CG is symmetrically located above the the cart

Hence, track width, t = wheel base

=> t = 480 mm

Now,

we have height of center of gravity above the floor, Y = 717.83 mm

Let tipping angle be _c

tipping angle, _c = tan^-1((t/2)/Y)

                            = tan^-1( (480/2) / 717.83)

                            = tan^-1(240 / 717.83) = tan^-1(0.3343)

                            = 18.485

or tipping angle is 18.485