Question

If the 4, 500 lb van has front wheel drive and the coefficient of static friction between the front wheels and the ground is mu = 0.8, determine the van's maximum acceleration and the normal force on the pairs of wheels at A and B. The rear wheels are free to roll. Neglect the mass of all wheels.

Answer 1

Forces on front wheel are, $N_A$ vertically upwards and frictional force $F_A$ in the forward direction

Forces on rear wheel are, $N_B$ vertically upwards and frictional force $F_B=0$

weight of van lies at G = and is vertically downwards

net vertical force is zero.

so $4500=N_A+N_B$ ------------(1)

The maximum acceleration occurs when front wheels are about to slip.

that is $F_A=\mu_s N_A$

$a_{max}=\frac{F_A}{m}=\frac{\mu_sN_A}{4500/32.2}$ -----------(2)

torques about center of gravity G ,

$N_B\times6=N_A\times3.5+F_A\times2.5$

$N_B\times6=N_A\times3.5+\mu_s N_A\times2.5$

$N_B\times6=N_A\times3.5+(0.8) N_A\times2.5$   ------(3)

using (1) and (3)

$N_B=2152\,lb$   and $N_A=2347.8\,lb$

substituting value of $N_A=2347.8\,lb$ in (2)

$a_{max}=\frac{(0.8)(2347.8)}{4500/32.2}=13.4\,ft/s^2$