Question

(b) Fig. 4.2 shows another elephant pushing horizontally against a vehicle with a force of 11 kN at a distance 1.8 m above the ground. Point M is the centre of mass of the vehicle.
(i) Calculate the moment about point A of the force exerted by the elephant.
ii) The mass of the vehicle is 1900 kg, and it does not slide when pushed by the elephant. Determine whether the elephant tips the vehicle over. Show your working.

Answer 1

Answer:

The moment about point $A$ is  $19.8$ $kN.m$. The vehicle will not be tipped by the elephant.

Explanation:

• The measure of the tendency to make the body rotate about a certain point or axis is called the moment of force.
• If the moment due to weight of the body is more than moment due to applied force the body will not tip.

The formula for the moment of force is:

$M=r*F$

where, $r$ is the perpendicular distance of force from the point.

           $F$ is the force magnitude.

Step 1:

(i)  Moment about point $A$, $M_{f}$  $=(1.8 m)*(11 kN)$

                                                  $= 19.8$  $kN.m$

So, about point $A$  force moment is  $19.8$ $kN.m$

Step 2:

(ii)  The moment due to vehicle weight about point A  is:

$M_{w} =(1.25 m)*(1900*9.8 N)$  

$M_{w} =23275$  $N.m$

$M_{w} =23.275$  $kN.m$

We see that about point A moment due to vehicle weight is greater than the moment due to elephant's force.

$M_{w} > M_{f}$

So, the vehicle will not be tipped by the elephant.