## Metric Problems

The procedure for solving lever and problems involving forces can be illustrated with the following example. You are using the 3-point hitch on a tractor to lift a large bale of hay. You have recently "weighted" the bale on a metric scale and its

FIGURE 4.18. Illustration of bale problem.

mass is 840 kg. The lift arm is attached to the lower arm of the hitch 0.5 m from the pivot point and the length of the lower hitch arm is 0.95 m. How much force must be produced by the lift arms of the 3-point hitch to raise the bale?

The first step in determining the required amount of force to raise the bale is to convert its mass to weight.

The second step is to calculate the required force using the equation for a class three lever. The equation for a class three lever is written in terms of a force or weight of an object, Fr = W. This is an example where a serious error can occur because the actual length of the resultant arm is not the length of the lower hitch arm, but the distance from the pivot point to the center of the mass of the bale, Figure 4.18.

Assuming a 1.5 m bale and an additional distance of 25.0 cm from the end of the lower lift arm to the front edge of the bale, the length of the resultant arm is:

The lift arm force required is:

The 840 kg bale will require the lift arms on the 3-point hitch to produce 3.2 E4 N of force to lift the bale.

The same procedure can be used to solve any of the other problems in this chapter.