Question

The bending of a bean varies directly as its mas. A beam is bent 20mm by a mass 0f 40kg. how much will the beam bend with a mass of 100kg?

Answer 1

50mm with the mass of 100kg

Answer 2

The beam will bend by 50 mm with a mass of 100kg?

Explanation:

The first step in solving the problem of direct variation is setting up the relation mathematically.

We can do this as follows:

The bending of the beam varies directly as its mass.

`20 \alpha 40kg`

`\alpha` here is the symbol representing direct variation. To remove this and replace it with an equality sign, we have to introduce a constant of proportionality, k

`20 = k * 40`

k = 20 /40 = 0.5

We can now use this to find the distance the beam will bend with a mass of 100kg?

This will be

`Bending = 0.5 * 100 =50mm`

There fore, the beam will bend by 50 mm with a mass of 100kg?