Question

13. We all know that the different well known effects of forces 4 come into play as a result of

the mutual interaction of two entities. The manifold effects of forces include a change in the speed of

the objects on which the force acts. It turns out that the energy associated with a moving object,

goes up by a factor of four, when its speed doubles, it goes up by a factor of nine when the speed

goes up by a factor of three and when it goes up by a factor of sixteen the speed goes up by a factor

of four.A force, acting on a surface also exerts a pressure on it and this pressure is dependent on

the area over which the force acts perpendicularly also there is one special kind of force which, in

general always tends to slow down a moving object.

4

(a) What do you mean by pressure?

(b) By what factor will the energy of a moving object go up if its speed increases by a factor of 6?

(c) A given force ‘F’ is acting parallel to a long plane surface of area ‘A’. ​

Answer 1

Answer:

Note that the first and last terms are perfect cubes and find:

27

x

3

+

54

x

2

+

36

x

+

8

=

(

3

x

+

2

)

3

Explanation:

Notice that the ratio between the first and second coefficients is not the same as that between the third and fourth.

That is:

27

54

≠

36

8

So this does not factor by grouping.

Note that the first and last terms are both perfect cubes:

27

x

3

=

(

3

x

)

3

8

=

2

3

So we might try

(

3

x

+

2

)

3

:

(

3

x

+

2

)

3

=

27

x

3

+

54

x

2

+

36

x

+

8

Yes - that's our factoring.