Everything Science Grade 11

11.8 CHAPTER 11. VECTORS

Example 10: Block on an incline plane

QUESTION

Determine the force needed to keep a 10 kg block from sliding down africtionless slope. The

slope makes an angle of 30 ◦with the horizontal.

SOLUTION

Step 1 : Draw a diagram of thesituation

�

Fg�

30 ◦

Required Force

The force that will keepthe block from sliding isequal to the parallel com-

ponent of the weight, but its direction is up the slope.

Step 2 : Calculate Fg�

Fg� = mg sin θ

= (10)(9,8)(sin30◦)

= 49N

Step 3 : Write final answer

The force is 49 N up theslope.

Vector addition using components ESBEN

Components can also be used to find the resultant of vectors. This technique can be applied toboth
graphical and algebraicmethods of finding the resultant. The method issimple: make a rough sketch of
the problem, find the horizontal and vertical components of each vector,find the sum of all horizontal
components and the sumof all the vertical components and then use themto find the resultant.

Consider the two vectors,A� andB�, in Figure 11.3, together with their resultant,R�.