How do you use vectors to solve questions of force?

Question

For example, if I was to have a truck weighing 6578 pounds on a driveway inclined at 17.5 degrees, what's the magnitude of the force required to keep the truck still?

I do know that the force of gravity on the truck is 6578sin(17.5), but I have no idea on how to find the force required to counteract the gravity.

Answer 1

a) draw a picture of the incline, and the truck on the incline

b) the weight of the truck is a vector straight DOWN to the ground, right? the is 6578 pounds.

c) This weight vector has two components, and the answer you want is one of those two components!

We break down the weight vector as: a vector NORMAL to the incline, and a vector PARALLEL to the incline.

It is this parallel vector you are looking for.

d) go back to the picture you drew in a) and the vector in b), and what you want is the weight vector to be the RESULTANT/ hypotenuse, of the vectors in c), ie, the vectors normal and parallel to the incline are the arms of the triangle, and the weight vector is the hypotenuse.

You will then see that sin (17.5) = Force paralle to incline/ weight vector

or force to keep it from rolling down the incline = sin (17.5) * 6578.

Good luck!

Answer 2

The weight of the lorry gives a downhill force of
F = 6578 x g x sin 17.5°
F = 6578 x 32 x sin 17.5 poundals
F = 63297 poundals
Require 63297 poundals acting uphill to keep truck still

Answer 3

The force needed to counteract is simply an equal force in the opposite direction.