When you put something on a slanted surface, like a ramp, two main forces are working on it: gravity and friction.

1. Gravity:

   • Gravity pulls things straight down.
   • We can look at gravity in two ways:
     • Perpendicular component: This is a part of gravity that pushes sideways against the ramp. It’s calculated using the formula ( mg \cos(\theta) ). Here, ( m ) is how heavy the object is, ( g ) is how fast things fall (which is about ( 9.81 , \text{m/s}^2 )), and ( \theta ) is the angle of the ramp.
     • Parallel component: This is the part of gravity that pulls the object down the ramp. It’s calculated with the formula ( mg \sin(\theta) ).

2. Friction:

   • Friction tries to stop the object from moving. The force of friction (( F_f )) can be figured out using this formula: $F_f = \mu F_n$ Here, ( \mu ) is a number that tells us how sticky the surfaces are (friction) and ( F_n ) is how hard the object is pressed against the ramp. On a ramp, this is equal to ( mg \cos(\theta) ).
   • So, we can write ( F_f = \mu mg \cos(\theta) ).

To find the total force acting on the object, we can use: $F_{net} = mg \sin(\theta) - F_f$

This helps us understand if the object will roll down the ramp or stay still. It all depends on how these two forces balance each other out.