A 25.0-kg box of textbooks rests on a loading ramp that makes an angle α with the horizontal. The coefficient of kinetic friction is 0.25, and the coefficient of static friction is 0.35. (a) As α is increased, find the minimum angle at which the box starts to slip. (b) At this angle, find the acceleration once the box has begun to move. (c) At this angle, how fast will the box be moving after it has slid 5.0 m along the loading ramp?

Explanation:

a ) When the box starts to slip

static friction = mg sinα

mg cosα x μ =  mg sinα (  μ is coefficient of static friction )

Tanα =  μ  = .35

α  = 19.2°

b ) Once box starts moving , kinetic friction will start applying on it

kinetic friction = mg cos19.2 x .25

= 2.31m

net force downward = mgsin19.2 - mgcos19.2 x .25

= m ( 3.22 - 2.31 )

= .91 m

acceleration downward ( a )   = .91 m / s²

c )

v² = u² + 2 a s

= 0 + 2 x .91 x 5

= 9.1

v = 3 m / s

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

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