A box is sliding on a rough patch of ice, and the only horizontal force acting on it is friction. You observe that it slides to a stop in 600 seconds over a distance of 23 meters. What magnitude coefficient of kinetic friction between the box and the ice?

The magnitude of the coefficient of kinetic friction is approximately 1.304 × 10⁻⁵

Explanation:

The given parameters are;

The time it takes for the box to stop, "t" = 600 seconds

The distance the box moves before coming to a stop, "d" = 23 meters

The work done by the friction force to stop the block = The kinetic energy lost by the box

The work done by the friction force to stop the block = ·m·g·d

The kinetic energy change of the block = 1/2·m·u²

Where;

g = The acceleration due to gravity = 9.8 m/s²

m = The mass of the box

= The coefficient of kinetic friction

d = The distance travelled by the block = 600 m

u = The initial velocity of the block

∴ ·m·g·d = 1/2·m·u²

·g·d = 1/2·u²

= 1/2·u²/(g·d) = 1/2·u²/(9.8 × 23) = u²/450.8

∴   = u²/450.8...(1)

The kinematic equation of motion of the block can be presented as follows;

v = u - a·t

Where;

v = The final velocity = 0 m/s (The block slides to a stop)

u = The initial velocity

a = The acceleration of the block (the minus sign indicates that the block's velocity is decreasing)

t = The time of motion of the block = 600 seconds

Therefore, by substituting the above values, we have;

0 = u - 600·a

∴ u = a·600

The kinematic equation of motion for the distance moved by the block, "s" can be expressed as follows;

s = u·t - 1/2·a·t²

Where;

s = The distance moved by the bloc = 23 meters

∴ 23 = a·600·600 - 1/2·a·600² = 360,000·a - 1/2·a·360,000 = 180,000·a

a = 23/(180,000)

u = 600 × (23/(180,000)) = 23/300

The initial velocity, u = 23/300 m/s

From equation (1), we have;

= u²/(450.8) = (23/300)²/450.8 = 23/1764000 ≈ 1.304 × 10⁻⁵

The magnitude of the coefficient of kinetic friction, ≈ 1.304 × 10⁻⁵

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