sled of mass m is given a kick on a frozen pond. The kick imparts to it an initial speed of 1.90 m/s. The coefficient of kinetic friction between sled and ice is 0.110. Use energy considerations to find the distance the sled moves before it stops.

Distance = 1.674m

Explanation:

By the work energy theorem:-

W = ΔKE

W is work while KE is kinetic energy

Now we know that w has a formula;

W = Force x Distance and KE = (1/2) mv²

Thus,

F (friction) x s = (1/2) mv²

Now frictional force is = μmg

Where,

μ is coefficient of kinetic friction

Thus,

μmg•s = (1/2) mv²

m will cancel out to give;

μg•s = (1/2) v²

Let's make s the subject;

s = v² / (2gμ)

From the question,

velocity; v = 1.9 m/s

μ = 0.11 while g is constant at 9.8 m/s²

Thus;

s = (1.9) ²/[2 x 9.8 x 0.11]

s = 3.61/2.156

s = 1.674m

1.6727 meters

Explanation:

The inicial kinetic energy of the mass can be calculated using the formula:

E = mv^2/2

where m is the mass and v is the speed, so:

E = m*1.9^2/2 = 1.805m

All this energy is lost to the friction between the mass and the ground.

The friction force is F = m*g*u, where g is gravity and u is the coefficient of kinetic friction.

The energy that this force will generate is:

E = F * d, where d is the distance.

So, making the inicial kinetic energy equal to the energy dissipated by the friction, we have:

1.805m = m*g*u*d

9.81*0.11*d = 1.805

d = 1.805 / (9.81*0.11) = 1.6727 meters