Use the work-energy theorem to solve each of these problems. You can use Newton's laws to check your answers. (a) A skier moving at 5.00 m/s encounters a long, rough horizontal patch of snow having a coefficient of kinetic friction of 0.220 with her skis. How far does she travel on this patch before stopping?

d = 5.8 m

Explanation:

Principle of work and energy

ΔE = Wf

ΔE = Ef-Ei

ΔE : mechanical energy change

Wf : Work done by kinetic friction force

Ef : final mechanical energy

Ei : initial mechanical energy

K = (1/2) mv² : Kinetic energy

U = mgh : Potential energy

m: mass (kg)

v : speed (m/s)

h: high (m)

Data

vi = 5.00 m/s

vf=0

hi=0

hf=0

μk=0.220

Kinetic friction force

fk = μk * FN

FN = W : normal force (N)

W = m*g : weight (N)

FN = 9.8*m (N)

fk = 0.220*9.8*m

fk = (2.156) * m Equation (1)

Work done by the kinetic friction force

Wf = - fk*d (J) Equation (1)

d: distance traveled by force

Principle of work and energy to the skier

ΔE = Ef-Ei

Ef = Kf + Uf = 0

Ei = Kf + Uf = (1/2) (m) (5) ² + 0

ΔE = - (1/2) (m) (5) ²

ΔE = Wf

0 - (1/2) (m) (5) ² = - fk*d

We replace fk = (2.156) * (m) of the equation (1)

- (1/2) (m) (5) ² = - (2.156) * (m) * d

We divide by (-m) both sides of the equation

(1/2) (5) ² = (2.156) * d

12.5 = (2.156) * d

d = (12.5) / (2.156)

d = 5.8 m