Answer:
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
