Answer:
2.65 m
Explanation:
From work-kinetic energy principle,
workdone by friction + workdone by gravity on sled = kinetic energy change of sled
Let h be the vertical height moved and d the distance moved along the incline. h = dsinθ where θ is the angle of the incline = 20°.
The workdone by gravity on the sled is mghcos180 = -mgh = -mgdsinθ
The frictional force = -μmgcosθ where μ = 0.20 and the work done by friction = -μmgcosθd
The kinetic energy change = 1/2m(v₂² - v₁²) where v₁ = initial speed = 2.0 m/s and v₂ = final speed = 0 m/s (since the sled stops)
So, -mgdsinθ - μmgcosθd = 1/2m(v₂² - v₁²)
-gd(sinθ - μcosθ) = 1/2(v₂² - v₁²)
d = (v₂² - v₁²)/-2g(sinθ - μcosθ)
substituting the values for the variables,
d = (0 - 2²) /[- 2 × 9.8(sin20 - 0.2cos20)]
d = -4 /[- 2 × 9.8(sin20 - 0.2cos20)]
d = -4/ - 1.51 = 2.65 m
It has moved up the incline a distance of 2.65 m.
