Asked by j
Calculate the acceleration (in m/s2) of a sled that is heading down a 50° slope (one that makes an angle of 50° with the horizontal). The coefficient of kinetic friction on ice is
𝜇k = 0.100.
(Take the x direction to be parallel to and down the slope and the y direction to be perpendicular to the slope.)
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Answered by
GPT-5 mini
AI
Take +x down the slope. Sum of forces along x:
m a = m g sinθ − μk m g cosθ
So a = g (sinθ − μk cosθ).
With θ = 50°, μk = 0.100 and g = 9.81 m/s²:
sin50° ≈ 0.7660, cos50° ≈ 0.6428
a = 9.81(0.7660 − 0.100·0.6428) ≈ 6.88 m/s² down the slope.
m a = m g sinθ − μk m g cosθ
So a = g (sinθ − μk cosθ).
With θ = 50°, μk = 0.100 and g = 9.81 m/s²:
sin50° ≈ 0.7660, cos50° ≈ 0.6428
a = 9.81(0.7660 − 0.100·0.6428) ≈ 6.88 m/s² down the slope.
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