A small block slides along a path that is without friction until the block reaches the section L = 3m, which begins at height h=3m on a flat incline of angle 37°, as shown. In that section, the coefficient of kinetic friction is 0.50. The block passes through a point A with a speed of√136 m/s . Find the speed of the block as it passes through point B where the friction ends.
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Answer:
The answer is VB = 3.99 = 4 m/s
Explanation:
Given data:
L = 3m
h=3m
μA = √136 m/s
θ = 37°
From figure;
AD = h/ Sinθ
Now
Vb^2 = μA^2 - 2gSinθ AD
Vb^2 = ( √136)^2 - 2 x 10 Sin 37° x ( 3/ Sin37°)
After cabcellation:
Vb^2 = 136 - 60 = 76
Vb = √76 m/s
From b - B => mgsinθ + μmgcosθ = ma
a = g (sinθ + μcosθ)
a = 10 (sin 37° + cos 37°)
a = 10.01 m/s^2
Now
VB^2 = Vb^2 - 2aL
= (√76)^2 - 2 x 10.01 x 3
VB^2 = 15.94
VB = 3.99 = 4 m/s
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