In the figure, a 4.1 kg block slides along a track from one level to a higher le
ID: 1262680 • Letter: I
Question
In the figure, a 4.1 kg block slides along a track from one level to a higher level after passing through an intermediate valley. The track is frictionless until the block reaches the higher level. There a frictional force stops the block in a distance d. The block's initial speed is v0 = 5.2 m/s, the height difference is h = 1.1 m, and ?k = 0.644. Find d.
In the figure, a 4.1 kg block slides along a track from one level to a higher level after passing through an intermediate valley. The track is frictionless until the block reaches the higher level. There a frictional force stops the block in a distance d. The block's initial speed is v0 = 5.2 m/s, the height difference is h = 1.1 m, and ?k = 0.644. Find d.Explanation / Answer
m be the mass of the block,
v0 be its initial speed,
h be the height difference,
d be the stopping distance,
u be the coefficient of kinetic friction,
g be the acceleration due to gravity.
Equating the block's initial kinetic energy to its increase in potential energy and the work done against friction:
mv0^2 / 2 = mgh + umgd
v0^2 = 2g(h + ud)
h + ud = v0^2 / (2g)
d = [ v0^2 / (2g) - h ] / u
= [ 5.2^2 / (2 * 9.81) - 1.1 ] / 0.644
= 0.432m to 3 sig. fig.
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