To determine the coefficient o kinetic friction of block of wood on a horizontal

Question

To determine the coefficient o kinetic friction of block of wood on a horizontal table surface, you are given the following assignment: Take the block of wood and shove it across the surface of the table. Using a stopwatch, measure the time it takes for the block to come to a stop (Delta t) and the total distance that the block travels after the push (Delta x). Show that from these measurement mu_k = 2 Delta x / [g (Delta t)^2] If the block slides a distance of 1.37 m in 0.97 s, calculate mu_k What was the initial speed of the block?

Explanation / Answer

a) Applying kinematic equation we get,

x= vf*t + 1/2*a*t^2

Since finally block stops , vf = 0m/s

x=  1/2*a*t^2

a= 2x/t^2  ---------------(2)

Applying Newton’s second law we get,

Ff = ma

uk*mg = ma

uk= a/g

From (1), uk = |2x/gt^2|

b)Plugging values,

uk = (2*1.37)/(9.8*0.97^2) = 0.3

c) From (2)

a= 2x/t^2 = (2*1.37)/(0.97^2) = 2.9 m/s^2

Since block stops finally ,a is deceleration

Hence a= - 2.9 m/s^2

Use equation,

vf= vi + at

0 = vi - 2.9*0.97     = > vi = 2.8 m/s^2

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