A small block of mass m is given an initial speed v_0 up a ramp inclined at angl

Question

A small block of mass m is given an initial speed v_0 up a ramp inclined at angle theta to the horizontal It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp. Express your answer in terms of the variables m, v_0Q , theta, d, and appropriate constants. mu_k = v_0^2-2dgsin(theta)/2dgeos(theta) What can you say about the value of the coefficient of static friction? Express your answer in terms of the variables m, v_0 , theta, d, mu_k, and appropriate constants.

Explanation / Answer

A) Using vf^2 - vi^2 = 2ad

0 - v0^2 = 2(a)(d)

a = - v0^2 / 2d

Using Fnet = ma

- mgsin@ - f = ma

f = m (v0^2/2d - gsin@)

in vertical,

N - mgcos@ = 0

N = mgcos@

f = uk N

uk = m (v0^2/2d - gsin@) / mgcos@ = v0^2 - 2dgsin@ / 2dgcos@

B) block comes to rest and remain rest if static friction is more than gravitational force along
the incline.

f >= mgsi@

f = us N = us mg cos@

us mg cos@ >= mg sin@

us > =tan@

ANS. tan@

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