A small block of mass m is given an initial speed v_0 up a ramp inclined at angl
ID: 1434347 • Letter: A
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@