A homogeneous, cylindrical ice hockey puck with mass m and radius R is to start

Question

A homogeneous, cylindrical ice hockey puck with mass m and radius R is to start with rest on a horizontal skating rink. The outer edge of the puck is now tangentially hit by an ice hockey stick. You can expect that the ice hockey stick is in contact with the puck for a given period Delta t, and that the ice hockey stick during this time affects the puck with a constant force F, see figure. The puck moves the given time Delta t on a smooth slope of the skating rink. Just after the stick has released the puck, the puck reaches a piece of skating rink which is not slippery. This piece has the length L, and the kinematic rubbing coefficient between puck and ice is on this piece mu_k. It is stated that the puck has sufficient speed to pass the whole piece. What's the puck's speed, v_s, just after it has passed the piece with the length L? A) v_s = (2 mu_k gL)^1/2 B) v_s = F Delta t/m - mu_k gL C) v_s = ((F Delta t/m)^2 - 2mu_k gL)^1/2 D) v_s = 2(F Delta t/m - mu_k gL) E) v_s = ((F Delta t/m)^2 - mu_k gL)^1/2

Explanation / Answer

change in momentum = F deltat

m (v- 0) = F t

v = F t / m

after that,

f = - uk m g

a = f / m = - uk g

Applying vf^2 - vi^2 = 2 a d

vs^2 - (Ft / m)^2 = 2 (- uk g ) L

vs = [ (F t / m ) - 2 uk g L]^(1/2)

Ans(C)

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