Problem #1 (30 pts) While practicing archery for a competition, an archer releas

Question

Problem #1 (30 pts) While practicing archery for a competition, an archer releases an 0.02-kg arrow horizontally towards a target at a speed of 60 m/s. The arrow hits and sticks into a 0.5-kg target which is resting on a horizontal surface. Once impacted, the target and the arrow then slide together across a low friction surface. Ignore any effect of air resistance in the problem. (a) (15 pts) What is the speed of the "arrow+ target" system immediately after the arrow hits the target? Assume that the time it takes for the collision is very small and negligible (b) (15 pts) If the arrow and target stops after sliding 0.85 m after impact, what is the coefficient of kinetic friction between the target and the low friction surface? If you did not find the velocity from part a), assume you know the quantity and solve algebraically. 17 PM 0/19/2017 ^ TO

Explanation / Answer

a)
from momentum conservation

momentum before collision = momentum after collision

m1*v1i + m2*v2i = m1*v1f + m2*v2f

m1 (arrow) = 0.02 kg

v1i = 60 m/s

m2 = 0.5 kg

v2i = 0

after collision v1f = v2f = v

(0.02*60) + (0.5*0) = (0.02+0.5)*v

speed of arrow + target = 2.31 m/s

---------------------

(b)

work done by friction = -uk*(m1+m2)*g*x

work done = change in kinetic energy

Wf = (1/2)*(m1+m2)*(vf^2 - v^2)

vf = 0

-uk*g*x = -(1/2)*v^2

uk*9.8*0.85 = (1/2)*2.31^2

uk = 0.32 <<<<<------------ANSWER

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