1 answer

Impulse and Momentum

Question:

A soccer player kicks the ball to a teammate 8 m away. The ball leaves the player’s foot moving parallel to the ground at 6 m/s with no angular velocity. Thecoefficient of kinetic friction between the ball and the grass is µk = 0.32. How long does it take the ball to reach his teammate? The radius of the ball is 112 mmand its mass is 0.4 kg. Estimate the ball’s moment of inertia by using the equation for a thin spherical shell: I = (2/3)mR2 . Using IMPULSE AND MOMENTUM.

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Answers

Given µ = 0.32, r = 0.112 m, g = 9.81 m/s2 , v = 6 m/s


The motion occurs in two phases.

(a) Slipping.

ΣFx : −µN = ma

ΣFy : N − mg = 0


ΣMG : −µN R = (2/3) mR2 α

Solving we find, a = −µg ⇒ v = v0 − µgt , s = v0t − (1/2) µgt2
α = − 3µg/2R

⇒ ω = − (3µg/2R)*t

When it stops slipping we have, v = −Rω ⇒ v0 − µgt = (3/2) µgt ⇒ t = 2v0 /5μg = 0.765 sec
v = 3.6 m/s, s = 3.67 m

(b) Rolling — Steady motion

a = 0, v = 3.6 m/s, s = (3.6 m/s)(t − 0.765 s) + 3.67 m

When it reaches the teammate we have

8 m = (3.6 m/s)(t − 0.765 s) + 3.67 m ⇒ t = 1.97 s

.

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