Chapter 09, Problem 037 A soccer player kicks a soccer ball of mass 0.45 kg that

Question

Chapter 09, Problem 037 A soccer player kicks a soccer ball of mass 0.45 kg that is initially at rest. The player's foot is in contact with the ball for 1.50 x 103 s, and the force of the kick is oiven by Fr)- [(9,51 × 105). (6.34 10eraj N for O s t s l 50 × 10-3 s where t is in seconds. Find the magnitudes of the following: (a) the impulse on the bal due to the kick, (b) the average force on the ball from the player's foot during the period of contact, (c) the maximum force on the ball from the player's foot during the period of contact, and (d) the ball's speed immediately after it loses contact with the player's foot. (a) Number (b) Number (c) Number (d) Number Units Units Units Units

Explanation / Answer

(A ) impulse = integral of Fdt

= (9.51 x 10^5) t^2 /2 - (6.34 x 10^8)t^3 /3

t is from 0 to 1.50 x 10^-3 s

IMpulse = 1.06875 - 0.71325

= 0.356 N s

(B) impulse = Favg t

Favg = 0.356 / (1.50 x 10^-3) = 237 N

(C) dF/dt = 9.51 x 10^5 - 12.68 x 10^8 t = 0

t = 0.75 x 10^-3 sec

Fmax = 355 N

(D) impulse = m (vf - v0)

0.356 = 0.45 (vf - 0 )

vf = 0.79 m/s

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