Question

A ball of mass 0.45 kg which is intially at rest is hit by bat the bat remains in contact with the ball for is$3*10^{-3}$. During this time period the force on the ball by the bat is given as F(t)=[(α*10^9)-(β*10^9)t^2]N where α and β are constants. The ball's speed immediately as it losees contact with the bat is 20m/s the correct relation between α and β

Answer 1

A soccer player kicks a soccer ball of mass 0.45 kg that is initially at rest. The foot of the player is in contact with the ball for

3.0×10−3s

, and the force of the kick is given by

F(t)=[(6.0×106)t−(2.0×109)t²]N

for

0≤t≤3.0×10−3s

, where t is in seconds. Find the magnitudes of: (a) the impulse on the ball 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 velocity immediately after it loses contact with the player’s foot.

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Answer 2

ans;$\alpha -2\beta =2$Explanation; imules j=change in momentum

mV-mU=∫f(t)dt

0.45(20)-0.45(0)

=∫[($\alpha$×10⁶)t-($\beta$×10⁹)t²]dt

9=$\alpha$×10⁶[t²/2]-$\beta$×10⁹×t³/3

9=$\alpha$×10⁶×9×10⁻⁶/2 -$\beta$27×10⁻⁹/3

9=9$\alpha$/2-9$\beta$

$\alpha$/2-$\beta$=2

∴$\alpha -2\beta =2$