4. The fastest runner in a track and field event is the one with the
1 answer:
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Answer:
a) w=(5*vo)/(2r)
b) w=(5*vo)/(2*r)
Explanation:
a) according to the attached diagram we have to:
vo is the velocity of the ball after being hit. if we use Newton's second law:
F=m*a (eq.1)
where F is the force of friction, m is the mass of the ball and a is the acceleration. The normal force is equal to:
N=m*g
Also F=u*N (eq. 2), where u is the coefficient of friction. Replacing eq. 1 in eq. 2, we have:
F=m*u*g (eq. 3)
analyzing equation 1 and 3:
m*a=m*u*g
a=u*g
The torque is equal to:
τ=F*r (eq. 4)
τ=m*u*g*r
The relation between torque and angular acceleration is named moment of inertia.
I=(2/5)*m*r^2
if we have:
α=τ/I=(5*u*g)/(2*r)
The time is equal to:
t=(vo-u)/a=vo/(u*g)
the angular velocity is equal to:
w=α*t=((5*u*g)/(2*r))*(vo/(u*g))=(5*vo)/(2r)
b) the angular momentum is equal to:
L=m*v*r
the initial angular momentum is equal to:
Li=-I*w + m*vo*r
The final angular momentum (Lf) is 0
Thus we have:
Li=Lf
Replacing:
-I*w + m*vo*r=0
-((2/5)*m*r^2)*w + (m*vo*r)=0
clearing w:
w=(5*vo)/(2*r)
