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A billiard ball of mass 168 g and radius 2.4 cm starts with a translational spee

ID: 1266046 • Letter: A

Question

A billiard ball of mass 168 g and radius 2.4 cm starts with a translational speed of 2 m/s at point A on the track as shown in the figure below. If point B is at the top of a hill that has a radius of curvature of 69 cm, what is the normal force acting on the ball at point B? Assume the billiard ball rolls without slipping on the track.

A billiard ball of mass 168 g and radius 2.4 cm starts with a translational speed of 2 m/s at point A on the track as shown in the figure below. If point B is at the top of a hill that has a radius of curvature of 69 cm, what is the normal force acting on the ball at point B? Assume the billiard ball rolls without slipping on the track.

Explanation / Answer

let v is the speed at point B,

Apply,loss of PE = gain in KE

m*g*h = 0.5*m*(v^2-u^2) + 0.5*I*w^2

m*g*h = 0.5*m*(v^2-u^2) + 0.5*(2/5)*m*r^2*w^2

m*g*h = 0.5*m*(v^2-u^2) + 0.2*m*v^2

m*g*h = -0.5*m*u^2 + 0.7*m*v^2


g*h = -0.5*u^2 + 0.7*v^2

0.7*v^2 = g*h + 0.5*u^2

v = sqrt(g*h + 0.5*u^2)/0.7

= sqrt(9.8*0.1 + 0.5*2^2)/0.7

= 2.47 m/s

a = v^2/R

= 2.47^2/0.69

= 8.84 m/s^2

Fnet = m*g - N

m*a = m*g - N

==> N = m*g - m*a

= m*(g-a)

= 0.168*(9.8 - 8.84)

= 0.161 N <<<<<---------Answer

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