A billiard ball, which we treat as a solid ball of mass M and radius R , is at r

Question

A billiard ball, which we treat as a solid ball of mass Mand radius R, is at rest on a frictionless table. The ballis hit sharply by a cue, which imparts a horizontal impulse ofmomentum at a height b above the center of the ball. Thestrike is centered, which means that the impulse of momentum liesin the vertical plane that includes the center of the sphere andthe point of impact.
Even though the surface is frictionless, if the ball is hit atjust the right height, it will roll without slipping immediatelyafter it is hit. For what value of b will thishappen?
Even though the surface is frictionless, if the ball is hit atjust the right height, it will roll without slipping immediatelyafter it is hit. For what value of b will thishappen?

Explanation / Answer

let an impulse of J is exerted on the solid cue then the impulsive torque on the solid ball is J*b we have angular velocity of the ball as J*b/I as I= J*b for solid ball I=2mr2/5 and Velocity of the ball is J/m for pure rolling motion v=r J/m=r*J*b*5/2mr2hence b=0.4r

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.