When you go bowling, you throw the ball (a uniform sphere of mass m and radius r) so that when it is projected along the lane surface it initially has a linear velocity vo and slips along the surface. Once it touches the surface kinetic friction reduces the velocity of the ball, eventually leads the ball to roll without slip. When the coefficient of kinetic friction between the ball and the surface is uz, determine: (a) the time tron at which the ball will start rolling without slipping, and (b) the linear and angular velocities of the ball at time tol.

A steel ball of mass M is held at a distance H above a massless rigid tabletop supported by undamped springs whose equivalent stiffness is K. If the ball is left to fall from rest on the tabletop. Deduce an expression for the velocity at which the ball will bounce back off the tabletop. On its way back, will the mass bounce back to its initial height? If it will not, where will the difference in energy go? Discuss mathematically! (Pls solve the question in detail with figure)

EXAMPLE 4 A solid ball with a mass m is thrown on the ground such that at the instant of contact it has an angular velocity and velocity components (VG) and (VG) as shown. If the ground is rough so no slipping occurs, determine the components of the velocity of its mass center just after impact. The coefficient of restitution is e. (va)yt (va)a

Bicycle wheels are manufactured having thin rims and tires of total mass D per unit length, and the spokes and axle may be ignored. Find the angular momentum of one bicycle wheel of radius r when the bicycle is traveling at velocity v, and hence comment upon whether you would prefer large wheels or small wheels to make a bicycle easiest to balance when riding it.

9. 2) The target is a thin 4.3-kg circular disk of radius r= 273 mm that can rotate freely about the z axis. Initially it is at rest. A 21-g bullet, traveling at v = 630 m/s, strikes the target at A and becomes embedded in it. The dimensions are di = 219 mm and d2 = 90 mm. If the impact time is 0.02 s, determine the average impact force between the bullet and the target. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper Sl unit. Take g = 9.81 m/s?. 'pe