Problem 72P

After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a linear speed of 2.85 m/s (Figure 10-23). To rthe the rack, the ball rolls up a ramp that rises through a vertical distance of 0.53 m. (a) What is the linear speed of the ball when it rthees the top of the ramp? (b) If the radius of the ball were increased, would the speed found in part (a) increase, decrease, or stay the same? Explain.

FIGURE

Solution 72P

a.)

Step 1 of 3

We have to find the linear speed of the ball when it reaches the top of the ramp.

The linear speed of the ball can be found by making use of conservation of mechanical energy for the system.

(constant)

The mechanical energy of the ball at the start is equal to its mechanical energy at the top of the track.

Where,

and are the initial and final

linear speed of the ball in m/s

= Moment of inertia of the ball =

(moment of inertia of the

sphere about the diameter)

and are the initial and final angular speed

of the ball ,

vertical distance the ball rises = 0.53 m