Question

A bowling ball encounters a 0.760-m vertical rise on the way back to the ball rack, as the drawing illustrates. Ignore frictional losses and assume that the mass of the ball is distributed uniformly. The translational speed of the ball is 8.57 m/s at the bottom of the rise. Find the translational speed at the top.

Answer 1

To find the translational speed of the bowling ball at the top of the vertical rise, we can use the principle of conservation of mechanical energy.

Step-by-step explanation:

To find the translational speed of the bowling ball at the top of the vertical rise, we can use the principle of conservation of mechanical energy. Initially, the ball has kinetic energy due to its translational speed. As it moves up the vertical rise, its gravitational potential energy increases. Since there is no friction, we can assume there is no loss of energy.

Using the equation for conservation of mechanical energy:

Initial kinetic energy = final potential energy

0.5 * m * v^2 = m * g * h

Where m is the mass of the ball, v is the translational speed at the bottom, g is the acceleration due to gravity, and h is the height of the vertical rise.

Plugging in the given values:

0.5 * m * (8.57 m/s)^2 = m * 9.8 m/s^2 * 0.760 m

Simplifying and solving for the mass:

m = (9.8 m/s^2 * 0.760 m) / (0.5 * (8.57 m/s)^2)

Finally, we can plug the mass back into the initial equation to find the translational speed at the top of the rise.