Question

A bowler uses a lane with a coefficient of kinetic friction of 0.184. The bowler releases her 5.70 kg bowling ball with a translational speed of 2.50 m/s.At the moment of release, the ball is not rotating. As the ball slides, it begins to rotate.What is the work Wnc done by friction on the ball before it transitions to rolling without slipping? Use =9.81 m/s² for the acceleration due to gravity. Wnc= ____ J

Answer 1

To determine the work done by friction on the bowling ball before it transitions to rolling without slipping, we can calculate the distance the ball slides before transitioning to this state. We can use the equation W = µmgd, where µ is the coefficient of kinetic friction, m is the mass of the ball, g is the acceleration due to gravity, and d is the distance the ball slides. By finding the decelerating force applied to the ball by friction and the distance traveled, we can calculate the work done by friction as 7.84 J.

Step-by-step explanation:

To calculate the work done by friction on the bowling ball before it transitions to rolling without slipping, we need to find the total work done due to friction when the ball is sliding and rotating. The work done by friction can be calculated using the equation W = µmgd, where µ is the coefficient of kinetic friction, m is the mass of the ball, g is the acceleration due to gravity, and d is the distance the ball slides. In this case, the ball is released with a translational speed of 2.50 m/s and a mass of 5.70 kg. We know that the final state will be rolling without slipping, so we can calculate the distance the ball slides before transitioning to this state.

First, we need to find the decelerating force applied to the ball by friction. This force can be calculated using the equation F = µmg, where F is the force, µ is the coefficient of kinetic friction, m is the mass of the ball, and g is the acceleration due to gravity. Plugging in the given values, we get F = (0.184)(5.70 kg)(9.81 m/s²) = 10.75 N. Next, we need to find the acceleration experienced by the ball. Since the ball is released with a velocity of 2.50 m/s and comes to a stop, the deceleration is given by a = vf² - vi² / 2d, where vf is the final velocity, vi is the initial velocity, and d is the distance. We can rearrange the equation to solve for d: d = (vf² - vi²) / 2a. Plugging in the values, we get d = (0 - (2.50 m/s)²) / (2(10.75 N / 5.70 kg)) = -0.730 m. We take the absolute value to get the distance traveled, which is 0.730 m. Finally, we can calculate the work done by friction using the equation W = Fd, where W is the work done, F is the force, and d is the distance. Plugging in the values, we get W = (10.75 N)(0.730 m) = 7.84 J. Therefore, the work done by friction on the ball before it transitions to rolling without slipping is 7.84 J.

Answer 2

A bowler uses a lane with a coefficient of kinetic friction of 0.184, the work Wnc done by friction on the ball before it transitions to rolling without slipping? Use =9.81 m/s² for the acceleration due to gravity. Wnc= 10.63 J

Step-by-step explanation:

When the bowling ball is released, it initially slides on the lane due to the presence of kinetic friction.

The work done by friction on the ball can be calculated using the equation Wnc = μk * m * g * d

Where

μk is the coefficient of kinetic friction

m is the mass of the ball

g is the acceleration due to gravity

d is the distance over which the ball slides.

In this case, the coefficient of kinetic friction is given as 0.184, the mass of the ball is 5.70 kg, and the acceleration due to gravity is 9.81 m/s².

Using the given values and the equation, we can calculate the work done by friction as follows:

Wnc = 0.184 * 5.70 * 9.81 * d = 10.6348 * d = 10.63d J

Therefore, the work done by friction on the ball before it transitions to rolling without slipping is 10.63 times the distance over which the ball slides, measured in joules.