How Do I Calculate the Final Resting Position of a Rolling Billiard Ball?

[mickg77]

My problem involves rolling a billiard ball with an initial x velocity of 2.4ms and an initial y velocity of 0.7ms. The rolling friction is 0.1 and I have to work out the final resting position of the ball. There is no sliding friction involved. I have to break this into 0.1seconds and return the results, i think that I have to work out the initial decelleration then the speed and new position, and then the next decelleration and so on?

the mass of the ball is 0.17kg

I'm pretty new to this, so sorry if its a bit basic.

Michael

 

[member 553083]

's solution:The first step is to calculate the deceleration of the ball. Since the rolling friction is 0.1, then the deceleration will be 0.17 x 0.1 = 0.017m/s2. Next, we need to calculate the speed and new position of the ball after 0.1 seconds. Since the initial velocity of the ball in the x direction is 2.4m/s, the final velocity in the x direction after 0.1 seconds will be 2.4m/s - 0.017m/s2 x 0.1s = 2.383m/s. Similarly, the final velocity in the y direction will be 0.7m/s - 0.017m/s2 x 0.1s = 0.683m/s. The final position of the ball after 0.1 seconds can be calculated by multiplying the final velocities by 0.1s. The final position in the x direction will be 2.383m/s x 0.1s = 0.2383m, and the final position in the y direction will be 0.683m/s x 0.1s = 0.0683m. Finally, we need to repeat this process for the next 0.1 seconds. The final resting position of the ball will be the sum of all the distances it has travelled in each 0.1 second interval.

 

[M98Ranger]

, you are on the right track with your approach to solving this problem. To find the final resting position of the ball, you will need to break the problem into smaller time intervals of 0.1 seconds. This will allow you to calculate the change in position and velocity for each interval and determine the final resting position.

Firstly, you will need to calculate the initial deceleration of the ball. This can be done using the formula a = F/m, where a is the acceleration, F is the force and m is the mass of the ball. In this case, the force is the rolling friction, which is given as 0.1. So, the initial deceleration can be calculated as 0.1/0.17 = 0.588 m/s^2.

Next, you will need to calculate the new speed and position for each time interval. This can be done using the equations v = u + at and s = ut + 1/2at^2, where v is the final velocity, u is the initial velocity, a is the acceleration, t is the time interval and s is the displacement. In this case, the initial velocity (u) in the x direction is 2.4 m/s and in the y direction is 0.7 m/s. So, for the first time interval of 0.1 seconds, the new speed in the x direction will be v = 2.4 + (-0.588)(0.1) = 2.34 m/s and the new position will be s = (2.4)(0.1) + 1/2(-0.588)(0.1^2) = 0.219 m. Similarly, for the y direction, the new speed will be v = 0.7 + (-0.588)(0.1) = 0.641 m/s and the new position will be s = (0.7)(0.1) + 1/2(-0.588)(0.1^2) = 0.063 m.

You will then repeat this process for each time interval, using the new speed and position as the initial values for the next interval. By the end, you will have a series of values for the final position of the ball at each time interval. The final resting position of the ball will be the last value in this series.

I hope this helps and good luck