Calculating how far a golf ball will travel on a green before it comes to rest?

I have been trying to calculate how far a golf ball will travel on a level green given the following variables:

The initial velocity of the ball is 1.49 m/s
The coefficient of friction between the ball and the green is .0409
The mass of the ball is 0.046kg
The diameter of the ball is 42.6mm

The fact that the ball is rolling, means that the movement is a combination of translational velocity and rotational velocity. However I am struggling to understand the method to calculate the rotational velocity and implement it within the equation.

MOI of a solid sphere = 2/5 mr^2

I have taken this frictional value from a text book, but am not sure whether I need to apply this value to calculate the rate of acceleration, or calculate an alternative rolling resistance value?

My attempt thus far (only taking translational movement into account):

Acceleration = mgu/m = gu = 9.81 * 0.046 = 0.4 m/s^2

Displacement = s = v^2 / 2a = 1.49^2 / 2 * .4 = 2.775 m

If anyone would be able to help/guide me, I would be most grateful.

Regards, George

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gneill
Mentor
If you think about it, when the golf ball is first struck it's probably not rolling. So it'll be sliding across the green. The resulting torque due to friction will start the ball turning, and when the tangential velocity of rotation matches the translational velocity, the ball is then rolling without slipping. Then the sliding friction goes away and the rolling friction takes over.

There's a lot of parts to this simple question!

berkeman
Mentor
I have been trying to calculate how far a golf ball will travel on a level green given the following variables:

The initial velocity of the ball is 1.49 m/s
The coefficient of friction between the ball and the green is .0409
The mass of the ball is 0.046kg
The diameter of the ball is 42.6mm

The fact that the ball is rolling, means that the movement is a combination of translational velocity and rotational velocity. However I am struggling to understand the method to calculate the rotational velocity and implement it within the equation.

MOI of a solid sphere = 2/5 mr^2

I have taken this frictional value from a text book, but am not sure whether I need to apply this value to calculate the rate of acceleration, or calculate an alternative rolling resistance value?

My attempt thus far (only taking translational movement into account):

Acceleration = mgu/m = gu = 9.81 * 0.046 = 0.4 m/s^2

Displacement = s = v^2 / 2a = 1.49^2 / 2 * .4 = 2.775 m

If anyone would be able to help/guide me, I would be most grateful.

Regards, George
Welcome to the PF.

How far the ball goes depends mainly on the rolling resistance, which depends on how long the grass is, how wet it is, the grain, etc.

Probably your best bet is to do a number of experiments taking those variables into account, and develop your numbers empirically.