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

• gprice9
In summary, the distance a golf ball travels on a level green depends on the initial velocity, coefficient of friction, mass, and diameter of the ball. The movement is a combination of translational and rotational velocity. The MOI of a solid sphere is 2/5 mr^2. The rolling resistance, affected by factors such as grass length and wetness, plays a significant role in determining the distance traveled. Conducting experiments to account for these variables may provide more accurate results.

#### gprice9

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 textbook, 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

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!

gprice9 said:
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 textbook, 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.

## 1. How is the initial velocity of the golf ball determined?

The initial velocity of the golf ball is determined by the force of the club hitting the ball. The harder the club hits the ball, the higher the initial velocity will be.

## 2. What factors affect the distance a golf ball will travel on a green?

The main factors that affect the distance a golf ball will travel on a green are the initial velocity, the angle at which the ball is hit, the slope of the green, and the surface of the green (such as grass type and moisture level).

## 3. How is the angle of the ball's trajectory calculated?

The angle of the ball's trajectory is calculated using the initial velocity, the angle of the club face at impact, and the loft of the club. This angle will determine the height and distance of the ball's flight.

## 4. What role does air resistance play in calculating the distance of a golf ball on a green?

Air resistance, also known as drag, can slow down the golf ball's flight and decrease the distance it will travel on a green. This is why golfers often use different types of clubs for different distances and weather conditions.

## 5. Can a mathematical equation accurately predict the distance a golf ball will travel on a green?

While there are many mathematical equations that attempt to predict the distance a golf ball will travel on a green, there are numerous variables that can affect the outcome. Therefore, it is difficult to accurately predict the exact distance a golf ball will travel on a green before it comes to rest.