# B Ball rolling on a grass slope

1. Sep 6, 2016

### ben9792

Hello, I play bowls on outdoor grass greens. I studied physics in school, and I've been wondering how physics works on the bowls in different areas of the green.

So for those who aren't familiar, you have a jack and a bowls. Jack is smaller and lighter, bowls larger and heavier. The bowling green is a crowned green, so has many slopes.

First, is sent with the same force on the flat which will travel further? I assume the jack, as it will have greater speed, the bowls will roll further though maybe?

Second, which will roll further up hill? I'm sure uphill the bowl will fall short of the jack, as it would need more energy to get up the hill?

Third, downhill which goes further? I assume the bowl, due to its potential energy?

How does friction impact the jack and bowl? Hoes does their size/weight impact them in these scenarios?

2. Sep 6, 2016

### jbriggs444

Too many variables, not enough information. When you say "launched with the same force", what does that mean? You can launch two balls with the same force exerted over the same length of time (resulting in the same momentum) or with the same force exerted over the same arc (resulting in the same energy). Which is it?

3. Sep 6, 2016

### ben9792

Honestly, I don't know. Surely the same arc and same force would take the same time? When you say arc I assume that's distance travelled along the arc?

4. Sep 6, 2016

### jbriggs444

If you are throwing a lighter ball with the same force, your hand will move faster. It will take less time and produce less momentum. Same energy, lower momentum.

Edit: if you contrive to exert the same force for the same time, your hand will still move faster. It will take the same time but travel farther and result in more energy. Same momentum, higher energy.

5. Sep 6, 2016

### ben9792

Ok, I'm with you now. I think you generally Bowl them with the same energy, so using same force and same arc.

6. Sep 6, 2016

### jbriggs444

So now we need a model for how the rolling resistance varies based on the ball size and mass (and speed). "Grass" is not something with a standard model in physics books.

7. Sep 6, 2016

### ben9792

And how would I describe that? That's essentially what I'm asking, how does the resistance effect the distance travelled with 2 different weight and size balls.

8. Sep 6, 2016

### ben9792

Having thought about it, what I'm really wanting to do is throw them both the same distance, with the same arc. So do I need more force uphill, and do I need more/less downhill. I think it's the potential energy that makes the difference.

9. Sep 6, 2016

### bsheikho

To throw them the same distance, consider that for a lighter object, the grass deformation would remove more of it's kinetic energy, which would slow it down. Versus the larger mass, which has more initial Kinetic energy. (assuming that their speeds are the same) So I would imagine if you would like them to end up at the same spot, you would aim the white ball roughly where it should go, versus the heavier ball you would aim it short, so it could roll to the final destination.

Of course it requires more force to throw the heavier ball with the same initial speed as the lighter ball. But if their speeds are similar, the losses of energy to friction would mean that the lighter ball needs to be thrown with a faster initial speed to climb the up hills.

10. Sep 6, 2016

### jbriggs444

It is easy to predict how something moves under a particular force law. Typically one solves a differential equation. But to do that, you must determine the force law. One might imagine various modes of energy loss for a ball rolling on grass. Some vary with speed, some vary with diameter, some vary with mass. The truth will have some contribution from each source. There is no way that we, sitting here at our desks can quote you a formula for your grass on your hill.

Consider, for instance, the loss of energy to the inelastic collisions with each blade of grass. The energy loss per grass blade scales with the square of the ball's velocity. Accordingly, the energy loss per unit distance scales with the square of the ball's velocity. Energy loss per unit distance is a force. So this energy loss results in a force that scales with the square of velocity but is independent of mass.

This loss of energy might be expected to scale with the diameter of the ball because more grass blades are impacted. However, it also has a complicated dependency on the ball diameter depending on grass height. The surface of a large ball will contact the grass more slowly than a small ball. I would hesitate to try to come up with a formula for this effect.

Then there is the loss of energy to grass blade friction. This loss will tend to be independent of velocity and mass but likely sensitive to diameter.

Then there is the loss of energy due to crushing of the soil and lack of resilient rebound in the grass. This is likely to scale strongly with mass and may have an inverse relation with velocity (at a higher velocity, you may tend to "plane" over the blades).

This is a problem area that is way too complex for an approach from first principles. It demands experiment.