# Why must a water skier at constant velocity lean back?

1. Jan 18, 2015

### Lola Luck

1. The problem statement, all variables and given/known data
Why must a water skier moving with constant velocity lean backward? What determines how far back she must lean? Draw a free-body diagram for the water skier to justify your answers.

2. Relevant equations
Equilibrium: Fnet=0 and Torquenet=0
rcenter of mass=(m1r1+m2r2+m3r3...)/(m1+m2+m3...)

This chapter also discusses stress, strain, elasticity etc. but I don't think it's applicable to this problem.

3. The attempt at a solution

In my free body diagram, the forces acting on the skier are air resistance and water resistance in the negative direction, and the tension in the rope she's holding in the positive direction.

The net force will always be zero because the tension will match resistance. The torque needs to be kept at 0 so she doesn't flip. I think she leans back to keep the torque at 0, but I'm not sure why that would work.

2. Jan 18, 2015

### Bystander

Just where are these forces acting on the skier.

3. Jan 18, 2015

### Lola Luck

Air resistance acts across the front of the skier (equivalent to being concentrated at the center of mass), and water resistance, which exerts more force, acts along the skis. The tension acts along her arms, probably near the center of mass.

4. Jan 18, 2015

### Bystander

And, how does she accomplish zero torque?

5. Jan 18, 2015

### Staff: Mentor

Don't overlook gravity! Gravity acts vertically downwards; you can often picture it being concentrated at about waist height, when standing.

6. Jan 18, 2015

### Lola Luck

by leaning back, apparently. is it because she shifts her center of gravity?

7. Jan 18, 2015

### Lola Luck

Oh yeah, completely forgot about gravity in the free body diagram...

8. Jan 18, 2015

### Staff: Mentor

So, can you show on a stick figure how gravity can counter the tendency of the tow line to produce a face plant (i.e., a rotation about the ankle straps)?

9. Jan 19, 2015

### CWatters

Show us the free body diagram. Did you include the normal force at the feet/lift force due to the skies?

10. Jan 19, 2015

### Lola Luck

I can't show the free body diagram but i have the tension of the cable, gravity, air resistance, water resistance (friction?), normal force (buoyancy?). Is it because leaning back causes gravity to have a torque that counters the water resistance?

11. Jan 19, 2015

### Lola Luck

ok it might be sideways but the top one is without leaning and the bottom one is with leaning

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12. Jan 19, 2015

### Staff: Mentor

That looks like the right idea, but .... If skiing at constant speed, fa whatever it is won't be there. I would keep the skis flat, and water resistance and bouyancy shouldn't change to act at an angle.

13. Jan 19, 2015

### Lola Luck

Fa is air resistance... I guess it's not necessary to include it. I think i have it figured out- thank you for your help!

14. Jan 20, 2015

### CWatters

Ski's aren't very bouyant. FB would be due to lift caused by the skis being at an angle to the water.

When you show the man leaning back I would leave the FB pointing vertically. You already have FW due to friction (drag) and I would suggest that FB and FW should be orthogonal (at 90 degrees to each other).