Why must a water skier at constant velocity lean back?

[Lola Luck]

Homework Statement

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.

Homework Equations

Equilibrium: F_net=0 and Torque_net=0
r_{center 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.

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.

 

[Bystander]

Just where are these forces acting on the skier.

 

[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.

 

[Bystander]

The torque needs to be kept at 0 so she doesn't flip.

And, how does she accomplish zero torque?

 

[NascentOxygen]

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.

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

 

[Lola Luck]

And, how does she accomplish zero torque?

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

 

[Lola Luck]

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

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

 

[NascentOxygen]

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

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)?

 

[CWatters]

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

 

[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?

 

[Lola Luck]

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

 

[NascentOxygen]

That looks like the right idea, but ... If skiing at constant speed, f_a 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.

 

[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!

 

[CWatters]

Ski's aren't very buoyant. F_B 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 F_B pointing vertically. You already have F_W due to friction (drag) and I would suggest that F_B and F_W should be orthogonal (at 90 degrees to each other).