How Much Acceleration Can a Man Generate While Towing an Airplane?

[wanos]

Homework Statement

an 85 kg man plans to tow a 109000 kg airplane along a runway by pulling on a cable attached to it at an angle 9 above the horizontal. the coefficient of static friction between his between his shoes and the runway is 0.77. what is the greatest acceleration that the man can give the plane assuming that the airplane is on wheels that turn without any frictional resistance.

Homework Equations

it depends which body I'm solving for. if we're studying the plane alone the pulling force would ultimately replace the man. and we use the mass of the plane alone, but then the plane has no friction because we assumed it was frictionless.

as for the man, the kinetic friction force. but does he have an acceleration? and if he does would it be the same as the plane's. if so, we can make one body diagram and the mass would be the sum of the man's and the plan's, in this case we would ignore the pulling force on the cable... would the static friction apply if we assume on big body?am I on the right track?

The Attempt at a Solution

 

[gorpkaiser]

Homework Statement

an 85 kg man plans to tow a 109000 kg airplane along a runway by pulling on a cable attached to it at an angle 9 above the horizontal. the coefficient of static friction between his between his shoes and the runway is 0.77. what is the greatest acceleration that the man can give the plane assuming that the airplane is on wheels that turn without any frictional resistance.

Re-reading the problem statement carefully is often helpful. I bolded some important parts. What you are ultimately interested in is the acceleration of the plane, right? So I would start with a free-body diagram for the plane and try to apply Newton's second law. If you find that you cannot go any further with that, you may find Newton's 3rd law to help, in which case you will need another (separate) free-body diagram. I would not start with a free-body diagram for the whole man-plane system since that is not directly related to the goal.

Homework Equations

as for the man, the kinetic friction force.

Kinetic friction? You sure?

Edit: I assume the "greatest force the man can give" means he can apply any amount of force unless his shoes start slipping.

 

[rl.bhat]

Hi wanos, welcome to PF.
If F is the force applied by the man at an angle θ,
what is its horizontal and vertical components?
what is the net normal reaction?
What is the frictional force?
Equate the frictional force to the horizontal force, and solve for F.
Mass of the plane is given. Find a.

 

[wanos]

i drew a free body diagram for the plan.
Fcos9=ma
i don't know the acceleration and i don't know the force by which the man is pulling :S

static friction, so I can slove for maximun acceleration of the man?
but if we;re talking about a cable, that means that there is also a tension force on the man which is equal to that on the plane?

if i solve for the tension force in the free bosy diagram of the man, and plug that into the equation with the free body diagram for the plane, i can figure out the plane's acceleration. but i don't even know if the man is accelerating, if he is then i can't solve this!

 

[rl.bhat]

Her man will be at rest till the plane start moving because the length of the cable is constant. Plane will move forward only when man moves forward. And he can move forward only when the frictional force in the forward direction is greater then horizontal component of reactionary force acting on him by the plane.

 

[gorpkaiser]

i drew a free body diagram for the plan.
Fcos9=ma
i don't know the acceleration and i don't know the force by which the man is pulling :S

static friction, so I can slove for maximun acceleration of the man?
but if we;re talking about a cable, that means that there is also a tension force on the man which is equal to that on the plane?

if i solve for the tension force in the free bosy diagram of the man, and plug that into the equation with the free body diagram for the plane, i can figure out the plane's acceleration. but i don't even know if the man is accelerating, if he is then i can't solve this!

You're almost there. You have 2 equations in 3 unknowns. The final piece of information is the constraint equation. As rl.bhat was saying, the bodies are rigidly connected, which means the acceleration must be the same for each,

$$a_{x, \mathrm{man}} = a_{x, \mathrm{plane}}$$

 

[wanos]

So I made 2 equations with 2 unknowns, the acceleration of the man/plane and the equal reaction pulling force between them. The normal force on the man is equal to his weight plus the vertical component of the pulling force. So we have the static friction force with respect to the pulling force. The friction force minus the horizontal component of the pulling force is equal to the man's mass times his acceleration. so basically I solved the two equations for acceleration, which ended up being of magnitude raised to to 10^-3. since the mass of the plane is much bigger than that of the man towing it, i guess it makes sense that the acceleration is relatively small?!


Thanks a million, both of you =)