Can a Man Tow a 109,000-kg Plane Using Newton's Laws?

[bulbasaur88]

1. A man seeking to set a world record wants to tow a 109,000-kg airplane along a runway by pulling horizontally on a cable attached to the airplane. The mass of the man is 85 kg, and the coefficient of static friction between his shoes and the runway is 0.77. What is the greatest acceleration the man can give the airplane? Assume that the airplane is on wheels that turn without any frictional resistance.

Homework Equations

PLANE --> Tension=mass of plane x acceleration

The Attempt at a Solution

How do I set up the equation for the net forces of man. Is force of friction - Tension = mass of man x acceleration the correct equation?

 

[Yuqing]

This question actually has little to do with tension. You are given the coefficient of friction and so you should be able to find the frictional force the ground can provide. How do you think this limits the way the man can pull the plane? As an limiting situation, think about the scenario situated on a giant ice rink, how would that change things?

 

[ehild]

The Attempt at a Solution

How do I set up the equation for the net forces of man. Is force of friction - Tension = mass of man x acceleration the correct equation?

Yes, it is correct.

ehild

 

[bulbasaur88]

thank u Dr. ehild

 

[bulbasaur88]

if anyone attempts this problem let me kno if u get ~ F = 0.49979 N thanks

 

[ehild]

This question actually has little to do with tension. You are given the coefficient of friction and so you should be able to find the frictional force the ground can provide. How do you think this limits the way the man can pull the plane? As an limiting situation, think about the scenario situated on a giant ice rink, how would that change things?

There is no friction between the airplane and the ground. So it is the tension of the cable that sets it into motion. The cable has to be pulled, no tension otherwise. The man pulls the cable, the cable pulls back the man. The man exerts a backward force on the ground, the ground pushes the man forward. This force can not exceed μmg.
The resultant of the forward force and the tension pulling the man backward is equal to the mass of the man multiplied by the common acceleration of man and airplane .

ehild

 

[Yuqing]

There is no friction between the airplane and the ground. So it is the tension of the cable that sets it into motion. The cable has to be pulled, no tension otherwise. The man pulls the cable, the cable pulls back the man. The man exerts a backward force on the ground, the ground pushes the man forward. This force can not exceed μmg.
The resultant of the forward force and the tension pulling the man backward is equal to the mass of the man multiplied by the common acceleration of man and airplane .

I don't see why the plane and man cannot be considered a single system. Tension is treated as an internal force in this case and irrelevant, it just seems simpler to me.

 

[ehild]

if anyone attempts this problem let me kno if u get ~ F = 0.49979 N thanks

What is F? What kind of force? The problem asked the maximum acceleration.

ehild

 

[ehild]

I don't see why the plane and man cannot be considered a single system. Tension is treated as an internal force in this case and irrelevant, it just seems simpler to me.

Yes, the plane and man can considered a single system, and the force of friction on the man is the external force, the internal ones cancelling out. But it is easier to understand and is no harm to draw free body diagrams, collecting all the forces on the individual masses.

ehild