Newton's third law problem/kinematics (Airboat problem/no friction)

In summary, the conversation discusses the use of an airboat and how to calculate the force of the air on the boat and its acceleration. The question of how far the boat will travel in one minute is also addressed, with the conclusion that it can travel a total of 1224 metres in a minute assuming no friction.
  • #1
Petronius
13
2
Homework Statement
An airboat is a special type of boat that has a large fan mounted on the back instead of a motor that sits in the water. It is used in places where the water is shallow and weedy, so motors that stick down into the water cannot be used.

If the force of the fan pushes the air backwards with 150 N, what is the forward force of the air on the boat? If the mass of the boat is 220 kg, and you ignore friction between the boat and the water, find how far the boat will travel in the first minute.
Relevant Equations
Based on unit notes I used:
Faction= -Freaction
F=ma
D= v1∆t + 1/2 at^2
Thank you very much your time!

I first found the force of the air on the boat using the principle of Newton's third law and the fact that no friction is involved.

Faction= -Freaction
150 N backwards = -150 N backwards
150 N backwards = 150 N forward

I then sought to determine the acceleration of the boat forward so that I would have enough information to solve for how far the boat will travel in the first minute (displacement).

F =ma
150 N [forward[ = (220kg)(a [forward])
a = 150 N [forward] / 220kg
a= 0.68m/s^2 |forward|

After this I sought to determine how far the boat would travel in one minute using the kinematics equation D= v1∆t + 1/2 at^2 .
My answer seems far too high and I am a bit perplexed and also wondering if there is an easier equation I could apply

I assumed v1 would be 0 since the the equation seems to state that the boat is starting from rest.

D= v1∆t + 1/2 at^2 .
D = 0 + 1/2(0.68 m/s^2)(60sec)^2
D= (0.34)(3600)
D=1224 metes

Therefore the boat travels a total of 1224 metres in a minute.

I hope my the way I have written the equations is acceptable as they do not seem to directly copy and paste from equation editor on Microsoft word.

Again, thank you for your time and any help/guidance provided.
 
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  • #2
Petronius said:
Homework Statement:: An airboat is a special type of boat that has a large fan mounted on the back instead of a motor that sits in the water. It is used in places where the water is shallow and weedy, so motors that stick down into the water cannot be used.

If the force of the fan pushes the air backwards with 150 N, what is the forward force of the air on the boat? If the mass of the boat is 220 kg, and you ignore friction between the boat and the water, find how far the boat will travel in the first minute.
Homework Equations:: Based on unit notes I used:
Faction= -Freaction
F=ma
D= v1∆t + 1/2 at^2

Thank you very much your time!

I first found the force of the air on the boat using the principle of Newton's third law and the fact that no friction is involved.

Faction= -Freaction
150 N backwards = -150 N backwards
150 N backwards = 150 N forward

I then sought to determine the acceleration of the boat forward so that I would have enough information to solve for how far the boat will travel in the first minute (displacement).

F =ma
150 N [forward[ = (220kg)(a [forward])
a = 150 N [forward] / 220kg
a= 0.68m/s^2 |forward|

After this I sought to determine how far the boat would travel in one minute using the kinematics equation D= v1∆t + 1/2 at^2 .
My answer seems far too high and I am a bit perplexed and also wondering if there is an easier equation I could apply

I assumed v1 would be 0 since the the equation seems to state that the boat is starting from rest.

D= v1∆t + 1/2 at^2 .
D = 0 + 1/2(0.68 m/s^2)(60sec)^2
D= (0.34)(3600)
D=1224 metes

Therefore the boat travels a total of 1224 metres in a minute.

I hope my the way I have written the equations is acceptable as they do not seem to directly copy and paste from equation editor on Microsoft word.

Again, thank you for your time and any help/guidance provided.

That looks right. Ignoring friction is perhaps not so realistic for a boat in the water! But that's the question setter's fault.
 
  • #3
Thank you very much for your time. I suppose the lack of friction means this hypothetical airboat can reach some monstrous speeds.
 
  • #4
Petronius said:
Thank you very much for your time. I suppose the lack of friction means this hypothetical airboat can reach some monstrous speeds.
Yes, exactly.
 

Related to Newton's third law problem/kinematics (Airboat problem/no friction)

What is Newton's third law?

Newton's third law states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force back on the first object.

How does Newton's third law apply to the Airboat problem?

In the Airboat problem, the air pushes the boat forward in one direction, while the boat pushes the air backwards in the opposite direction. This is an example of Newton's third law in action.

Why is there no friction in the Airboat problem?

In the Airboat problem, it is assumed that there is no friction between the boat and the water. This is because the boat is gliding on a cushion of air, and there is minimal contact between the boat and the water's surface.

How does understanding Newton's third law help in solving kinematics problems?

Newton's third law helps us understand the forces acting on objects, which is a crucial component in solving kinematics problems. It allows us to accurately calculate the acceleration of an object based on the forces acting on it.

What are some real-life applications of Newton's third law?

Newton's third law can be observed in many everyday situations, such as when a person walks, a bird flies, or a car drives. It is also the principle behind rocket propulsion and can be seen in sports like swimming and rowing.

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