Balancing Forces in a Towing Scenario

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In summary, the conversation revolves around a physics problem involving a motor boat towing two skiers. The boat exerts a force on the two skiers and the question is asking for the force that propels the boat, given that it is moving at a constant velocity and the drag of friction is 325 Newtons. There is some confusion about the direction and magnitude of the forces and how they relate to the constant velocity. However, the problem can be solved by considering all the forces on the boat and using Newton's third law to balance them. The drag of friction may vary for different subjects and is not necessarily the same for all three in this scenario.
  • #1
craptacular
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I'm at my wit's end trying to solve this question and I'm out of luck. Please help or suggest ideas. I have tried looking for similar problems in texts that are available but I keep arriving at the same answer I worked out which does not agree with the key's. Here's how the problem goes:

A motor boat is towing 2 skiers. At a particular moment, the boat exerts a force of 457 N on the 1st skier and a force of 525 Newtons East 30 degrees South on the 2nd skier. If the boat is moving at a CONSTANT velocity and the drag of friction is 325 Newtons, find the force that propels the boat [Answer: 1274 East 16 degrees South]
 
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  • #2
Is the drag of 325 Newtons for the boat? Is friction here considered proportional to velocity? What is the orientation of force for the 1st skier?
 
  • #3
As you are dealing with vectors, it is essential to know both the magnitude and the direction. Since the problem did not clearly state the directions of forces, it is impossible to solve. But, in any case the force that "propels" a subject that has CONSTANT velocity would be zero, as the subject is not in acceleration. However, I think what the problem is trying to ask is that: what is the reaction force of all the forces mentioned above. And the answer to that would be the inverse vector of the resultant resistance(the resultant force of draging the two skiers and the friction in this case). You can now find the answer using basic trigonometric calculations(assuming you know both the magnitude and the direction of the forces of course).
 
  • #4
oooops, yes the orientation of skier 2!

First, thanks for responding. I think I agree with the questions you're asking me, too, but if you're asking the same questions I'm wondering about then this problem may not have been written well.

However I ommitted a given info. If this given info helps you solve this problem, please carry on and respond. So the boat exerts a force of 457 Newtons East on skier 2. And as for the other follow up questions, there is no other information provided. The drag force is simply 325 Newtons. Tell me, does this question make sense at all?

Thanks for your comments.
 
  • #5
Idealy, the direction of the friction is considered the opposite of the direction in which the subject is traveling. However, the direction and the magnitude of the forces don't seem to match up very well, it might just be me, but the question you posted here is kind of messy, if you organize the question a bit and write it clearly, I might be able to help you more, and maybe draw a diagram.
 
  • #6
The question really goes like this

Pardon the messiness and thank you for responding. The question is worded this way:

A motor boat is towing 2 skiers. At a particular moment, the boat exerts a force of 457 Newtons East on the 1st skier and a force of 525 Newtons East 30 degrees South on the 2nd skier. If the boat is moving at a CONSTANT velocity and the drag of friction is 325, find the force that propels the boat. [Key's answer is 1274 Newton East 16 degrees South]

Earlier, someone commented that what the question was really asking was about the reaction force. Can you please comment some more?

I tried looking at all the forces acting on each subject: skier1, skier 2 and the boat. Correct me if I'm wrong but if I draw a free-body diagram on each subject, the forces acting on skier1 alone are the force with which the boat pulls on it [457 Newtons East] and friction which is opposes it AND upon resolving the component of forces along the horizon, the sum of the forces is 0 (since due to motion of constant velocity). Similarly, resolving the components on skier2, the sum of the forces is 0 (due to constant velocity) as well. But what I don't understand is how the drag friction comes into play which is 325 Newtons. Shouldn't this drag friction be the same for all three subjects? Aren't all three subjects moving at a constant velocity, too?

Thanks again.
 
  • #7
Constant velocity in a medium like water may assume constant viscous force on an object: F(v)=kv=ma. The skiers have friction, a force resolvable into forward and sideways components, biased according to the direction of their skis relative to the boat (ignoring the bias of the propeller).
 
  • #8


Originally posted by craptacular
A motor boat is towing 2 skiers. At a particular moment, the boat exerts a force of 457 Newtons East on the 1st skier and a force of 525 Newtons East 30 degrees South on the 2nd skier. If the boat is moving at a CONSTANT velocity and the drag of friction is 325, find the force that propels the boat. [Key's answer is 1274 Newton East 16 degrees South]
This seems straightforward. Consider all the forces on the boat. The two skiers exert forces on the boat (use Newton's 3rd law). These forces must be balanced by the force propelling the boat minus the drag. (The drag and the propelling force are along the same line.) All forces add to zero, since it moves at constant velocity.

So... add up the forces due to the skiers. Call the (vector) sum Fskiers. The propelling force minus the drag must be equal and opposite Fskiers.
Shouldn't this drag friction be the same for all three subjects? Aren't all three subjects moving at a constant velocity, too?
Don't worry about the skiers. Since they are also moving at constant velocity (we presume) the net force on them must be zero as well. But who cares? (No reason to think that the drag would be the same for all three!)
 
  • #9
Thank You Loren B., and fffbone for your comments. I think I know how to tackle this problem now although I still welcome your and anyone else's worked out solution to this problem. Thank you for the good ideas.

Yours truly,
Michael (aka craptacular)
 

What are balanced forces?

Balanced forces are forces that are equal in size and opposite in direction, resulting in a net force of zero. This means that the object will remain stationary or continue moving at a constant velocity.

What is the difference between balanced and unbalanced forces?

The main difference between balanced and unbalanced forces is that balanced forces result in a net force of zero, while unbalanced forces result in a net force that causes a change in motion. Balanced forces do not cause objects to accelerate, while unbalanced forces do.

How do you calculate balanced forces?

To calculate balanced forces, you must add all of the forces acting on an object and determine if they are equal in size and opposite in direction. If they are, the forces are balanced and the net force is zero. If they are not, the forces are unbalanced and the net force will cause a change in motion.

Can balanced forces ever cause an object to move?

No, balanced forces do not cause objects to move. This is because the net force is zero and there is no acceleration. However, balanced forces can keep an object in motion at a constant velocity.

What are some examples of balanced forces?

Some examples of balanced forces include a book sitting on a table, a person standing still on the ground, and a car traveling at a constant speed on a straight road. In each of these examples, the forces acting on the object are equal in size and opposite in direction, resulting in a net force of zero.

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