Understanding Tension Forces in a Motorboat and Water Skiing Scenario

[mHo2]

Homework Statement

A high powered motorboat pulls a water skier who is testing some prototype skis. A heavy-duty spring scale that is attached to the tow rope reads 1000 N. The forces of air resistance and water resistance on the skier combine to give a total drag force of 750N

Determine the tension on the rope

Homework Equations

N/A

The Attempt at a Solution

At first, these are the two answers i had:

1) 1000N
Because this is what the spring scale reads, this is what force is being applied in the 'left' direction.
2) 1750N
Because this is the addition of all of the forces. If i can remember correctly, if i am pulling on two sides of a spring scale, it will add up all of the forces both in the left and right direction.

However when looking at the answer key, the answer was 750N.

Why is this? It doesn't seem to compute for me. Is the tension on the rope the addition of all the resistive forces?

I don't think i fully understand the definition of 'tension'.

Thanks!

 

[PhanthomJay]

The tension in the rope is given as 1000 N? What question are you trying to answer? Tensions don't add lke that, if I pull on you with a rope with a force of 1000N, then per Newton 3, you pull on me with a force of 1000 N, and the rope tension is 1000 N. But again, you gave an answer to a question you did not state.

 

[mHo2]

The tension in the rope is given as 1000 N? What question are you trying to answer? Tensions don't add lke that, if I pull on you with a rope with a force of 1000N, then per Newton 3, you pull on me with a force of 1000 N, and the rope tension is 1000 N. But again, you gave an answer to a question you did not state.

The question is 'Determine the tension on the rope'
The spring scale connected to the rope, reads 1000N. If you read through my first part of my question, perhaps you will have a better idea of what I'm trying to ask?

 

[PhanthomJay]

The question is 'Determine the tension on the rope'
The spring scale connected to the rope, reads 1000N. If you read through my first part of my question, perhaps you will have a better idea of what I'm trying to ask?

The actual question was not to determine the tension on the rope

I am confused as to wheter that is the question or is not the question. Please clarify.

 

[mHo2]

I am confused as to wheter that is the question or is not the question. Please clarify.

The actual question wasn't to determine the tension on the rope.. it was kind of a side question, my fault for adding that in, ignore that last sentence. The original post has been edited to remove it.

 

[PhanthomJay]

If the spring scale reads 1000 N, it is reading the tension force in the rope.

 

[mHo2]

If the spring scale reads 1000 N, it is reading the tension force in the rope.

Odd. I would agree, but can you elaborate? I understand why there would be 750N of tension on the rope, to compensate for the 750N of drag force, then another 250N of tension to accelerate the skier?
I'm pretty much just asking what is causing the rope to experience 1000N of tension.

 

[PhanthomJay]

It would be good if you could state the entire question, but the high powered motor boat while accelerating is exerting a tension force in the rope of 1000 N on the skier. The total force delivered by its engine motor must be greater than that, since it must overcome the boat's mass as well. The net force on the skier is 250 N (F_net = F_t - F_r = 1000 -750 = 250). That net force accelerates the skier at the same rate, per Newton 2.

 

[mHo2]

It would be good if you could state the entire question, but the high powered motor boat while accelerating is exerting a tension force in the rope of 1000 N on the skier. The total force delivered by its engine motor must be greater than that, since it must overcome the boat's mass as well. The net force on the skier is 250 N (F_net = F_t - F_r = 1000 -750 = 250). That net force accelerates the skier at the same rate, per Newton 2.

Unfortunately that was the whole question. There was a diagram, with a spring scale attached to a boat, and a skier attached to a rope which was in turn attached to that spring scale.

I think it was just a really badly worded question.

Thanks!