Solving Ice Boat Problem Homework Statement

[Cole07]

Homework Statement

A 600- kg ice boat moves on runners on essentially frictionless ice. A steady wind blows, applying a constant force to the sail. At the end of an 7- s run, the acceleration is 0.4 m/s2. What was the acceleration at the beginning of the run? Answer: 0.4m/s

What was the force due to the wind?
Answer:240N

What retarding force must be applied at the end of 4 s to bring the ice boat to rest by the end of the next 4 s? (The wind is still blowing. Assume the boat was at rest at time t = 0.)
Answer:?


2. Governing equations

Vf=Vi+at

The Attempt at a Solution

I understand the first two questions i have them figured out but the last one i can't seem to figure out. i used the equation

0.4=0+a(4)

and i get a=0.1 which i multiply by 600kg using the formula EF=ma and get EF=60N i don't understand why this is wrong any help would be appreciated.

 

[berkeman]

If you apply the same force as the wind, then what will the velocity do? What force did the boat feel for the first 4s? If that force stopped suddenly at 4s, what force would it take to stop the boat in the next 4s? What if the wind force stays there -- how much total reverse force is required to stop the boat in that next 4s?

 

[Cole07]

i reread the question and realize that the finally velocity needs to be zero would that make Vi=0.4

 

[berkeman]

It says the boat was at rest at t=0, so Vi=0.

Re-read my hints about what the situation is if the wind stops at t=4s.

 

[AlephZero]

i reread the question and realize that the finally velocity needs to be zero would that make Vi=0.4

In the first part, you have an acceleration of 0.4 for 7 seconds. What does that make the velocity after 7 seconds?

 

[Cole07]

If you apply the same force as the vind the velocity slows down,would it not feel a force of 60 for the first four seconds?

 

[berkeman]

If you apply the same force as the vind the velocity slows down,would it not feel a force of 60 for the first four seconds?

You calculated a wind force of 240N. If you let the boat accelerate for 4s with that force at its stern, and leave the wind on for t>4s and push back on the bow with 240N, what happens to the velocity of the boat (hint -- it does not slow down). If you remove the wind for t>4s and push back with 240N, what happens to the velocity?

 

[Cole07]

In the first part, you have an acceleration of 0.4 for 7 seconds. What does that make the velocity after 7 seconds?

would it be 2.8? that seems weird though.

 

[berkeman]

would it be 2.8? that seems weird though.

Yeah, I don't think the question about 7s is relevant to the question. The way I read the 3rd question is what do you have to do to stop the boat by applying a force for the time period 4s<t<8s.

 

[Cole07]

You calculated a wind force of 240N. If you let the boat accelerate for 4s with that force at its stern, and leave the wind on for t>4s and push back on the bow with 240N, what happens to the velocity of the boat (hint -- it does not slow down). If you remove the wind for t>4s and push back with 240N, what happens to the velocity?

it would be kind of like a wall and would not move anywhere

 

[berkeman]

it would be kind of like a wall and would not move anywhere

No. Think about it. F=ma. If the sum of the forces is zero, the acceleration is zero, but that doesn't constrain the velocity. What determines the velocity? What was the boat doing just before 4s?

 

[Cole07]

Just before 4s the boat was moving with a constant velocity

 

[berkeman]

Just before 4s the boat was moving with a constant velocity

Correct. If the sum of the forces is zero, the change in velocity has to be zero. That's what your initial equation:

Vf = Vi + at

expresses. Now, Tell us what would happen if the wind stopped at t=4 and you applied the 240N backwards for 4s. Then tell us the solution to this problem.

 

[Cole07]

the boat would then slow down

 

[berkeman]

Keep going. Figure it out...you're almost there!

 

[Cole07]

i don't understand what you mean by the change in velocity must be zero does this mean the Vf and Vi are the same number, and i don't understand how to apply 240N to this equation.

 

[berkeman]

the boat would then slow down

How long would it take it to stop? Remember, the wind's force of 240N applied for the first 4s got it up to some velocity. If that wind stops at 4s, and you push back with the same 240N force on the bow, how long does it take the boat to stop?

And then the next step to get to the final solution for -3- is to keep the 240N wind force blowing for t>4s, and ask yourself what the total reverse force is that you must apply on the bow to stop in the next 4s.

 

[Cole07]

ok the acceleraton would be 0.4 the final velocity would be zero because you want to find t when the boat is stopped so to find the vi would be how fast the boat is going with the wind pushing right. so i get that it take 4s for the boat to stop.

 

[AlephZero]

Yeah, I don't think the question about 7s is relevant to the question. The way I read the 3rd question is what do you have to do to stop the boat by applying a force for the time period 4s<t<8s.

Yes you are right. Sorry, I misread the question. I thought the boat accelerated for 7 sec and the you had to stop it in ANOTHER 4 sec (i.e. from 7 sec to 11 sec). Forget about that velocity of 2.8 (even though it was the right answer).

 

[Cole07]

thats ok it happens i just really don't get this question i got the first two but this one just confuses me.

 

[berkeman]

ok the acceleraton would be 0.4 the final velocity would be zero because you want to find t when the boat is stopped so to find the vi would be how fast the boat is going with the wind pushing right. so i get that it take 4s for the boat to stop.

Good, almost done. Now add back in the wind force. You can see that it will take more than 240N to stop the boat now in the 4s, right? How much more... ?

 

[Cole07]

ok i got it 480N. thank you so much for your time i really do appreciate it.

 

[berkeman]

Woo-hoo! Where's that dancing banana smiley-face thing...?