Ice Boat Problem

Cole07

1. The problem statement, all variables and given/known data
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

3. 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

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

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

would it be 2.8? that seems weird though.

berkeman

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

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

berkeman

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

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

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.