Finding maximum speed (known: Force output, drag, time)

[JohnLCC517]

1. In general, dense fluids (such as water) produce a drag force that is directly proportional to the speed of an object moving through them. Suppose a boat is moving through the water and experiencing a fluid drag force of F=-8 v. Suppose the boat has a motor which can output up to 450 Newtons of force. What is the maximum speed of the boat? If the boat starts from rest at t=0, find the speed of the boat as a function of time.2. To get started I am inclined to find velocity, however, I am not aware of any way in which I can find velocity from force (the 450 Newtons of force output by the motor).3. My initial attempt would be to enlist Newton's 3rd law and set up the equation 450 N = 8v (negative sign removed since the velocity will be measured in the positive direction. From there I could find v as follows; (450 N/8) = v which would further suggest that v = 56.25 N. This would create a drag force equal to the force propelling the boat through the water. From here I'm thinking that I should put my findings into a kinematics equation but there appears to not be enough information to do so. Am I missing something crucial?

 

[SteamKing]

1. In general, dense fluids (such as water) produce a drag force that is directly proportional to the speed of an object moving through them. Suppose a boat is moving through the water and experiencing a fluid drag force of F=-8 v. Suppose the boat has a motor which can output up to 450 Newtons of force. What is the maximum speed of the boat? If the boat starts from rest at t=0, find the speed of the boat as a function of time.2. To get started I am inclined to find velocity, however, I am not aware of any way in which I can find velocity from force (the 450 Newtons of force output by the motor).3. My initial attempt would be to enlist Newton's 3rd law and set up the equation 450 N = 8v (negative sign removed since the velocity will be measured in the positive direction. From there I could find v as follows; (450 N/8) = v which would further suggest that v = 56.25 N. This would create a drag force equal to the force propelling the boat through the water. From here I'm thinking that I should put my findings into a kinematics equation but there appears to not be enough information to do so. Am I missing something crucial?

Yes, quite crucial.

How does anybody starting from rest attain a velocity, i.e., what must happen to that body in order to change the velocity over a period of time from zero to a finite value?

Didn't a chap called Newton have something to say about how forces acting on a body change its motion?

 

[CWatters]

3. My initial attempt would be to enlist Newton's 3rd law and set up the equation 450 N = 8v (negative sign removed since the velocity will be measured in the positive direction. From there I could find v as follows; (450 N/8) = v which would further suggest that v = 56.25 N.

Units?

This would create a drag force equal to the force propelling the boat through the water. From here I'm thinking that I should put my findings into a kinematics equation but there appears to not be enough information to do so. Am I missing something crucial?

Correct. The problem statement is missing something crucial.

 

[JohnLCC517]

Yes, quite crucial.

How does anybody starting from rest attain a velocity, i.e., what must happen to that body in order to change the velocity over a period of time from zero to a finite value?

Didn't a chap called Newton have something to say about how forces acting on a body change its motion?

Guessing that you are alluding to Newton's first law of motion. An external force must act upon an object to change its acceleration vector from zero. In this case the motor is the external force. From there I move to Newton's second law of motion which states "The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object" or the infamous F = ma equation. Knowing the force = 450 Newtons, and that the force in the negative direction (in this case the drag) has to be equal to the Force in the positive direction (due to Newton's 3rd law) I can set up the equation 450 N = -8v which, when manipulated, suggests to me that the mass of the boat is 56 kg and the acceleration is 8 m/s². Does it seem like I am on the right track?

 

[SteamKing]

Guessing that you are alluding to Newton's first law of motion. An external force must act upon an object to change its acceleration vector from zero. In this case the motor is the external force. From there I move to Newton's second law of motion which states "The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object" or the infamous F = ma equation. Knowing the force = 450 Newtons, and that the force in the negative direction (in this case the drag) has to be equal to the Force in the positive direction (due to Newton's 3rd law) I can set up the equation 450 N = -8v which, when manipulated, suggests to me that the mass of the boat is 56 kg and the acceleration is 8 m/s². Does it seem like I am on the right track?

Newton's second law of motion is
F_NET = ma = m (dv/dt)

You are given that the boat motor can produce a thrust of 450 N and that the drag force countering the boat's motion is proportional to the boat's velocity, such that Drag = 8v

What is the net force acting on the boat when it is in motion at speed v?

How is that net force related to the speed of the vessel?

BTW, there is no direct correlation between the mass of a boat and how much thrust its motor can produce.