# Friction Force and Decelerating Boat

• Arman777
In summary, the conversation discusses a problem involving a 1000 kg boat traveling at 100km/h and the frictional force between the boat and water. The frictional force is proportional to the boat's speed and the goal is to find the time required for the boat to slow down to 45 km/h. The solution involves setting up and solving a differential equation using the given data.
Arman777
Gold Member

## Homework Statement

A 1000 kg boat is traveling at 100km/h when its engine is shut off.The magnitude of the frictional force ## \vec f_k## between boat and the water is proportional to the speed v of the boat:##f_k=70v##,where v is in meters per second and ##f_k## is in Newtons.Find the time required for the boat to slow to 45 km/h

## Homework Equations

## \vec F=m \vec a##
##v-v_0=at##

## The Attempt at a Solution

I turned km/h to m/s which its ##100km/h=27.7 m/s## and ##45km/h=12.5m/s##
then ;
##ma=-70v##
here the connfusing part is ##a## decreases when v decreases.Theres no constant decelaration.I thought integral but without distance I stucked.
##∫mdv=∫-70vdt##

I don't know what to do.

Thank you

Arman777 said:
##ma=-70v##
here the connfusing part is ##a## decreases when v decreases.Theres no constant decelaration.I thought integral but without distance I stucked.

Indeed the deceleration is not constant. Note that ##a = dv/dt## and so what you have is a differential equation describing how velocity changes with time. You will need to solve this differential equation.

Arman777
Orodruin said:
Indeed the deceleration is not constant. Note that ##a = dv/dt## and so what you have is a differential equation describing how velocity changes with time. You will need to solve this differential equation.

I didnt learn diff equation.I am fresman student and uni teaches us second year.Like I have no clue

Arman777 said:
.I thought integral but without distance I stucked.
∫mdv=∫−70vdt
That's not the correct equation. You need to separate the variables.
So you can do integrals and differentials separately, right? I guess your only problem is to set up differential equations using the given data?
Arman777 said:
I didnt learn diff equation.I am fresman student and uni teaches us second year.Like I have no clue
As orodruin pointed out, use a=dv/dt.
What will be the equation of the force on the boat? Which force is acting on it?

## 1. What is friction force?

Friction force is a force that opposes the motion of an object. It is caused by the contact between two surfaces and can be affected by factors such as the type of surface, the force pushing the surfaces together, and the roughness of the surfaces.

## 2. How does friction force affect a decelerating boat?

As a boat decelerates, the water exerts a drag force on the boat, which is a type of friction force. This force acts in the opposite direction of the boat's motion, slowing it down. The amount of friction force depends on the speed of the boat, the surface area of the boat that is in contact with the water, and the roughness of the water's surface.

## 3. What factors affect the amount of friction force on a boat?

The amount of friction force on a boat can be affected by the speed of the boat, the surface area of the boat that is in contact with the water, and the roughness of the water's surface. Additionally, the type of surface of the boat and the water can also impact the amount of friction force.

## 4. How does friction force impact the deceleration of a boat?

Friction force is one of the main factors that contributes to the deceleration of a boat. As the boat moves through the water, the friction force acts in the opposite direction of the boat's motion, slowing it down. The amount of friction force can vary depending on the factors mentioned previously, and it can also be affected by other forces acting on the boat, such as wind or currents.

## 5. Can friction force be reduced to increase a boat's deceleration?

Yes, friction force can be reduced to increase a boat's deceleration. This can be achieved by decreasing the speed of the boat, reducing the surface area of the boat that is in contact with the water, or making the boat's surface smoother. However, it is important to note that completely eliminating friction force is not possible, and other factors such as wind and currents can also impact a boat's deceleration.

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