Calculating Displacement with Friction and Air Resistance

[ImAlwaysConfu]

Homework Statement

A car is rolling down a hill, it has a velocity of 54.22m/sec at the bottom of the hill. When it reaches the bottom of the hill, a fan begins to blow on it causing a drag force of 250N. Also, the tires create a friction coefficient of .1. The car eventually stops due to the Drag Force/Friction. Calculate how far the car will travel before stopping.



I can't figure out how to take into account the drag force. I know that before taking drag force into account, the car can travel 27.66m. I'm not sure if that helps or not. All I need to know is what formula to use and where I implement the drag force! Also, my homework is due TOMORROW AT 3PM EST. Any help before then will be awesome.

 

[WillemBouwer]

How did you come to the 27.66 m? show your calcs without the drag force and I'll help with implementing the drag force...

 

[ImAlwaysConfu]

First, I calculated for the Kinetic Energy which would be 1/2mv^2. 1/2(1700kg)(54.22m/sec) = 46,087J. Next, I calculated the impact friction would have: f=u(coeficcient of friction)F .1(1700)(9.8) = 1,666N. Then I calculted the work that would be done: Work = F(displacement) 46087J = 1,666N(displacement) then I divided 46087 by 1666 and came with 27.66M. If this is incorrect, could you tell me how to do it please? Thanks!

 

[WillemBouwer]

I think if I tell you that you would realize how easy it is. So you have an object working to the right with kinetic energy = 0.5*mv^2 your answer here is incorrect, do the calculation again... Now what is the total forces working against the vehicle? friction and drag, draw a FBD for your vehicle... Your methodology is good and accurate just combine everything now... The total force on the car is not just friction?

 

[Nickie]

To calculate the displacement of the car with friction and air resistance, we can use the following formula:

d = (v^2 - u^2) / 2a

Where:
d = displacement
v = final velocity (in this case, 0 m/sec since the car stops)
u = initial velocity (54.22 m/sec)
a = acceleration (caused by drag force and friction)

To take into account the drag force, we need to calculate the acceleration caused by it. We can use the formula:

a = F / m

Where:
a = acceleration
F = force (250 N)
m = mass of the car

We also need to calculate the acceleration caused by friction, using the formula:

a = μg

Where:
a = acceleration
μ = friction coefficient (0.1)
g = acceleration due to gravity (9.8 m/s^2)

Now, we can plug in the values into the first formula to calculate the displacement:

d = (0^2 - 54.22^2) / 2((250/1000) + (0.1*9.8))

d = -2955.42 / 4.9

d = -603.17 m

Therefore, the car will travel approximately 603.17 meters before stopping, taking into account both the drag force and friction. It is important to note that the negative sign in the final displacement indicates that the car will travel in the opposite direction of its initial velocity.