Solve Fun Power Question: Frictional Force & Velocity

[Panphobia]

Homework Statement

Found a pretty fun question on power from one of my friends old physics exams just wanted to see if I was doing it right so far.

The Attempt at a Solution

So the first thing I did was draw a free body diagram and used Newtons Second law so

ƩFx: F - (250 + 0.7v^2) - mgsin10 = ma

Says that the driving force F must overcome the frictional force, so then ma = 0 and F = 250 + 0.7v^2 + mgsin10. A little stumped here, I am trying to find out the velocity, but I have two unknowns and one equation (please don't give me the answer, I want to solve it myself)!

 

[tiny-tim]

Hi Panphobia!

(try using the X² and X₂ buttons just above the Reply box )

… ƩFx: F - (250 + 0.7v^2) - mgsin10 = ma

Says that the driving force F must overcome the frictional force, so then ma = 0 and F = 250 + 0.7v^2 + mgsin10. A little stumped here, I am trying to find out the velocity, but I have two unknowns and one equation …

I'm confused … the question says a = 1 and v = 27.

 

[Panphobia]

But that is initial, the v is always changing, and in my head I was thinking that there is a maximum velocity because of the air resistance. Oh my was I overthinking that? But anyway I was actually talking about deriving an expression for the power P that is required to drive the wheels. The other part is pretty easy.

 

[Panphobia]

Then F = 1150 + 250 + 0.7(27)^2 + (1150)(9.8)sin10
P = Fv
P = 3867.3*27
= 104 kW or 140 hp

Deriving would just be without numbers right?

 

[tiny-tim]

Then F = 1150 + 250 + 0.7(27)^2 + (1150)(9.8)sin10
P = Fv
P = 3867.3*27
= 104 kW or 140 hp

(i haven't checked your calculations, but …)

yes, those equations look correct ​

… I was actually talking about deriving an expression for the power P that is required to drive the wheels.

Deriving would just be without numbers right?

an expression would be without numbers, yes