Mechanics Question from Patel (1 Viewer)

[MOP777]

Question 2 from Exercise 7A
I'm hopeless at Mechanics so I'm doing lots of questions to get better.

The combined air and road resistance of a car in motion is proportional to v^2, where v is its speed. When the engine is disengaged the car moves down an incline making an angle sin^-1(1/30) with the horizontal, with a velocity of 30m/s. Find the force required to drive the car up the incline with a steady speed of 24m/s given that the mass of the car is 1200kg.

The answer is 656 N

Edit: I have worked it out myself, however I would still like someone else to attempt the question because I feel my working is a bit fudged so I would like to see how others attempt the question.

 

[Affinity]

Probably same as yours..
1. we know that resisitance r = kv^2, use inforamtion form the first part to work out k:
Total Force in the cirection down the slope: F = gm/30 - kv^2
In particular, F = 0 when v = 30, gives k = gm/27000

The seconf part asks you to find the additional Force F up the slope such that when v is 24, the total resultant force is 0

F - mg/30 - k(24)^2 = 0
F = mg ( 1/30 + 24^2 / 27000)
F = 65.6g = 656 N if you take g = 10.

0 = gm/30 - 900k

k = gm/27000

f - gm/30 - 24^2k

 

[MOP777]

Thanks for that mate, I have another question from Patel

8. A truck of mass 2000kg starts to climb an incline of angle given by theta = tan^-1(1/10). The total resistive force is 2000N
Find the retardation it experiences

 

[physicss]

Hey, I was wondering which part of mechanics is this from?