What is the Total Retarding Force Required to Stop a Race Car Using a Parachute?

[ChopSuey]

hi, i m a new member and i m taking this AP physics class that is kind of weird... the teacher doesn't give me any clue of how to do these online homework assignments. I usually takes hours to finish it, but this time it's like half the day and i m still stuck on this one and i would appreciate it if you give me an idea of how to do this :!) by the way, this assignment is actually due in like 11 p.m. tonight so i m in desparate need for help

The parachute on a race car of weight 8970 N
opens at the end of a quarter-mile run when
the car is traveling at 35 m=s.
The acceleration of gravity is 9:8 m=s2 :
What total retarding forcemust be supplied
by the parachute to stop the car in a distance
of 1056 m? Answer in units of N.

 

[mezarashi]

It should quickly be recognized by the given parameters that this is a kinetics problem (energy).
- weight (given)
- g (given)
- m (from W/g)
- initial velocity (given)
- final velocity (given)
- distance (given)

You have an initial kinetic energy, and your final kinetic energy is zero. The drag force will be doing work over a distance of 1056m. How will you approach the question now?

 

[ChopSuey]

um... i think i got it now, thanks. Just one more question, is the total retarding force going to be negative? because it needs a total amount of negative force to stop the race car?

 

[mezarashi]

Well, forces and displacement are vectors. They need to point in certain directions. When you draw out a diagram, just be consistent on which direction you consider as positive and negative. If the displacement of 1056 is positive, then the force vector will be in the negative direction or vice versa. Hope that helps ^^

Edit: hopefully you haven't touched upon air resistance right? I don't remember doing that back in the day (AP Physics C), but just checking, because if this is an air resistance problem, the approach is entirely different and involves a second order differential.

 

[lightgrav]

This is a straightforward Sum of Forces = ma problem,
where you use defiinitions of acceleration and velocity.

the average velocity during deceleration is simple to find;
the duration of deceleration is just distance/avg.velocity.
acceleration is change in velocity / duration.
you're asked for the total (horizontal) Force to cause "ma".

You don't care whether the brakes or air drag caused F.