Maximizing Acceleration on an Icy Hill: A Work and Energy Approach

[Arsham]

Consider a car (Mass m) above a hill (Slip angle is alpha) , which is covered with ice (Snow). if the car slips down the hill, in which circumstances its acceleration would be higher?
1- The driver push the break and hold it.
2- The driver let the car slips freely.

 

[tiny-tim]

Welcome to PF!

Consider a car (Mass m) above a hill (Slip angle is alpha) , which is covered with ice (Snow). if the car slips down the hill, in which circumstances its acceleration would be higher?
1- The driver push the break and hold it.
2- The driver let the car slips freely.

Hi Arsham! Welcome to PF!

Show us what you think, and why, and then we'll know how to help.

 

[Arsham]

Hi Arsham! Welcome to PF!

Show us what you think, and why, and then we'll know how to help.

The idea is simple. Just consider three situations:
1- (Holding break)The wheels cannot rotate, where the car and its wheels should be treated as a solid body, which is a simple case (I assume!)
2- (Slipping freely)The wheels can rotate but because of the small friction, they won't rotate. I don't know if this situation is possible or not, but if it is, I assume that it should be like No.1. Again considering the whole car as a rigid body and therefore the free diagram would be similar to no.1's
3-(Slipping freely)The wheels can rotate and they will. My question is in this part. How the free diagram should be sketched? what would be the applied forces? How the friction can be calculated? How the linear acceleration can be calculated?

 

[tiny-tim]

energy

Hi Arsham!

(btw, it's "brake" when it's to do with a vehicle )

… How the free diagram should be sketched? what would be the applied forces? How the friction can be calculated? How the linear acceleration can be calculated?

In a case like this, forces are confusing …

try using energy and work done instead …

if the wheels are rotating, how does that affect the energy and the speed and the work done by friction?

 

[Arsham]

Thanks for the hint!

I would try to solve it with work & energy. Although I have to check my books to remember the procedures! Anyhow, many thanks for your comments and help. Will let you know if I succeed.