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

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Homework Help Overview

The discussion revolves around a scenario involving a car on an icy hill, focusing on the conditions affecting its acceleration as it slips down. The subject area includes concepts from mechanics, particularly work and energy, as well as friction and motion dynamics.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore different scenarios regarding the car's acceleration when the driver either holds the brake or allows the car to slip freely. Questions arise about the implications of wheel rotation, the treatment of the car as a rigid body, and the calculation of forces and friction in these contexts.

Discussion Status

Some participants have offered hints and suggestions, such as considering energy and work done instead of focusing solely on forces. There is an acknowledgment of confusion regarding the forces involved, and participants are encouraged to clarify their thoughts and reasoning to facilitate further discussion.

Contextual Notes

Participants note the importance of understanding the effects of friction and the conditions under which the car's wheels may or may not rotate. There is also a mention of checking textbooks for procedures related to work and energy, indicating a reliance on external resources for clarification.

Arsham
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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.
 
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Welcome to PF!

Arsham said:
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. :smile:
 


tiny-tim said:
Hi Arsham! Welcome to PF!

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

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?
 
energy

Hi Arsham! :smile:

(btw, it's "brake" when it's to do with a vehicle :wink:)
Arsham said:
… 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? :smile:
 


Thanks for the hint! :redface:

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

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