Free Body Diagram of Car on Mountain

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Discussion Overview

The discussion revolves around the forces acting on a car positioned at the top of a mountain while moving with an initial velocity. Participants explore the implications of different interpretations of the scenario, including the effects of gravity and the nature of the road surface, as well as the representation of initial velocity and acceleration.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants question whether the only forces acting on the car are the normal force and gravity, suggesting that other forces may need to be considered depending on the context.
  • There is a discussion about the assumptions made in physics problems, particularly regarding the neglect of friction and other forces.
  • One participant emphasizes the importance of representing initial velocity and acceleration accurately, particularly in relation to the curvature of the mountain.
  • Another participant points out that the interpretation of "top of a mountain" could imply a flat road, leading to different conclusions about acceleration and the components of gravitational force.
  • There is a noted difference in interpretation regarding the phrasing of the problem, with some participants suggesting that clearer language could help avoid confusion about the scenario being discussed.

Areas of Agreement / Disagreement

Participants express differing interpretations of the scenario, particularly regarding the implications of the car being at the "top of a mountain." There is no consensus on the assumptions that should be made, and the discussion remains unresolved regarding the exact nature of the forces acting on the car.

Contextual Notes

Participants highlight the ambiguity in the problem statement, which may lead to different assumptions about the road's slope and the forces involved. The discussion also reflects varying levels of familiarity with vector decomposition and the representation of forces in free body diagrams.

TimeInquirer
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If a car is on top of a mountain moving with an initial velocity, will it only forces acting on it be the normal force counteracted by the force due to gravity?
 
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No. Is this in relation to a homework problem? Often times you are intended to make assumptions like to ignore certain types of friction, but the intent may be to have you ignore these forces.
 
It was an open based discussion in my physics class after various demos. We often neglected reaction forces such as forces between the tires and the ground. I am mostly interested in how to represent the initial velocity and acceleration of such a vehicle.
 
TimeInquirer said:
If a car is on top of a mountain moving with an initial velocity, will it only forces acting on it be the normal force counteracted by the force due to gravity?
The normal force will be less than the gravitational force. Part of the gravitational force will be used to change the direction of the velocity vector as the car travels in the arc over the crest of the mountain.
 
It depends on what you mean by 'top of a mountain.' I interpret that to mean that the road is flat which means the velocity would be horizontal, and there would be no acceleration (assuming the person is not using the controls to do so). If, on the other hand, the car is going up or downhill then there will be a component of gravity that points along the slope.

If you have experience with vectors you may be able to draw the components of the gravitational force that are parallel and perpendicular to the road without much difficulty. You can use this to find an expression for the acceleration of the car under ideal conditions. If you look up 'block on a frictionless inclined plane' I bet you'll find some more detail (though you should try the diagram yourself first!).
 
side question related to a different problem involving a spring. I calculate the frequency to be 2.65 (which is f= 2pi/w) but the answer is 0.265? What can be the reason for this? My angular velocity w is correct because it was given. Thank you.

I have noticed it is because of the way I put it into the calculator sqrt(4/1.4)/2pi vs 1.69/2pi
 
If you are calculating frequency your formula is incorrect. Check your units (angular velocity has units of inverse seconds).
 
brainpushups said:
It depends on what you mean by 'top of a mountain.' I interpret that to mean that the road is flat which means the velocity would be horizontal, and there would be no acceleration (assuming the person is not using the controls to do so).
We clearly have a difference in interpretation here. In the problem statement, they didn't have to mention that it was on the top of a mountain if they didn't expect you to take into account the curvature (and, instead, assume the car was on a flat horizontal surface).

Chet
 
I agree with you 100%, but why not say 'on a hill' or something? 'Top of a hill' to me says something different. I think you're right that the author of the question intends to discuss the component of gravity on a sloped surface.
 
  • #10
brainpushups said:
I agree with you 100%, but why not say 'on a hill' or something? 'Top of a hill' to me says something different. I think you're right that the author of the question intends to discuss the component of gravity on a sloped surface.
I never said that. I said the author intended us to consider a curved mountain surface when the car is at the peak of the mountain.
Chet
 
  • #11
Yes, after reading your initial post again I see that is what you meant. I think we can probably agree that the question could have been phrased more clearly and leave it at that.
 
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