Will the car make it to the top of the hill?

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Homework Help Overview

The problem involves a 1500 kg car approaching a frictionless hill while running out of gas at a speed of 10 m/s. The main question is whether the car will reach the top of the hill, with discussions focusing on the forces acting on the car and energy conservation principles.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the car's acceleration and the forces acting on it, including gravitational force and the absence of friction. Questions about kinetic and gravitational potential energy are raised, along with attempts to apply energy conservation principles.

Discussion Status

Some participants have identified the correct speed of the car and acknowledged the lack of friction. There is ongoing exploration of the forces acting on the car, with suggestions to draw a free body diagram to clarify the situation. Multiple interpretations of the problem are being discussed without a clear consensus.

Contextual Notes

The problem is constrained by the assumption of a frictionless surface, which raises questions about how the car's motion is affected by gravitational forces alone.

Dillion
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Homework Statement


A 1500 kg car is approaching an icy (i.e. frictionless) hill as shown below. The car then runs out of gas traveling at a speed of 10 m/s. a) Will the car make it to the top of the hill?

picture is attached

Homework Equations



vf^2 = vi^2 + 2ax[/B]

The Attempt at a Solution



Vf is 0. Vi is 10. x is 10 (sin30 = 5/x)

0 = 0 +10a

i'm lost here at acceleration. If the car is running out of gas, how are we supposed to know how much it is slowing down by? :(
 

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What force causes the car to slow down?

Are you familiar with kinetic energy? and gravitational potential energy?
 
billy_joule said:
What force causes the car to slow down?

Are you familiar with kinetic energy? and gravitational potential energy?

1/2mvi^2 + mgh = 1/2mvf^2 + mgh

75000+73500=750vf^2+147000

vf = 1.4

as for what forces cause the car to slow down...i would say friction but this problem says frictionless.
 
You've found the correct speed.
You're right that there is no frictional force. What other forces are acting on the car? Can you draw a free body diagram? The relevant force is the same force that's stopping you from floating up out of your chair right now..
 
billy_joule said:
You've found the correct speed.
You're right that there is no frictional force. What other forces are acting on the car? Can you draw a free body diagram? The relevant force is the same force that's stopping you from floating up out of your chair right now..

Gravitational force. The gravitational force will point straight down which will be (9.8 x 1500) = 14700 N.
 
Dillion said:
Gravitational force. The gravitational force will point straight down which will be (9.8 x 1500) = 14700 N.
Correct. If we draw a free body diagram and define our positive x direction to be parallel to the incline and to the right then there will be some component of the gravitational force acting in the negative x direction. That is the force decelerating the car.
You could've also found the same answer you found via conservation of energy by applying Newtons second law. Though, in this case, the method you did use is faster/simpler.
 

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