How Does Angle Affect Speed and Distance of a Toy Car on a Ramp?

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SUMMARY

The discussion focuses on the relationship between the angle of an inclined ramp and the speed and distance traveled by a toy car. The angles considered range from 10 to 20 degrees, with participants predicting significant differences in performance, particularly between the 12 and 14-degree angles. Key equations used include Fnet = ma and vf^2 = vi^2 + 2ad, which relate to the forces acting on the car and its motion. The consensus indicates that as the angle increases, the gravitational force component driving the car down the ramp outweighs friction, leading to increased speed and distance.

PREREQUISITES
  • Understanding of Newton's second law (Fnet = ma)
  • Knowledge of kinematic equations (vf^2 = vi^2 + 2ad)
  • Familiarity with gravitational force components (Fgx = mg sin(theta))
  • Concept of friction and its impact on motion (coefficients of friction)
NEXT STEPS
  • Derive equations for speed and distance as functions of angle (theta)
  • Explore the effects of varying coefficients of friction on toy car performance
  • Conduct experiments to measure speed and distance at different angles
  • Learn about energy conservation principles in inclined planes
USEFUL FOR

Students studying physics, educators teaching mechanics, and hobbyists interested in toy car dynamics and ramp experiments.

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Homework Statement



The toy car has been placed on an inclied ramp facing downward. angles are as follows 10degrees , 12 degrees , 14 degrees , 16degrees , 18 degrees, 20 degrees.

after acceleratin down the ramp for 15cm, the car continues on a leveled plane.
between which consecutive angles will show a big difference in their speed and distance traveled.



Homework Equations



Fnet = ma
Fgx - Ff = ma

vf ^2 = vi ^2 + 2ad

The Attempt at a Solution



my prediction is that there will be biggere difference in 12 and 14 degree angles because the
car hasnt put to its full potential yet and at low angles like this one, it is easier to see the performance increase.
or would it be the other way around 16 degree angle and 18 degree angle?
i know that as the angles increase the x-component of the gravitational force increases more than the frictional force which is the reason why the car travels further and further.

can someone please help with this concept Help !
 
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Derive an equation for the speed and for the distance traveled as a function of theta. Then decide what the answer should be based on those.
 
what do you mean as a function of theta?

Fgx - Ff = ma
mg (sin theta - coeff of static friction ) = ma
g (sin theta - coeff of static friction ) = a


vf ^2 = vi ^2 + 2ad
0 = vi^2 + 2(g(sin theta - coeff of static friction))d

and solve for d? , is this what you mean by function of theta? I am don't understand
Help
 

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