A ball is rolled down a frictionless incline at some angle [tex]\theta[/tex] below the horizontal. If you increase the angle of the incline by a factor of two (make the ramp steeper downward by twice as much), does the ball roll down at double the speed?(adsbygoogle = window.adsbygoogle || []).push({});

Here is what I said:

No. because of the following relation

[tex] \[

\begin{array}{l}

Speed = \sqrt {\left( {v_i \cos \left( \theta \right)t} \right)^2 + \left( {h + v_i \sin \left( \theta \right)t + \frac{1}{2}gt^2 } \right)^2 } \\

2Speed \ne \sqrt {\left( {v_i \cos \left( {2\theta } \right)t} \right)^2 + \left( {h + v_i \sin \left( {2\theta } \right)t + \frac{1}{2}gt^2 } \right)^2 } \\

\end{array}

\]

[/tex]

Where [tex]v_i[/tex] is the initial velocity of the ball, [tex]\theta[/tex] is the angle of the ramp below the horizontal, [tex]h[/tex] is the initial height of the ball, [tex]g[/tex] is the acceleration due to gravity, and [tex]t[/tex] time.

because

[tex]

\[

\begin{array}{l}

\cos (\theta ) \ne \cos (2\theta ) \\

\sin (\theta ) \ne \sin (2\theta ) \\

0 < \theta < \frac{\pi }{2} \\

\end{array}

\]

[/tex]

Is this a correct way to show that increasing the downward angle by a factor of two does not double the speed of the object rolling down the incline?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Ball rolling down frictionless incline - Does doubling the angle double the speed?

**Physics Forums | Science Articles, Homework Help, Discussion**