MHB Darshit P's question at Yahoo Answers regarding conservation of energy

[MarkFL]

Here is the question:

I need help in physics!?

What minimum speed does a 200g puck need to make it to the top of a 3.7m -long, 26 degrees frictionless ramp?

Here is a link to the question:

I need help in physics!? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

 

[MarkFL]

Hello Darshit P,

Initially the puck has kinetic energy, and finally it has gravitational potential energy, and since only conservative forces are at work, we may equate the two:

$$\frac{1}{2}mv_i^2=mgh$$

Multiply through by $$\frac{2}{m}$$:

$$v_i^2=2gh$$

Take the positive root since we are asked for speed:

$$v_i=\sqrt{2gh}$$

Now, we need to know the height $h$ of the ramp. Let $L$ be the length of the ramp and $\theta$ be the angle of inclination. From the definition of the sine function, we may state:

$$\sin(\theta)=\frac{h}{L}\,\therefore\,h=L \sin(\theta)$$

and so we have:

$$v_i=\sqrt{2gL\sin(\theta)}$$

Now, plugging in the given and known data, we find:

$$v_i=\sqrt{2\left(9.8\,\frac{\text{m}}{\text{s}^2} \right)(3.7\text{ m})\sin\left(26^{\circ} \right)}\approx5.64\,\frac{\text{m}}{\text{s}}$$

To Darshit P and any other guests viewing this topic, I invite and encourage you to post other algebra based physics problems in our http://www.mathhelpboards.com/f22/ forum.

Best Regards,

Mark.