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

#### MarkFL

Staff member
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

Staff member
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:

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

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

$$\displaystyle v_i^2=2gh$$

Take the positive root since we are asked for speed:

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

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:

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

and so we have:

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

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

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

To Darshit P and any other guests viewing this topic, I invite and encourage you to post other algebra based physics problems in our Other Topics forum.

Best Regards,

Mark.