Ballistic Pendulum Prelab

Due start of class, week of Nov 5

Name:                                                                  Section:                   

In the ballistic pendulum experiment the prediction of the range depended on the height the pendulum arm swung up and the height of the chair. Equation (8) of your write-up states that the range, $x$. is given by

$$x = \frac{(m+M)}{m} 2 \sqrt{hy}$$

and .

$$\frac{\Delta x}{x} = \frac{\Delta y}{2y} = \frac{\Delta x}{2h}.$$

Let $y = 0.55$ m, $\Delta y=0.005$ m, $h= 0.090$ m, $\Delta h=0.002$ m, $m= 50$ g and $M = 200$ g. What is the relative uncertainty in $y$ and $h$? Set $h$ to 0.09, change $y$ by 0.01 and find the change in the range. Then keep $y$ set to 0.55 and change $h$ by 0.002 and find the change in range. In each case compare the change to $\Delta y/2y$ and $\Delta h/2h$. Comment on the contribution to the uncertainty of the range by each variable and why $y$ has a larger absolute uncertainty but smaller contribution to the uncertainty of $x$.