Question

A block of clay is suspended as part of a ballistic pendulum. You have a gun that uses compressed air to fire a small 5.00 g ball into the clay. As you change the pressure of the air used to fire the ball, you can adjust the speed of the ball as it emerges from the gun. You fire the ball into the clay at a series of known speeds and measure the height to which the clay rises after the ball embeds within it. Your data are shown in the table below:

Speed (m/s) Height (mm)

100	8.8
110	10.6
120	12.6
130	14.8
140	17.2
150	19.7

Using the "best-fit" line that you drew in Part A, determine the mass of the block of clay. Express your answer in kilograms to two significant figures.

Answer 1

Let the mass of the block is while the mass of the small ball is . By applying the conservation of momentum, and for perfectly inelsatic collision

By using conservation of energy,

Hence we find that height is proportional to the square of velocity. Now plotting the graph between and

From the best fit line, we find that slope of the line is hence