Question

the table, to the point vertically below the front of the carl, when at the starting position. in Table-1. (use St Units for all these quantities) the track at the height of 10 em. Make computer ready to record the graph of velocity to its marked starting position. Press the tart recording dats by the I- Set versus time for the cart. Pull the cart up the track red button on the left bottom corner of the monitor screen to s Motion Sensor Release the cart from rest at the t op of the track, make sure you release the cart from the same position each time. craph of velocity versus time on the computer monitor, and determine the slope graph, on the screen, you will be sown how to do this). This slope is the scceleration 3- Enlarge the of the cart down the track . Record the value of a (in m's') in Table-1 5. Lower the end of the track by 1- em for each new angle and record your data in Tal 6 Repeat t step above for a total of 7 angles, until the height of the cart is 4-em. Table-1 Acceleration (a) m/s2 from! computer graph velocity versus time Table-2 Acceleration a (m/s) Height in meters 0.10 m 0.09 m 0.08 m 0.07 m 0.06 m 0.05 m 0.04 m sine

the equation for 'g' using table 2

Answer 1

First we need have the values of $sin\theta$ in table 2.

Plot the graph of acceleration vs $sin\theta$.

Slope of this would give us the value of gravitational acceleration.

This can be seen from following explanation:

From the above diagram, we can write

$ma=mgsin\theta$

$\therefore a=gsin\theta$

$\therefore \frac{a}{sin\theta}=g$

Now when object is sliding along the curved path, the value of angle will keep on changing and from the above equation, we can say that the value of acceleration is dependent on sin of angle.

Therefore the graph which is plotted above will have a constant slope. And from the above equation, we can see that the slope should be equal to the gravitational acceleration.