MAR-23-2015 Trajectories

Trajectories

(Projectile Motion Lab)

Purpose:  To demonstrate our understanding of 2-dimensional kinematics in order to predict the impact point of a projectile (a ball) on an inclined board.

Procedure:  We first assembled the experiment apparatus.  This includes an aluminum "v-channel", steel ball, board, ring stand, clamp, paper, and carbon paper (to know where the ball strikes the floor).  Below is a complete apparatus setup.

(Apparatus on table)

Once this was set up, we used a phone app (Clinometer) in order to determine the angle between the two aluminum "v-channels".  We recorded the angle to be 28.0 degrees (+ - 0.1 degrees).  Then, we released the ball from rest at a set point on the upper "v-channel", and noticed where the projectile landed on the floor.  After seeing this, we then placed carbon paper on the floor in order to record where the projectile would hit an additional five times.

(Carbon paper being set-up in a fixed position via TAPE!!)

After we allowed the ball to drop five additional times, we recorded each mark's horizontal distance from the edge of where it left the lower "v-channel".  

 (Recording horizontal distance traveled from end of lower "v-channel")

Now we've collected all the data necessary to calculate the ball's velocity as it leaves the lower "v-channel".  Once this value is determined, we can predict where the ball should impact an inclined board as depicted below.  

(Inclined board set in place)

We recorded the horizontal distance from the end of the "v-channel" to where the ball impacted the floor to be:

Run 1:   71.4 cm

Run 2:   71.9 cm

Run 3:   72.2 cm

Run 4:   72.2 cm

Run 5:   73.0 cm

avg distance = 72.1 cm

We measured the vertical distance from the end of the "v-channel" to the floor to be:

y = 93.0 cm

Organizing this data together, we can determine the time it took the ball to hit the floor after leaving the lower "v-channel", and then use that determined time to find the value of initial horizontal velocity the ball had when leaving the "v-channel".  This work is depicted below:

(Determining initial horizontal velocity)

Now that we have the initial horizontal velocity, we can predict where on the inclined board the ball will hit, it will be some distance d.  The work to determine d is shown below.

(Determining impact distance on wooden board)

Conclusion:  Sadly, our ball was landing at approx. 0.39 m on the inclined wooden board.  Upon further investigation, I found that our initial angle measurement (between the "v-channels") had been altered, someone nudging the table or even the apparatus slightly could have caused this discrepancy.  Our theoretical calculations were all correct though!