Abstract

In this experiment we studied the motion of an object in free fall, that is an object being dropped from a certain height to Earth’s surface. In this experiment we tested the idea that no matter what the size, shape, color, etc. of the object if it would still experience the same constant acceleration throughout its fall (short distance). The constant downward acceleration it experiences is due to Earth’s gravitational force (g). We measure the position, and velocity of a ball to get the experimental g. We then measured reaction time with a ruler. We used our data and g, to get an average distance and time.

Report Questions

1. The parabolic curve opens upward in the position vs. time graph, because this graph is measuring the position of the ball from the sensor. The ball is at first falling down and then bounces back up. This would cause the ball to move away from its original position, downward, and then as it hits the floor and bounces back up the graph would show this by curving back up to its original position.

2. The slope of the velocity vs. time graph represents the acceleration of the object. If you were to take the derivative of this graph, you would get the graph for acceleration vs. time. Since the object shows the velocity graph as a straight increasing line, this shows that the slope is constant, which proves that acceleration of this object is a constant nonzero number.

3. The ball bouncing back up from the floor after being dropped represents the ball no longer being in free fall. This is because when an object is in free fall the only force that is acting on it is g, the constant acceleration due to Earth’s gravitational force. When the ball is bouncing back up it is receiving an additional force from the floor, making g not the only thing acting on the object.

4. It is possible for the ball’s velocity and acceleration to point in different directions. This happens when the ball bounces off the floor, as the velocity would be moving in a positive direction. The acceleration would be negative as it is still g based on Earths gravity. Also the acceleration is negative because the velocity is slowing down as it reaches its maximum height at the parabola and becomes 0 at the top.

5. There are moments when the ball’s velocity is equal to 0. This happens twice, once when the object reaches its peak, which is at the top of the parabola. This also happens between hitting the floor and the object still falling. This is because when the ball is in free fall the only thing acting on it is the force of gravity, but when it hits the floor the floor is adding a force. The velocity would be 0 in between these two states. 6. The percent error is calculated from the equation of the (experimental value- the actual value) then divided by the actual value, and then concluded by multiplying by 100 to convert the number to a percent. The experimental value for my group was 10.6m/s2, and the actual value of g is 9.81m/s2. So this would yield the equation ((10.6m/s2 – 9.81m/s2)/ 9.81m/s2) * 100. This gave me a percent error of 8.05%.

One thing that could’ve caused this error is air resistance, although the air resistance is seen as negligible there is still a very small amount acting on the ball adding to the experiment. Another thing that could’ve caused this error was friction from the floor that the ball bounced off of. To reduce these errors, I would include air resistance into the experiment and also use a frictionless surface instead. 7. The average reaction time I got when using the equation was 0.2613 seconds. The uncertainty about this reaction time is that the measurements could be off; your partner may hit the stopwatch a few second after you catch the ruler.

This would cause you to be using times that aren’t precise to get your average reaction time. 8. I would not be able to catch the $100 bill. I figured this out by the equation t (time in seconds)= the square root of (2*D (distance in meters)) divided by g, the acceleration due to gravity. I plugged in .15m for the distance multiplied it by 2, divided this number by 9.81m/s2, which is g, and then concluded by taking the square root of that number. This gave me a time of 0.1749 seconds, which is less time when compared to my reaction time of 0.2613 seconds.

Conclusion

In this experiment, I learned about the force of gravity on an object, and the relation between position, velocity and acceleration. My group was able to determine that the ball accelerating downward to the ground is equivalent to the speed of gravity. We were able to determine this because gravity was the only thing acting on the ball as it was in free fall. We were able to determine that when the ball bounces off the floor an additional force is now acting on the ball from the floor. Due to this we were able to discover that the velocity at its peak is zero, and moving in a positive direction towards its peak whereas the acceleration is moving in the opposite negative direction. Our experimental value was 10.6m/s2 for acceleration and when compared to the actual value of 9.81m/s2 only 8.05% error was seen. This error could be brought about from the air resistance, that although we ignore because it’s a small number it is still acting on the ball, and also the friction from the floor as it is not a frictionless surface.