In class, we completed a lab dealing with the range of a projectile. First, we dropped a metal ball down an inclined channel followed by a horizontal channel. We timed the ball on the horizontal channel and used this time and the channel length to find horizontal velocity of the ball. Then, we used the vertical distance from the tabletop to the floor to find the vertical time (the contraption was set up on a table. eventually we let the ball drop from the table, like a projectile, and predicted its landing point, its range). Finally, we used the horizontal velocity and the vertical time to find the displacement of the ball.
My question is why does this experiment support the premise that the horizontal and vertical components of motion do not affect each other?
The time for the ball to hit the floor would have been independent of the speed of the ball on the horizontal channel. The vertical fall time depends only upon the distance that it falls, if the intial horizontal velocity component is zero.
This experiment supports the premise that the horizontal and vertical components of motion do not affect each other because the ball's motion in the horizontal direction is independent of its motion in the vertical direction.
In this experiment, the metal ball is dropped down an inclined channel and then moves along a horizontal channel. The time it takes for the ball to travel through the horizontal channel is measured, along with the length of the channel. This information is used to calculate the horizontal velocity of the ball.
Next, the vertical distance from the tabletop to the floor is measured, and this distance is used to calculate the vertical time it takes for the ball to fall from the table as a projectile.
Finally, using the measured horizontal velocity and the calculated vertical time, the displacement or range of the ball is determined.
The fact that the horizontal velocity and the vertical time are used separately to calculate the displacement shows that the horizontal and vertical components of motion are treated independently. The horizontal velocity is only influenced by the length of the horizontal channel, while the vertical time is only determined by the vertical distance and gravity.
Therefore, based on the results of this experiment, we can conclude that the horizontal and vertical components of motion are unrelated and do not affect each other.
This experiment supports the premise that the horizontal and vertical components of motion do not affect each other because when we analyze the motion of a projectile, we can consider the horizontal and vertical motions independently. Here's an explanation of how this experiment demonstrates that concept:
1. Dropping the ball down an inclined channel: When the ball is dropped down the inclined channel, its initial velocity is purely vertical. This means that the horizontal component of its motion is zero, while the vertical component is affected by gravity. The time it takes for the ball to travel through the inclined channel is not relevant to the horizontal motion.
2. Timing the ball on the horizontal channel: Once the ball exits the inclined channel and enters the horizontal channel, it continues moving horizontally with a constant velocity until it reaches the end. By timing how long it takes for the ball to travel the length of the horizontal channel, we can determine its horizontal velocity. This part of the experiment helps us to isolate and measure the horizontal component of motion.
3. Measuring the vertical time: Next, the vertical component of motion is determined by measuring the time it takes for the ball to fall from the tabletop to the floor. This allows us to calculate the time it spends in the air, which is crucial to finding the vertical displacement.
4. Calculating the range: Finally, by combining the horizontal velocity obtained from the horizontal channel with the vertical time of flight, we can determine the displacement of the ball. The range of the projectile can then be calculated by multiplying the horizontal velocity by the total time of flight.
By performing these steps, we are able to analyze and calculate the motion of the projectile separately in the horizontal and vertical directions. The results show that the horizontal and vertical components of motion are independent of each other, which supports the premise that they do not affect each other.