a spring loaded "cannon" on a wheeled car fires a metal ball vertically. the car is given a push and set in motion horizontally with a constant velocity. A pin is pulled with a string to launch the ball, which travels upward and then falls back into the moving cannon everytime. why does the ball always fall back into the cannon? explain
The cannon and the ball are moving with constant velocity in the horizontal plane all during this experiment. The cannon pushed the ball UP. It did not change the velocity horizontal plane.
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To understand why the ball always falls back into the moving cannon, we need to consider two key factors: the horizontal motion of the car and the vertical motion of the ball.
1. Horizontal Motion of the Car:
When the car is set in motion with a constant velocity, it continues to move forward without any acceleration. This means that the car maintains its horizontal velocity throughout the entire motion.
2. Vertical Motion of the Ball:
When the pin is pulled, the spring-loaded cannon launches the metal ball vertically. Initially, the ball moves upward due to the force applied by the spring. However, once the ball leaves the cannon, it is only subject to the force of gravity acting downwards.
Now, let's analyze the ball's motion at different points in time:
a. When the ball is launched upwards:
At this point, the ball has the same initial horizontal velocity as the car. However, since the ball is given an upward vertical velocity, it starts to rise while the car keeps moving forward.
b. At the highest point of the ball's trajectory:
Here, the ball reaches its maximum height and begins to fall back down due to gravity. However, since it initially had the same horizontal velocity as the car, the horizontal distance covered by the ball while falling is the same as the distance covered by the car during that time.
c. When the ball falls back into the moving cannon:
As the ball falls back down, it regains its initial horizontal velocity as it re-enters the cannon. Since the car has been continuously moving forward at a constant velocity, and the ball's vertical motion takes the same amount of time for each upward trajectory, the car and the ball coincide in the horizontal position each time the ball falls back into the cannon.
In summary, the ball always falls back into the cannon because its vertical motion takes the same time for each upward trajectory, and the car maintains its constant horizontal velocity. This ensures that the ball and the cannon are in the same horizontal position when the ball falls back down, allowing it to re-enter the moving cannon.
The ball always falls back into the moving cannon because of the principle of inertia and the force of gravity acting on the ball.
Firstly, let's consider the concept of inertia. The car and the ball are initially at rest, so they have zero velocity. When the car receives a push and starts moving horizontally with a constant velocity, according to Newton's first law of motion, the ball tends to maintain its state of rest or motion in a straight line. This means that as the car moves forward, the ball will also move forward with it.
Now, let's focus on the vertical motion of the ball. When the pin is pulled and the ball is launched vertically, it experiences an upward force due to the spring-loaded cannon. As a result, the ball gains upward velocity and starts moving against the force of gravity.
However, gravity is still acting on the ball, pulling it downward. This downward force gradually slows down the upward motion of the ball until it eventually comes to a stop and starts falling back down towards the Earth.
During this upward and downward motion, the horizontal velocity of the car remains constant. As a result, when the ball falls back down, it still has the same horizontal velocity as the car. The ball and the car are essentially moving together, and due to the inertia of the ball, it falls back into the moving cannon.
In simpler terms, the ball falls back into the moving cannon because both the ball and the car have the same horizontal velocity, and the force of gravity acting on the ball does not affect its horizontal motion. Therefore, regardless of the upward and downward motion of the ball, it maintains the same horizontal velocity as the car and falls back into the cannon.