Solving Motion of a Ball Fired by Compressed Air

• grothem
In summary, a 50g ball was fired vertically upward from a 1.0-m-tall tube using compressed air. The air exerted an upward force of 2.0N on the ball while in the tube. To determine the height the ball reached above the top of the tube, the equation ma=F+mg was used to find the acceleration of the ball, which was found to be 30.2 m/s^2. To find the height, a kinematics equation connecting initial and final velocities, acceleration due to gravity, and height was used.
grothem
Compressed air is used to fire a 50g ball vertically upward from a 1.0-m-tall tube. The air exerts an upward force of 2.0N on the ball as long as it is in the tube.

How high does the ball go above the top of the tube?

I used ma=F+mg to find acceleration and came up with 30.2 m/s^2. I think from here I need to use a kinematics equation to get the velocity of the ball just as it leaves the tube, but to find the height? I only have acceleration, I don't know which equation to use.

Use the one connecting initial and final velos, g and the height.

I would suggest using the kinematic equation for displacement, which is d = vi*t + 1/2*a*t^2. In this equation, d represents the displacement or height, vi represents the initial velocity (which is 0 since the ball starts from rest), a represents the acceleration (which you have calculated to be 30.2 m/s^2), and t represents the time. Plugging in these values, we get d = 0 + 1/2 * 30.2 * t^2.

To find the time, we can use another kinematic equation, vf = vi + a*t, where vf represents the final velocity (which is also 0 since the ball stops at its maximum height), vi represents the initial velocity (again, 0), a represents the acceleration (30.2 m/s^2), and t represents the time. Solving for t, we get t = vf/a = 0/30.2 = 0 seconds.

Therefore, the ball reaches its maximum height in 0 seconds, and we can plug this value back into our first equation to find the displacement or height. d = 0 + 1/2 * 30.2 * (0)^2 = 0 meters. This means that the ball reaches a maximum height of 0 meters, which makes sense since it is fired vertically upward from a 1.0-m-tall tube.

In order to find the height above the top of the tube, we need to add the initial height of the tube to the maximum height of the ball. So the final answer would be 1.0 meters.

I would also like to note that this calculation assumes ideal conditions and does not take into account factors such as air resistance, which may affect the actual height reached by the ball. Further experimentation and data collection may be necessary for a more accurate calculation.

1. How does compressed air affect the motion of a fired ball?

Compressed air provides the force necessary to propel the ball forward, causing it to accelerate and travel in a specific direction.

2. What factors influence the trajectory of a ball fired by compressed air?

The angle of the barrel, the initial velocity of the compressed air, the mass and size of the ball, and any external forces such as wind resistance can all impact the trajectory of the fired ball.

3. How do you calculate the velocity and acceleration of a ball fired by compressed air?

The velocity can be calculated using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. The acceleration can be determined using the equation a = F/m, where a is the acceleration, F is the force from the compressed air, and m is the mass of the ball.

4. What are the potential hazards of using compressed air to fire a ball?

The high pressure of compressed air can cause the ball to be fired at a dangerous speed. This can result in injury to individuals in the path of the ball or damage to property. It is important to follow safety precautions and use appropriate protective gear when conducting experiments involving compressed air.

5. How can the motion of a ball fired by compressed air be applied in real-world situations?

The principles of motion can be applied in various industries, such as sports (e.g. soccer, basketball), transportation (e.g. rockets, jets), and manufacturing (e.g. assembly line processes). Understanding and controlling the motion of a ball fired by compressed air can lead to advancements in technology and improve efficiency in various fields.

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