# Motion and Projectiles Homework-Due tommorow

Two identical steel balls are released from rest above cylinders containing oil as shown in the diagram below.The balls travel vertically until they reach the bottom of the cylinder. The graph below is the velocity-time graph for steel ball A.

Diagram:
-steel ball A is above cylinder container 1 with oil filled to the top
-steel ball B is above cylinder container 2 which has oil filled to half way

Velocity-time Graph:
in the graph steel ball A has a curved line in which as the time goes on the velocity rate decreases but there is still more velocity with more time but less and less until a certain point where the reaction stops.At the end of the curved line there is a line going downwards.

Describe and explain how the motion of steel balls A and B will differ and why.Your answer should include:
-How the velocity and acceleration of steel ball A and B vary with time
-An account of the forces acting and their sizes
-A sketch of the velocity-time graph that would represent the motion of steel ball B (you may wish to draw this over the graph above)

Continue this task on lined paper writing with good English and attach it behind this sheet.

Write as much as you can.

Please help as I'm stuck on this question with no clue and have gone over it many times.
All i have come up with is:
The more the oil the less the friction so the faster the ball moves in the oil so steel ball A would be faster as the oil is filled to the top. Steel ball b first goes through air which has more friction than oil so is slower.

## Unless your oil is magic, it may be slippery but has far more resistance (viscosity) than air. In fact on the scale you are talking about I think the air is effectively friction less and the steel ball being thousands of times as dense as air will fall at about constant acceleration, g, about 9.81 m/s^2

The speed of the steel ball will therefore be proportional to time and distance to time squared in air. That means as long aas it is in air the oath will be parabolic, getting steeper and steeper.

NOW when the ball hits oil, suddenly the world changes. It hits with the same initial speed as the first ball at that height, but rapidly reaches what we all "terminal velocity". That is when the friction up equals the weight down and the speed becomes constant. From then on height versus time is a straight line.

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## Would ball B be faster then, as oil has more friction than air so make the ball slower?

Thank you, could you also help with the things you have to include which is:

Describe and explain how the motion of steel balls A and B will differ and why.Your answer should include:

-How the velocity and acceleration of steel ball A and B vary with time
-An account of the forces acting and their sizes
-A sketch of the velocity-time graph that would represent the motion of steel ball B (you may wish to draw this over the graph above)

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## To fully answer the question and complete the extended writing task, let's break it down step by step:

1. Describe how the motion of steel balls A and B will differ:
The motion of steel balls A and B will differ due to the different forces acting on them. Steel ball A, which is released above cylinder container 1 filled with oil up to the top, will experience less friction compared to steel ball B, which is released above cylinder container 2 with oil filled only halfway. This difference in friction will affect the velocity and acceleration of each ball.

2. How the velocity and acceleration of steel ball A and B vary with time:
Steel ball A will initially have a higher velocity compared to steel ball B. As time passes, the velocity of both balls will decrease due to the opposing force of gravity acting on them. However, the rate at which steel ball A's velocity decreases will be slower than that of steel ball B due to the reduced friction in the oil. As a result, steel ball A will maintain a higher velocity for a longer period of time compared to steel ball B.

The acceleration of both balls will be the same, since both are subjected to the same gravitational force. Acceleration due to gravity is denoted by the value 'g' and is equal to approximately 9.8 m/s^2.

3. Account for the forces acting and their sizes:
For steel ball A, the main force acting on it is the force of gravity pulling it downward. There is also the force of friction between the ball and the oil, which opposes the motion but is smaller in magnitude compared to the force of gravity.

For steel ball B, in addition to the force of gravity, there will be more significant friction acting on it as it descends through the air. This friction arises due to the higher viscosity of air compared to oil. Hence, the force of friction acting on steel ball B will be larger than that acting on steel ball A.

4. Sketch of the velocity-time graph for steel ball B:
Based on the given information, we can deduce that the velocity-time graph for steel ball B will show a similar initial curved line indicating a decrease in velocity with time. However, the curve will be steeper, representing a faster decrease in velocity due to the increased friction caused by the air. Eventually, the graph will flatten out, indicating that the ball has reached terminal velocity. Terminal velocity is the maximum velocity attainable by an object when the drag force equals the gravitational force.

Unfortunately, as an AI text-based bot, I cannot directly draw the velocity-time graph here. However, I recommend taking a sheet of paper and sketching it out yourself based on the description provided.

Remember to write your extended response on lined paper, using proper English, and attach it behind the question sheet. You can expand on the information provided above, adding more details and explanations to ensure a comprehensive and well-structured response. Good luck with your homework!