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Motion Graphs Simulation: Thrown and Bouncing Ball

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Motion Graphs Simulation: Thrown and Bouncing Ball

Motion Graphs: Ball Thrown and Bouncing

v8

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What happens

Initial speed, u15.0 m/s

Dropped from1.00 m Bounciness, e0.80

Air resistance

Terminal velocity25 m/s

Where

Positive direction

Simulation controls

Speed0.5×

Which graphs

Displacement against time

Distance against time

Velocity against time

Acceleration against time

Ghost the case without air resistance

Results

Equations

Live values

Time Height above the start Distance travelled Velocity, v Speed Acceleration, a

Displacement is measured from the starting point, so for a thrown ball it returns to zero. Distance keeps adding up, so it ends at twice the greatest height.

With air resistance ignored, the acceleration is constant at g downwards throughout, including at the highest point where the ball is momentarily at rest.

Air resistance here is taken as proportional to the speed, which is the case Stokes\u2019 law describes: F = 6πηrv for a small sphere moving slowly through a fluid. A ball thrown through air is really closer to a drag proportional to the square of the speed, but the effects shown are the same.

With air resistance included the flight is no longer symmetrical. Going up, drag and weight both act downwards, so the ball slows faster than g and reaches a lower height in less time. Coming down, drag acts upwards, so it accelerates at less than g and returns more slowly than it left.

On a bouncing ball the acceleration graph is drawn as a constant value between bounces. The bounce itself involves a very large upward force for a very short time, which is left off the graph.

The gradient of the displacement graph is the velocity, and the gradient of the velocity graph is the acceleration. The area under the velocity graph is the displacement.

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