# P449

The Magnus effect is a phenomenon where an object spinning through a fluid creates a disturbance in the fluid it is moving through. This disturbance causes a force perpendicular to the direction of motion. The following diagram depicts the directionality of the Magnus force relative to angular velocity and tangential velocity.

**Figure 1**. Magnus force on a rotating object.

This phenomenon is commonly seen in sports such as baseball and soccer (i.e. in a ‘curveball’). The Magnus effect can be measured through the following equation:

_{M}= S(wv)

**Equation 1**

where F_{M} is the Magnus force, which acts perpendicular to motion. S is a constant dependent on the air resistance, w is the angular velocity, or the speed of rotation, and v is the velocity of the object. This phenomena, in especially strong wind conditions, has been even seen in warfare during the firing of cannons. When cannons are fired, the force which propels a cannonball is often asymmetrical which allows the cannonball to spin through the air and experience the Magnus forces.

In our system, a cannon is placed on the edge of a cliff 200 m high. Near it are 3 cannon balls waiting to be launched at 25 m/s. All three balls are of the same size and weight, labeled 1, 2 and 3, as in the following figure.

**Figure 2**

Cannonball 1 will be launched horizontally, cannonball 2 is launched at 45° angle, and cannonball 3 is launched at a 60° angle.

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