Two footballs (a & b) are thrown with the same amount of force. football a has a greater mass. describe the acceleration for each football.

Newton's second law gives the relationship between force applied to an object, its mass and its acceleration:

where F is the force, m the mass and a the acceleration.

A force F is applied to football A, whose mass is , and so the acceleration of this football will be given by (re-arranging the previous equation)


Similarly, the acceleration of football B will be

where  is the mass of football B, and where the force F applied to the two footballs is the same.

Since football A has greater mass than football B, , if we compare the two previous formula we see that the acceleration of football B is greater than the acceleration of football A:

Therefore, if the same force is applied to the two footballs, football B will accelerate more than football A.

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