If you took a time machine back 50 years and watched a soccer game, you'd notice a most differences. Helmets, pads, shoes, jerseys---artificial turf means even the playing field itself has changed. Yet one thing has actually not. Not also a tiny bit.

You are watching: What is the mass of a football

It's the football.

But let's say you could modify the ball. Take your time machine five decades forward. Might a quarterback might throw the farther? Let’s find out.

Suppose you toss a football right into the air. What identify how far it will certainly go? 2 things. The quarterback interacts v the round (the throw), and the sphere moves v the air.

The goal of the throw is to obtain a football from rest to some higher velocity and also release that at some angle such the the ball ends up wherein you want it---hopefully in the hands of your best receiver. In order come accelerate any object, you should exert a pressure on it.. This force comes from the quarterback's arm. The final speed of the ball depends on:

The massive of the ballThe force the player exertsThe distance


But how rapid will it it is in going? In this case, we have the right to use the Work-Energy Principle. It states that the job-related done ~ above the round (by the force) will certainly be equal to the change in kinetic energy of the ball. I have the right to write the as:


You can see that boosting the massive of the ball (but maintaining the person the same) would certainly decrease the launch velocity that the football. Therefore if you wanted get better performance---a longer-distance pass, let's say---maybe we'd desire to to decrease the fixed of the football itself.

But that relies on the way the round moves through the air.

Once the round leaves the player’s hand, two pressures determine that motion: the gravitational force and the wait resistance force.


The gravitational force is reasonably straightforward, however air resistance is much more complicated. It depends on speed, but also the cross-sectional size of the object---I'll contact that area A---and the shape of the object, denoted by the change C.

Technically, it additionally depends on the density of the waiting (we favor to use the Greek letter ρ) but that wouldn’t change too lot in a normal football game. The other necessary point around air resistance is the it action in the contrary direction as the velocity the the ball. Placing this every together provides the following model for the size of the wait resistance force.


If you desire a football to go the farthest, girlfriend would desire a smaller cross sectional area and a little drag coefficient (C ). However, just changing the fixed will likewise have an influence on the football selection because that the relationship in between force and also acceleration.

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With the very same force, an object with a better mass will have a smaller acceleration. If girlfriend throw two balls v the exact same velocity and also the exact same air resistance force, the more huge ball will go farther. So there you have actually it. Much more mass provides the round harder to litter but much more mass also makes it less susceptible to air resistance.