Why is there a difference between a golf club needing to be light as possible so you can swing harder, but if you make a ball lighter you can’t necessarily throw it further than a baseball/cricket ball?
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It depends. The bulk of power comes from swing speed-that is created by the torque of the body, the distance between the downswing and contact with the ball and correct hitting of the ball (spin). Some golfers prefer lighter clubs and some prefer heavier clubs. There is a lot more energy going in to hitting a ball with a club than throwing one.
Through the swing you continue to apply force. The force you apply to a lighter object accelerates it faster because force / mass = acceleration, which means a lighter object will accelerate faster than a heavier object given the same force.
The same is true for when you contact the ball. A lighter ball will accelerate faster and the energy transferred to it will cause it to move faster. But the hitch is inertia. Once you’re no longer in contact with the ball, now the only (meaningful) forces acting on it are gravity and air resistance, which are both acting against the ball’s inertia. A lighter ball will have less kinetic energy for a given speed, which means the air resistance will slow it down more (relative to a heavier ball).
So these two competing concepts, the energy required to make the ball fly and the energy sufficient to keep it flying for an appropriate distance are at odds. Use the reductio ad absurdum principle. If you hit a bowling ball with a golf club, it will move, but only barely. If you hit it with sufficient force to make it fly, it’s really going to fly (think a cannonball) and nothing is going to stop it. The effects of wind resistance seem negligible compared to the kinetic energy of the bowling ball. If you hit a ping pong ball, it will certainly move and move fast, but it won’t carry much energy, so it will quickly lose speed and fall to the ground.
Balls are actually not particularly aerodynamic, meaning air resistance/drag is a significant factor on how far they can be thrown. A lighter ball would reach its terminal velocity faster.
The head of a golf club is designed to be aerodynamic, so drag is less of an issue. Also, you are providing a constant force on the club to turn it, rather than just providing an initial force and letting natural forces take over as you would with a thrown object.
So I think it’s because they are different energy transfers. Golf club hitting is an inelastic collisions so the energy of the club gets transferred to the ball, and with a lighter ball the energy creates more speed (E=1/2 mv^2).
Throwing something is moving the ball at the same speed as your hand until release. I imagine that your arm is able to move at about the same speed with a baseball as a goofball, weight of the ball isn’t the limiting factor until like 3 or 4 pounds.
With respect to throwing a ball: there is a limit to how fast you can move your arm. Disregarding wind or other forces, the ball can never leave your hand going faster than your hand did.
Generally, you can throw a lighter ball faster than a heavy ball. But as you make the ball lighter and lighter, you hit a point of diminishing returns, where the added speed gets smaller and smaller in proportion to the reduced weight. Eventually you’ll hit a point where making it lighter makes no difference as you’ve reached the limit to how fast your arm can move.
Now, in a vacuum, that would still result in you being able to throw a lighter ball further. The lighter ball leaves your hand at the fastest speed, and so it will go the furthest. However, you don’t throw balls in a vacuum – you throw them through air. And air pushes back against the ball, eating away at its speed. A heavier ball has more inertia and so this drag force will have less effect on it – the ball will still be slowed but less so (every second or every meter of flight) than the lighter ball.
This drag force is the reason why there is a sweet spot for throwing things far, which is not too heavy but not too light either. Too heavy, and you won’t be able to impart enough speed on the ball (or other object) to make it go far. Too light, and you will hit your speed limit, while the ball will quickly be slowed to a stop by air resistance after leaving your hand.
The lighter the ball the higher the effect of the air on it, thus reaching less.
Same reason one would put lead in bullets
For golf clubs:
Imagine a super gigantic hammer, you would not be able to swing it accurately, and will be too slow to give speed to the ball. But if you use something super light, your arms can’t swing it as fast as it could theoretically go. So the club you feel good with, is the heaviest club you can’t swing without losing accuracy or speed.
For the ball:
The energy you give to the ball is: giving speed to its mass.
If the mass is enormous, the ball would barely move. Let’s rule out using a bowling ball for the task.
If the mass is very little, like a ping pong ball, it will move very very fast.
But there’s a a way to that: the faster the ball goes the more the air will slow it down. For every double in speed you get quadruple drag. A ping pong ball will be super fast, but will also experience enormous air resistance. And being so light, the mass of the ball will be stopped easily by air. Now a ping pong ball needs to fly only 1/10 of a second to reach its goal, and 1/10 of a second of air friction is not enough to give troubles.
But at golf the ball has to fly several seconds. Imagine shooting out this super fat ball that just 20 meter from you is already half as fast. The trajectory would be so difficult to calculate for your brain. Factor in the wind, and you can’t hit a thing accurately, definitely not the 5 inch hole at 10m.
So we can rule out the ping pong ball too.
What is left as viable, is a ball heavy enough to carry its movement undisturbed, light enough to be shot at high speed and small enough to have less problems cutting through the air for so many seconds.
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