Does a heavier or lighter rod hit a ball farther when swung by a motor?

[becheras]

Hi all, i hope someone can help me out here.

I have a rod (not massless) hanging like a pendulum. As its axis of rotation there's a motor that applies a constant torque. The rod will be rotated upwards, and then downwards to hit a ball like a golf club.

Qn: Will a heavier rod or a lighter rod cause the ball to travel farther?

 

[viscousflow]

Lets assume: 1 degree of rotational freedom, Rod is rigid, motor shaft is rigid.

The moment equation boils down to $$\sum M=I_z\alpha$$ So, this would imply you want $$I_z$$ to be larger to gain a higher moment. Since its a rod, and mass is your only variable, yes a heavier rod would cause a larger moment thus allowing the ball to travel further.

However, you have to factor in motor torque, i.e. can your motor produce the required torque to achieve the required $$\alpha$$ with the heavier rod? I don't know what masses you're dealing with so I don't even know if this would be a major factor. However, You may want to get some equations and optimize for $$\alpha$$ and Rod mass.

 

[Shockman]

Hi

I think this problem is more complicated. Next to the high Kinetic energy you need a high velocity to. There is a correlation betven the motors performance and the rods optimal inertia.

 

[AlephZero]

Shockman is right, this is more complicated.

The first issue is the velocity of the rod when it hits the ball. When the rod falls from its highest (stationary) position, it gains some kinetic energy from its change in potential energy as its center of mass falls. The motor can provide more kinetic energy. The time available for the motor to do this (and therefore the required power and torque) depends on the size of the system and how high the rod was raised.

The second issue is what happens during the impact with the ball. Depending on the mass and inertia of the ball and the rod, not all the energy in the rod will be transferred into the ball. If the rod is too light, it will tend to bounce backwards and not move the ball much. If it is too heavy, it will hit the ball but keep swinging forwards, and again not all the energy will end up in the ball. The ideal situation would be for the rod to hit the ball and stop dead, the same as when two equal sized balls collide with each other and all the kinetic energy gets transferred from one to the other.

So you have a tradeoff between two causes of inefficiency. Too much motor power that swings a light rod very fast will be wasted when if it hits a heavy ball. But a heavier rod will move slower, with the same size of motor.

Without knowing the actual parameters of the system, I would say it is a good bet that if everything is constant except the mass of the rod, there will probably be an optimum mass for the rod, and that either heavier or lighter than the optimum will be worse.

For a real motor which is not 100% efficient, where the torque curve depends on the motor speed, the problem may get even more complicated...

 

[Shockman]

Yep, i agree. I think it is not essential to give all energy from the rod to the ball. Especially not if you want shot more balls continouosly:)