Am i using the right equation?

Question

PEgrav = mass * g * height
PEgrav = m * g * h
In the above equation, m represents the mass of the object, h represents the height of the object and g represents the acceleration of gravity (approximately 10 m/s/s on Earth).

I want to find out how many pounds of force there are behind a punch/kick...if i were using a weighted pendulum and based on how high it goes when you hit it, would this equation give me what i am looking for...if not what would?

Answer 1

I would say that it could be done. Once you get the gravititional potential energy of the weighted pendulum when it reaches the highest point, you would know the kinetic energy when the pendulum started to move after the punch/kick (neglecting air friction).

By substituting in the formula
KE = (1/2)mv^2
where m is the mass of the pendulum,
you can calculate the velocity (v) when the pendulum started to move after the punch/kick. By taking the pendulum as stationary (velocity = 0) before it's being punched/kicked, you can find the acceleration of the pendulum using the formula
a=(v-0)/t
where t is the time the punch/kick is in contact with the pendulum.

Finally, use the formula F=ma to find the force delivered.

Answer 2

This equation would give you the energy transferred to the target by your punch. This is not the same as force.

What you want to do is not well defined in terms of physics. If you punch air, there will be hardly any force. If you punch a brick wall, there will be a lot of force. If you start with your hand in contact with the brick wall and attempt to punch, there will be a medium force. The bottom line is the forces involved in an impact depend on the exact conditions of the impact and could be almost anything. You can measure it with a force transducer and high-rate data capture device.

If you want to know how much force your arm is applying to your fist, then put some bathroom scales against the wall and slowly push your fist against them. Your effective punch force is proabably slightly less than this because some of the force is used to accelerate the rest of your arm.

The energy you measure with your pendulum is probably a more meaningful figure and a more fun experiment to do. You should try it with different pendulum masses and different cushioning for your fist/foot to see how much variation there is. You can also work out the velocity you gave to the target (from PE at top = kinetic energy at bottom) and the momentum (=mass x velocity) you transfer to the target.

Answer 3

Based on the top height you can calculate the potential energy using that equation you cited. That is the right equation to calculate the potential energy.

You can then assume that the kinetic energy transferred to the weighted pendulum by the kick equal to that potential energy. That allows you to calculate the top speed of moving of the pendulum caused by the kick using the equation: KE = 0.5 * m * v ^2.

However after knowing the top speed, v, you cannot precisely calculate the force of the kick. Force is time-rate of change of momentum, F = m * dv/dt; or mass times acceleration, F = m* a. You need not only v but its rate of change with time, or the kick's contact time. Without the time info a weak long lift may give a final pendulum height higher than a strong but short touch.