Pendulum Impact Force Calculation

[mh5594]

Hi,

I am performing a set of tests using a pendulum. The test involves a pendulum of length 0.55metres, the weight of the entire pendulum is 2kilos.

The test involves letting the pendulum go from a set height and calculating the force when it impacts an object held in a vice at the bottom of the arc.

Force values need to be calculated for releasing the pendulum at 5 through to 45 degrees in 5 degrees incremements and with the weight of the pendulum changing from 1, 1.5, 2, 3kilos respectively.

I have spent a number of hours trying to work it out however the formula I am using are not producing sensible results. Please could any of you help me with the necessary formula that I will need to perform the calculations.

Cheers,
Michael.

 

[Troels]

Hi,

I am performing a set of tests using a pendulum. The test involves a pendulum of length 0.55metres, the weight of the entire pendulum is 2kilos.

The test involves letting the pendulum go from a set height and calculating the force when it impacts an object held in a vice at the bottom of the arc.

Force values need to be calculated for releasing the pendulum at 5 through to 45 degrees in 5 degrees incremements and with the weight of the pendulum changing from 1, 1.5, 2, 3kilos respectively.

I have spent a number of hours trying to work it out however the formula I am using are not producing sensible results. Please could any of you help me with the necessary formula that I will need to perform the calculations.

Cheers,
Michael.

Force is bad choice here, because the force depend on the time the impact takes (which can be very short indeed).

You'd be much better off with momentum; you would want to calculate the momentum of the pendulum, right before the impact, and then apply conservation of momentum, which does give you the subsequent motion of the impacted object (under suitable constraints). If you then really need the force, you can get it from Newtons 2nd Law:

$$\vec F=\frac{\Delta \vec p}{\Delta t}$$

where $$\Delta \vec p$$ is the change in momentum of one of the bodies.

 

[tomcue]

Hello Michael,

Thank you for sharing your experiment and the difficulties you are facing with calculating the impact force of your pendulum. I understand the importance of accurate calculations in any experiment and I am happy to assist you with finding the necessary formula.

To calculate the impact force of a pendulum, we can use the equation F = mgh, where F is the force, m is the mass of the pendulum, g is the acceleration due to gravity (9.8m/s^2), and h is the height from which the pendulum is released.

In your experiment, the mass of the pendulum (m) is given as 2 kilograms, and the height (h) can be determined by the length of the pendulum (L) and the angle (θ) at which it is released. The formula for calculating h is h = L(1-cosθ).

For example, if the pendulum is released at 5 degrees, h = 0.55m(1-cos5) = 0.027m. Plugging this value into the equation F = mgh, we can calculate the impact force for a pendulum with a mass of 2 kilograms released at 5 degrees.

F = (2kg)(9.8m/s^2)(0.027m) = 0.5292N

Similarly, you can calculate the impact force for different angles and pendulum masses using this formula. I suggest double-checking your calculations and making sure you are using the correct units for mass, length, and force (kilograms, meters, and Newtons respectively).

I hope this helps and wish you success in your experiment.

Best regards,