Conservation of Energy Help

[megaforcetkd]

This isn't really a homework problem I am just trying to figure out how to do it..

I've attached a really badly drawn picture of the setup... But I'll type it out here too.

I have to use a steel ball as a pendulum. A razor blade is attached to a pole on the test so when the string swings past the blade, it cuts the string and the ball flies. There is a cup on the floor and somehow I have to get the ball to fly into the cup.

What equations do I use to figure out how to get it to land in there? I really have no idea =/

 

[Doc Al]

I assume the problem is: At what angle do you have to release the pendulum so that the ball falls into the cup?

As a first cut, ignore any complications due to energy loss when the string is cut or the height of the cup sides.

Do it in two parts. The second part is just a projectile motion problem: by the time the ball hits the ground, it must move horizontally enough to land in the cup. Use this thinking to figure out the speed of the pendulum at the bottom position.

Then use conservation of mechanical energy to figure out the angle you have to lift the pendulum to get such a speed at the bottom.

 

[ogb p]

Hello,

Thank you for reaching out for help with your experiment. I would approach this problem by first understanding the principles of conservation of energy. This law states that energy cannot be created or destroyed, it can only be transferred from one form to another. In the case of your experiment, the potential energy of the steel ball is converted into kinetic energy as it swings down and cuts the string.

To get the ball to land in the cup, you will need to calculate the initial potential energy of the ball at the top of the swing, and then use the conservation of energy equation to find the velocity of the ball just before it cuts the string. This velocity will determine the distance and angle at which the ball will fly.

You can use the equation: PE = mgh, where PE is potential energy, m is the mass of the ball, g is the acceleration due to gravity, and h is the height at which the ball is released. Once you have calculated the potential energy, you can use the equation: KE = 1/2mv^2, where KE is kinetic energy and v is the velocity of the ball. Set the two equations equal to each other and solve for v.

Next, you will need to consider the trajectory of the ball after it cuts the string. This will depend on the initial velocity and angle at which it is released. You can use the equations of projectile motion to calculate the distance and angle at which the ball will land in the cup.

I hope this helps guide you in your experiment. Remember to always approach problems with a strong understanding of the fundamental principles and equations involved. Good luck!