What Is the Maximum Kinetic Energy of a Pendulum Bob?

[envscigrl]

Pendulum problem...Need help!

PROBLEM:
A pendulum consists of a string of length L=4.50m and a bob of mass m=1.6kg. The string is brought to a horizontal position and the bob is given the minimum initial speed enabling the pendulum to make a full turn in the vertical plane with the string staying stretched to full length the whole way around. What is the maximum kinetic energy of the bob?

I have tried what seems like a million times to solve this. I tried using the conservation of mechanical energy formula which is:
Kf + Uf= Ki +Ui where K is kinetic energy and U is potential energy. I ended up with .5 *m *vsquared = m* g * h and then solving for velocity and then plugging it into .5 *m *vsquared and solving for kinetic energy.
Somehow though that doesn't seem right but i am unsure of what else I can do.

 

[Tide]

Energy conservation is a good start but you also need to apply the condition that the bob is able to make it all the way around to the top. This means that the minimum speed is such that the tension in the string is zero when the bob reaches the top so the centripetal force at that point is equal to mg. Once you figure out the intitial speed from that go back and find out what the maximum kinetic energy was during the trip around.

 

[wais]

RESPONSE:
Hi there! It looks like you're on the right track with using the conservation of mechanical energy formula. However, there are a few things you can check to make sure your calculations are correct.

First, make sure you are using the correct values for the variables. In this problem, the mass is given as 1.6kg and the length of the string is 4.50m. Also, make sure you are using the correct units for each variable. For example, the value for gravitational acceleration (g) should be in m/s^2.

Next, check your equation for potential energy. The formula for potential energy in a pendulum is U = mgh, where h is the height of the bob above its lowest position. In this problem, the bob is starting at its lowest position and making a full turn, so the potential energy should be zero. This means that your equation should be Kf = Ki, and you can solve for the final kinetic energy directly.

Lastly, make sure you are using the correct formula for kinetic energy. The formula you mentioned, 0.5mv^2, is for linear motion. For rotational motion, the formula is 0.5Iω^2, where I is the moment of inertia and ω is the angular velocity. In this problem, the bob is moving in a circular motion, so you should use the formula for rotational kinetic energy instead.

I hope this helps! If you're still having trouble, don't hesitate to ask for more clarification. Good luck with your calculations!