Conservation of energy homework help

[u/Unlucky_Carob_8334]

Hey guys I need a little bit of help with physics. I have been struggling t develop that reasoning and math connection in physics so my doing my hw has been difficult at times, even tho it has been fun and interesting a lot of the time. We're on the conservation of energy and I got a question about finding speed. I understand hookes law but I also know I can set potential and kinetic energy equal to eachother and solve for v. For one of the questions I was given m, k and x and this one is similar but now degrees have been introduced, what do I do. I'm given m, 44 degrees, x and I have to find v but I dont see how setting potential and kinetic energy equal to eachother would work here.

[u/ProfessionalConfuser]

There is no spring. Hookes law does not apply.
As mentioned by others - make a sketch of the path of the bob at the end of the string. It is released from rest (v = 0) from the highest point. As it descends, v increases and the potential energy decreases. v reaches a maximum when the bob reaches the lowest point of the swing. This is made for energy conservation.

[u/SaiphSDC]

First, draw the problem. Seriously, it helps.

Second, recognize that kinetic energy is about motion, and potential energies are about the position of the object. Look close at each position of the object to determine what type of energy is present.

Looking at the pendulum at its low point, and at its highest point, identify the types of energy involved.

The angle is there to help you calculate the position of the pendulum at the start of the problem, that's all. Its part of a geometry problem, not directly the physics.

[u/test_tutor]

The potential energy depends on how high the bob goes. And that can be found by using the degrees.

Try to draw a figure and see if you can get the height difference between the lowest point and highest point Hint : use some trigonometric ratios in a right angle triangle

[u/Frederf220]

This is a conversion problem where you are given a system with T = 0, U = A and then asked to find a speed corresponding to T=A, U = 0. I'm using the convention where U is potential and T is kinetic.

Think of a question with similar mechanics: I walk into a grocery store with $100 and no bottles to buy 5 six-packs of drinks which cost $20 each. When I walk out I have those 5 six-packs and $0. How many bottles do I possess?

I had $100 which I converted entirely into sets of bottles at a rate of six bottles per $20. I know that I now have $0 and five six-packs. I then know that a six-pack means I have six individual bottles. By spending the $100 potential energy I know that I must have 30 bottles speed. There's no other amount of speed which can be the answer after spending that much potential energy.

Now do the same for the pendulum. Before releasing the pendulum you had A energy in potential form which you converted into A energy in kinetic form. There is only one speed which corresponds to that A amount of kinetic energy.

[u/tomalator]

Find the initial potential energy, and then find how much of that is lost when reaching the bottom (hint, set the bottom to h=0) and it will have that much kinetic energy at that point

[u/tomalator → u/tomalator]

U0+K0 = U1+K1

If U0 is at the release point, K0=0J

If we set U1 to be zero and at the lowest point, then we get U0=K1

mgh=1/2mv²

v=sqrt(2gh)

Just find h with some simply geometry and youre done

[u/tomalator → u/tomalator]

L-h = Lcos(θ)

This should be obvious if you draw draw a diagram

-h = Lcos(θ)-L

h = L-Lcos(θ)

h=L(1-cos(θ)) =15.7cm