Physics pendulum - If I swing a pendulum, does it accelerate towards the midpoint?
If I got a pendulum and brought it away from the midpoint and let go, would it accelerate or would the acceleration decrease slowly?
Original post by mqb2766
Gravity accelerates down and the midpoint is the lowest so ...
It would always accelerate down/towards the midpoint, but at the midpoint, the speed is maximum and acceleration zero. Simple harmonic motion.
It would always accelerate down/towards the midpoint, but at the midpoint, the speed is maximum and acceleration zero. Simple harmonic motion.
The graphs show the kinetic and potential energies of the pendulum.
Yes, I thought it would accelerate towards the midpoint too, that means that the velocity is increasing exponentially. But shouldn't that mean the the kinetic energy of the pendulum would increase more rapidly (since it's v^2). I don't understand why the gradient of the kinetic energy slowly decreases as we go from the left hand side towards the midpoint
Original post by muhammad0112
The graphs show the kinetic and potential energies of the pendulum.
Yes, I thought it would accelerate towards the midpoint too, that means that the velocity is increasing exponentially. But shouldn't that mean the the kinetic energy of the pendulum would increase more rapidly (since it's v^2). I don't understand why the gradient of the kinetic energy slowly decreases as we go from the left hand side towards the midpoint
Yes, I thought it would accelerate towards the midpoint too, that means that the velocity is increasing exponentially. But shouldn't that mean the the kinetic energy of the pendulum would increase more rapidly (since it's v^2). I don't understand why the gradient of the kinetic energy slowly decreases as we go from the left hand side towards the midpoint
No, in several things.
* Velocity does not increase exponentially.
* Energy is conserved, to KE is max at the centre, GPE is max at the extremes where The velocity and hence KE is zero. The acceleration is largest at these points.
The acceleration is proportional to the negative displacement, assuming the amplitude is small. This means it's acceleration always points towards the centre. Acceleration is largest at the amplitudes, and zero in the midpoint. Just do a resolution of forces with small angle approximation.
Can you upload the page you working from, so I've an idea what you've covered.
https://en.m.wikipedia.org/wiki/Pendulum_(mathematics)
Here the amplitudes are "large" so there is a vertical component as well to ensure circular motion. However, the acceleration switches left /right as it passes through the midpoint and so always points (horizontal component) towards the midpoint.
(edited 3 years ago)
Original post by mqb2766
No, in several things.
* Velocity does not increase exponentially.
* Energy is conserved, to KE is max at the centre, GPE is max at the extremes where The velocity and hence KE is zero. The acceleration is largest at these points.
The acceleration is proportional to the negative displacement, assuming the amplitude is small. This means it's acceleration always points towards the centre. Acceleration is largest at the amplitudes, and zero in the midpoint. Just do a resolution of forces with small angle approximation.
Can you upload the page you working from, so I've an idea what you've covered.
https://en.m.wikipedia.org/wiki/Pendulum_(mathematics)
Here the amplitudes are "large" so there is a vertical component as well to ensure circular motion. However, the acceleration switches left /right as it passes through the midpoint and so always points (horizontal component) towards the midpoint.
* Velocity does not increase exponentially.
* Energy is conserved, to KE is max at the centre, GPE is max at the extremes where The velocity and hence KE is zero. The acceleration is largest at these points.
The acceleration is proportional to the negative displacement, assuming the amplitude is small. This means it's acceleration always points towards the centre. Acceleration is largest at the amplitudes, and zero in the midpoint. Just do a resolution of forces with small angle approximation.
Can you upload the page you working from, so I've an idea what you've covered.
https://en.m.wikipedia.org/wiki/Pendulum_(mathematics)
Here the amplitudes are "large" so there is a vertical component as well to ensure circular motion. However, the acceleration switches left /right as it passes through the midpoint and so always points (horizontal component) towards the midpoint.
That sounds pretty advanced, I'm only an A-level physics student. TBH, I don't really understand what you wrote.
I got it from the CGP revision guide.
"The acceleration is proportional to the negative displacement, assuming the amplitude is small. This means it's acceleration always points towards the centre. Acceleration is largest at the amplitudes, and zero in the midpoint"
This sounds like a contradiction to me, because it sounds like the acceleration slowly decreases to 0 as it goes from the left side to the midpoint. In other words,it's decellerating. Is that true?
Drop here!
Drop here!
(edited 3 years ago)
Original post by muhammad0112
That sounds pretty advanced, I'm only an A-level physics student. TBH, I don't really understand what you wrote.
I got it from the CGP revision guide.
Drop here!
I got it from the CGP revision guide.
Drop here!
Do you understand what happens with a spring SHM?
https://www.khanacademy.org/science/high-school-physics/simple-harmonic-motion/introduction-to-simple-harmonic-motion/a/introduction-to-simple-harmonic-motion-review
Original post by muhammad0112
If I got a pendulum and brought it away from the midpoint and let go, would it accelerate or would the acceleration decrease slowly?
Technically, I think it would be "accelerating" all the time, right up until the pendulum is at a standstill. Acceleration is normally assumed to be a vector. The pendulum follows a arc-like path. That alone means it is accelerating, due to the pendulum's path constantly deviating from a straight trajectory.
I used to be a nerd.
A lot of these stupid exam-style questions don't test your ability to problem-solve, or even your knowledge. You could have perfectly reasonable understanding of these things, yet the exam questions will still catch you out with dumb technicalities which come down to nothing more memorising the small print of annoying definitions of terms.
For example... if you were to compute the problem you're describing, assuming that acceleration is scalar (not vector)... then you might be right, and you could argue that then the pendulum is in fact de-accelerating (slowing down) from the moment when it passes the lowest point.
All of this is just fking common sense though, lol.
I did engineering at uni, and depending on what literature you're given... different authors and different schools of thought, make different assumptions, and come up with slightly different definitions of what are basically the same things.
You've got acceleration in SHM but it's not constant acceleration. you want to make sure you're using the correct formula for SHM because SUVAT will not help you here.
the size of the acceleration gets smaller as the bob approaches the equilibrium position... but the bob is still getting faster right until it gets to the equilibrium point - a smaller acceleration is still an acceleration.
at the equilibrium point the acceleration is zero but the speed is maximum
at maximum displacement from the equilibrium position the speed is zero and the acceleration is maximum
The pendulums you'll be thinking about at A level will have the amplitude of the SHM much smaller than the length of the pendulum - you're assuming that the pendulum bob is moving in a straight line rather than an arc which is quite an accurate approximation for small angles (but terrible for large angles like 90 degrees)
the size of the acceleration gets smaller as the bob approaches the equilibrium position... but the bob is still getting faster right until it gets to the equilibrium point - a smaller acceleration is still an acceleration.
at the equilibrium point the acceleration is zero but the speed is maximum
at maximum displacement from the equilibrium position the speed is zero and the acceleration is maximum
The pendulums you'll be thinking about at A level will have the amplitude of the SHM much smaller than the length of the pendulum - you're assuming that the pendulum bob is moving in a straight line rather than an arc which is quite an accurate approximation for small angles (but terrible for large angles like 90 degrees)
Original post by muhammad0112
If I got a pendulum and brought it away from the midpoint and let go, would it accelerate or would the acceleration decrease slowly?
Simple Harmonic Motion relies on the acceleration toward a mid / equilibrium point being proportional to the displacement from it. In the case of a pendulum, this is an approximation that is valid only for small displacements.
We measure the displacement of a pendulum as its angle from the vertical (in radians). We then breakdown its weight into two components, one perpendicular to the pendulum and one along it. As the pendulum is inextensible, only the component perpendicular to it is relevant. This component is . Using the small angle approximation, this gives (approximately) . Using "F=ma" (for angular quantities) gives us (i.e. always towards zero displacement).
This gives us sinusoidal displacement, speed, and acceleration (in the direction of travel). When the displacement is zero, the (absolute) speed hits its maximum. When the displacements is at its (absolute) maximum, the speed is zero.
(edited 3 years ago)
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