Classical mechanics: forces on a pendulum

In summary, the conversation discussed the direction and magnitude of the net force and acceleration acting on a pendulum immediately after it is released from its equilibrium position. It was determined that the centripetal force is not zero and that the centripetal acceleration is dependent on the velocity, which changes as the pendulum moves. This is due to the tension in the string, which is a self-adjusting force.
  • #1
REVIANNA
71
1

Homework Statement


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A simple pendulum is pulled sideways from the equilibrium position and then released.
I figured this part out -
Immediately after the pendulum is released, the net force acting on it is directed:
it is perpendicular to the string
(I REASONED THAT THE DIRECTION OF ACCELERATION(PERPENDICULAR TO THE STRING) IS THE DIRECTION OF THE NET FORCE)

but next part to this question of the question says
"My answer to part 1 is justified because:"
AND the answer is " The centripetal acceleration is zero"

I don't understand how the centripetal force is zero?
if it is zero why the circular motion? Does tangential force alone causes it?
 
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  • #2
REVIANNA said:
I don't understand how the centripetal force is zero?
if it is zero why the circular motion? Does tangential force alone causes it?

The centripetal force is not zero. If you stand on the floor you don't move downwards... does that mean the gravitational force is zero?
 
  • #3
stockzahn said:
The centripetal force is not zero

sorry I meant to say how the CENTRIPETAL ACCELERATION (NOT FORCE) is zero?(as the ans says)
coz the pendulum is after all tracing a semi -CIRCULAR arc.
 
  • #4
You are right, the centripetal acceleration is not zero. I'd say a badly expressed answer. I think the answer should say "the radial velocity is zero" to point out that the distance of the mass from the center is constant. But as the centripetal acceleration points in radial direction and the radial velocity is zero, I suppose the expressions got mixed up.
 
  • #5
figure7-1-alt.png

this makes me think
if net force perpendicular to the string mgsin(theta) causes Tangential acceleration then what causes Centripetal acceleration (which causes change in direction) as the net force along the string is zero?
 
  • #6
If the string would be cut (when the pendulum is already in motion), the mass would proceed linearly in tangential direction. The string forces the mass to change the direction of the velocity - due to the inertia the tension in the string increases. Now the net force gets a component in radial direction.

As you wrote in the statement:

REVIANNA said:
Immediately after the pendulum is released, the net force acting on it is directed: [...]

EDIT: I should have read the statement properly in the first place. In the first moment, immediately after the pendulum is released, there is no centripetal acceleration - sorry, my bad.
 

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  • #7
Hmm ... well, but we know that the centripetal acceleration, by definition, depends on the velocity, right?
 
  • #8
Is the velocity the same everywhere?
 
  • #9
stockzahn said:
due to the inertia the tension in the string increases. Now the net force gets a component in radial direction.
okay this means that immediately after letting the pendulum go the net force is perpendicular to the string (completely tangential ) but as the pendulum goes on- tension increases (as it is a self adjusting force like normal force) such that the acceleration and net force vector have both tangential and radial components which would cause a change in magnitude and direction of the velocity vector respectively.
 
  • #10
GoodPost said:
Is the velocity the same everywhere?

no it changes both in magnitude and direction.That's why we are talking about acceleration and net force. Remember Newton's 1st law constant velocity (same speed in a stg line) requires no force at all.
 
  • #11
GoodPost said:
Hmm ... well, but we know that the centripetal acceleration, by definition, depends on the velocity, right?

you are right about centripetal acceleration being v^2/r. but as @stockzahn said the centripetal acceleration is zero immediately after the pendulum is released when the velocity is zero too.after that the centripetal force has a certain magnitude.
 
  • #12
Exactly! So at the moment when we just release the ball, the net force along the tension axes is :
T - mg*cos(theta) = m*ac = m*(v^2/r) = m*(0) = 0

And now the force "mg*sin(theta)" will cause the ball to move and so causing the velocity to increase. Hence, ac is changing too (increasing or decreasing) due to the change in velocity.

As a result, the net force along the tension axes is not zero anymore! (centripetal force is not zero)

Good Luck!
G.P.
 
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  • #13
REVIANNA said:
okay this means that immediately after letting the pendulum go the net force is perpendicular to the string (completely tangential ) but as the pendulum goes on- tension increases (as it is a self adjusting force like normal force) such that the acceleration and net force vector have both tangential and radial components which would cause a change in magnitude and direction of the velocity vector respectively.

Yes, that's it
 
  • #14

1. What is a pendulum and how does it work?

A pendulum is a weight suspended from a pivot point that can swing back and forth. The motion of a pendulum is controlled by the force of gravity and the length of the pendulum. The weight of the pendulum pulls it downward, while the pivot point keeps it from falling. As the pendulum swings, it gains energy from gravity and converts it into kinetic energy, causing it to swing back and forth.

2. What is the role of force in a pendulum?

The force of gravity is the primary force acting on a pendulum. As the pendulum swings, the force of gravity acts on the weight, pulling it downward. This force creates the pendulum's motion, causing it to swing back and forth. Other forces, such as air resistance and friction, may also affect the pendulum's motion.

3. How does the length of a pendulum affect the forces on it?

The length of a pendulum affects the forces acting on it by changing the time it takes for the pendulum to complete one swing. A longer pendulum will take longer to complete one swing and therefore experience a lower force from gravity. This is because the weight has more time to move horizontally, reducing the vertical distance it travels and the force of gravity acting on it.

4. What is the relationship between the mass of a pendulum and the forces on it?

The mass of a pendulum does not affect the forces acting on it. The force of gravity is dependent on the weight of the pendulum, but the weight is directly proportional to the mass. Therefore, as the mass of a pendulum increases, the force of gravity and other forces acting on it will also increase, but the ratio of these forces will remain the same.

5. How does the amplitude of a pendulum affect the forces on it?

The amplitude, or the maximum angle of swing, of a pendulum does not affect the forces acting on it. The force of gravity is always acting on the pendulum with the same strength, regardless of its amplitude. However, a larger amplitude will result in a longer period of oscillation, meaning the pendulum will experience more force over time.

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