What is the approach for solving a non-inertial pendulum problem?

In summary, the conversation discusses a practice problem involving a pendulum suspended on a truck accelerating at 2.6m/s/s. The first part of the problem asks for the horizontal deviation of the mass, which is determined to be 20.6cm. The second part involves finding the tension in the cord, which is solved using the Pythagorean equation and is determined to be 4.06N. The conversation also includes a discussion on how to approach the problem and the steps to take in solving it.
  • #1
inner08
49
0
Hi,

I have this practice problem I'm trying to figure out.

A pendulum 80 cm in length has a mass of 0.4g is suspended on the roof of a truck accelerating at 2.6m/s/s. Find a) the horizontal deviation of the mass; b) the tension in the cord.

For a, I know the answer is 20.6cm but I really have no clue as to where to start, what formulas to use. I've been trying for a couple of hours with the formulas I have and can't seem to get the correct answer. I do know this would be a non-inertial frame of reference type of problem but I'm stuck as to how I arrive to that answer.

For b, I thought i'd use the pythagorean equation since we have the weight and the force F' making a 90 degree angle. So I did sqrt((mg)^2 + (ma)^2) = 4.06N.

Any insight on how I should approach the first problem and the steps I should take to solve it would be greatly appreciated!

Thanks,
 
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  • #2
For (a) start by drawing a FBD of the mass. Note that the mass will be accelerating at the same rate as the truck.
 
  • #3
Ok. So there are 3 forces (mg, ma and T) acting on the object.

Fx = Tcos(theta) - F'
Fy = Tsin(theta) - mg

Is that right? If so, where do I go from here?
 
  • #4
Carefull, if you are saying that theta is the angle with the verticle, then you mixed up the sine and cosine.
 

Related to What is the approach for solving a non-inertial pendulum problem?

1. What is a non inertial pendulum problem?

A non inertial pendulum problem refers to a scenario where a pendulum is not in a state of constant motion, but instead experiences acceleration or deceleration due to the motion of its support system. This can be caused by the rotation or translation of the pendulum's support, creating a non-inertial reference frame.

2. How does a non inertial pendulum differ from an inertial pendulum?

An inertial pendulum is one that is in a state of constant motion, without any external forces acting on it. This means that the pendulum's support system remains stationary, creating an inertial reference frame. In contrast, a non inertial pendulum experiences acceleration or deceleration due to the motion of its support system, creating a non-inertial reference frame.

3. What are some real-life examples of non inertial pendulum problems?

One example is a Foucault pendulum, which demonstrates the rotation of the Earth by changing its direction of swing due to the Earth's rotation. Another example is a pendulum on a moving vehicle, where the motion of the vehicle causes the pendulum to experience acceleration or deceleration.

4. How do you solve a non inertial pendulum problem?

Solving a non inertial pendulum problem involves taking into account the acceleration or deceleration of the pendulum's support system. This can be done by using equations of motion that take into account the non-inertial reference frame, such as the Coriolis and centrifugal forces.

5. What are the applications of understanding non inertial pendulum problems?

Understanding non inertial pendulum problems is important in fields such as physics, engineering, and navigation. It can also have practical applications, such as in designing pendulum-based devices, predicting the behavior of pendulum systems in different reference frames, and understanding the effects of Earth's rotation on objects on its surface.

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