haruspex said:
With the usual anticlockwise convention, yes.theone said:
For the first equation, which two terms did you identify as wrong? Is it the P and N terms?haruspex said:
In each of the terms involving a trig function, the other factor is related to acceleration or force in either the vertical or horizontal direction. You should expect that all of one direction take cos, and all of the other direction take sin.theone said:
They're both vertical, so should match the same trig function.theone said:
so is the final answer including the signs correct: [tex]Psin\theta-mgsin\theta-Ncos\theta=m\ddot x cos\theta+ml\ddot\theta[/tex]haruspex said:
Not quite. The left hand side appears to be taking up and.left as positive, the right hand side down and right as positive.theone said:
haruspex said:
What about the ##ml\ddot \theta## term? Also, you said the rod has mass, so that should be in the equation, and you need a contribution from the torsion spring.theone said:
haruspex said:
The ##ml\ddot \theta## term is the acceleration of the mass (in the tangential direction) relative to the acceleration of the block.theone said:
The spring applies ##{K_t\theta}## of torque , so then the force it applies is ##\frac{K_t\theta}{l}##, with l being the length of the rod from the pivot to the combined COG?haruspex said:
That's the force applied to the mass, if the rod is massless. But as I wrote, if you consider the mass and rod as a single unit, you need to deal in terms of their common mass centre, and how far that will be from the joint.theone said:
haruspex said:
Yes, except that you've made the ##m\ddot x## term positive again (you said it was meant to be negative), and you've introduced a cos factor on the ##\ddot \theta## term.theone said:
haruspex said:
up and lefttheone said:
Yes, the torque from the spring reacts on the block exactly opposite to its torque on the arm. This is in addition to P and N.theone said:
To draw a free body diagram for a pendulum, you will need to identify all the forces acting on the pendulum. These include the weight of the pendulum, the tension force from the string, and air resistance (if any). Draw a dot to represent the pendulum's mass and arrows to represent each force acting on it, with the direction of the arrow indicating the direction of the force. Make sure to label each force appropriately.
The purpose of a free body diagram for a pendulum is to visually represent the forces acting on the pendulum. This allows us to analyze the motion of the pendulum and understand how the forces affect its movement. It is a useful tool in solving problems related to pendulums.
As a pendulum swings, the forces acting on it change. At the highest point of its swing, the only force acting on the pendulum is its weight. As it moves downwards, the tension force from the string increases while the weight decreases. At the lowest point of its swing, the tension force is at its maximum and the weight is at its minimum. As the pendulum swings back up, the forces reverse and the tension force decreases while the weight increases.
The forces acting on a pendulum are independent of its mass. This means that a pendulum with a larger mass will experience the same forces as a pendulum with a smaller mass. However, a pendulum with a larger mass will have a greater inertia, which affects its motion and period (time for one swing).
Air resistance can affect a pendulum's motion by slowing it down. As the pendulum swings, it displaces air molecules which create a resistance force. This force increases with the pendulum's speed and can cause the pendulum to lose energy and slow down over time. This is why pendulums in a vacuum can swing for a longer period of time compared to those in the presence of air.
