Solving a Problem: Forces Acting on P

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Homework Statement
The smooth particle P is attached to an elastic cord extending from O to P. Due to the slotted arm guide, P moves along an horizontal path(##r=0.8sin(\theta)##) with constant angular velocity of ##\dot{\theta}=5rad/s##.
The mass of P is 0.08kg, the cord stiffness is k=30N/m and its unstretched length 0.25m.

Find the forces of the guide acting on P for theta=60
Relevant Equations
velocity and acceleration components in polar coordinates, Newton's 2nd law.
Screenshot 2021-11-22 174214.jpg
Hello guys,

here's a problem which I'm having troubles solving.
It asks for the forces acting on P when ##\theta=60^{\circ}##.
I thought for this problem it would have been convenient to consider a polar reference system(r, theta). Drawing the FBD of pin P at a moment in time, we will have 3(?) forces acting on P:
-one(##F_S##) along the r direction(pointing towards O caused by the spring-modeled cord, function of its stretch and k;
-one(##F_P##) along the positive(direction of movement) theta direction, caused by the push "from backwards" of the guide exerted on P;
-a last normal force, exerted by the circle normal to the path, thus not aligned with the r-theta system defined.

Could you tell me if these are all the forces acting, and thus the equations of motion(FBD+KD) might be built from them?
In case yes, now we could start writing down the EOMs to solve for ##F_P##.
$$
\left\{\begin{matrix}
F_S-Ncos\phi=m(\ddot{r}-r\dot{\theta}^2)\\
F_P-Nsin\phi=m(r\ddot{\theta}+2\dot{r}\dot{\theta})
\end{matrix}\right.$$

We may calculate ##F_S## from Hooke's law, but to solve for ##F_P## and N we still need ##\phi##.
The procedure to calculate such angle seemed kinda convoluted and thus got me thinking I wasn't on the right path... I was as well confused on the problem's request: do they mean "my" ##F_P## by "forces of the guide acting on P"?

Greg
 
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Yes, those are the forces.
There is an isosceles triangle formed among points O, P and center of circle.
Two of its angles should be 90-60 degrees.
 
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greg_rack said:
##\dots~##we still need ϕ.
Suppose you defined ##\phi## as the angle subtended by the center of the wheel when the particle is at ##\theta## and such that ##\phi=0## when ##\theta=0## (particle at the 6 o'clock position). Note that ##\phi=180^{\circ}## when ##\theta=90^{\circ}## (particle at the 12 o' clock position). Can you deduce a general relation between ##\theta## and ##\phi##? After all, the dependence between ##\theta## and ##\phi## can only be linear. If you'd rather measure ##\phi## conventionally, i.e. relative to the 3 o' clock position, then it's a matter of adding (or subtracting) ##90^{\circ}##. Draw a good picture and you will see.
 
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Thank you so much guys, now I see the relation!
I didn't realize that the direction of the normal force, was that of the radius of the circle. That helped me the most to spot ##\phi=f(\theta)##.
Too many triangles and scribbles o_O
 
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Related to Solving a Problem: Forces Acting on P

What is the definition of "forces acting on P"?

Forces acting on P refer to the external forces that are applied to an object or system, causing it to change its state of motion or shape.

How do you identify the forces acting on P?

To identify the forces acting on P, you must first determine the object's mass and acceleration. Then, you can use Newton's Second Law of Motion, F=ma, to calculate the net force acting on P. The net force is the vector sum of all the individual forces acting on the object.

What are the types of forces that can act on P?

The types of forces that can act on P include gravitational force, normal force, frictional force, tension force, and applied force. These forces can be either contact forces, which require physical contact between objects, or non-contact forces, which act at a distance.

How do you solve a problem involving forces acting on P?

To solve a problem involving forces acting on P, you must first draw a free-body diagram to represent all the forces acting on the object. Then, you can use Newton's Second Law of Motion and apply the appropriate equations to calculate the net force and acceleration of the object. Finally, you can use kinematic equations to determine the object's displacement, velocity, and time.

What are some real-world examples of forces acting on P?

Some real-world examples of forces acting on P include a person pushing a shopping cart, a car accelerating down a hill, a book resting on a table, and a ball falling towards the ground. These examples demonstrate the different types of forces, such as applied force, gravitational force, normal force, and frictional force, that can act on an object in everyday situations.

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