Can Velocity be Determined from Force as a Function of Angle in Mechanics?

In summary, the conversation is about a person's question regarding determining the velocity of a particle in a point described by coordinates (\alpha;R) when there is a force acting on the particle as a function of angle. The other person suggests using energy conservation and determining a potential to find v(alpha).
  • #1
Gloyn
41
0
Hello!

I've been doing some excercises in mechanics and stopped for a moment over the thing that sometimes bothers me. I have a set of particles of masses M and m, M>m. If I have force acting on m particle as a function of angle:

F=(Mmg(1+cos[itex]\alpha[/itex]))/(M+m)

(m is moving in on the surface of a verticle circle of radius R, powered by the falling M particle, both particles are connected by a string)

is there a way to determine the velocity of particle in a point described by coordinates ([itex]\alpha[/itex];R)? If force was in funtction of time, that would be obvious, but what about the function of the coordinate?
 
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  • #2
Hmm, your force looks strange. However, if you know F(alpha), you can determine a potential and get v(alpha) via energy conservation.
 

FAQ: Can Velocity be Determined from Force as a Function of Angle in Mechanics?

1. What is the relationship between force and angle?

The relationship between force and angle is described by the law of cosines, which states that the magnitude of the force vector is equal to the cosine of the angle between the force and displacement vectors multiplied by the magnitude of the displacement vector.

2. How does force change with respect to angle?

As the angle between the force and displacement vectors changes, the magnitude of the force vector also changes. This can be seen by the changing value of the cosine function as the angle increases or decreases.

3. Can force be negative in terms of angle?

Yes, force can be negative in terms of angle. This indicates that the force vector is acting in the opposite direction of the displacement vector.

4. What is the maximum force that can be exerted at a certain angle?

The maximum force that can be exerted depends on the angle between the force and displacement vectors. At certain angles, the force can be greater or less than the maximum force that can be exerted.

5. How is force affected by changes in angle?

Changes in angle can affect the magnitude and direction of the force vector. As the angle increases or decreases, the force vector can also increase or decrease, and its direction can change accordingly.

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