Can Derivative Methods Determine the Correct Angle in Physics Problems?

In summary, the conversation revolves around finding the angle of a force acting on an arc. The correct method is to take the point of action of the force as anywhere along its line of action and consider the force acting at the centre of the arc. The horizontal component then has no moment and the angle can be easily calculated.
  • #1
Tapias5000
46
10
Homework Statement
Determine the moment of the force with respect to point O as a function of θ . for what value of θ in the range between 0° and 180° is the moment at its maximum? what is the value of the moment in this case?
Relevant Equations
Mo= R x F
This is the image of the problem:
Captura.PNG

I tried to solve it and I got the following is it correct?

1631573856591.png

derive and equal to 0 because it is between an angle of 0 and 180° is this statement correct?
 
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  • #2
Looks fine, though you should specify units everywhere, e.g. ##1500\sin(\theta)Nm##.

You can take the point of action of a force as anywhere along its line of action, so it is simpler to consider the force acting at the centre of the arc. The horizontal component then has no moment about O, and you can write the answer down immediately.

Btw, you put "momentum" in the title instead of "moment".
 
  • #3
haruspex said:
Looks fine, though you should specify units everywhere, e.g. ##1500\sin(\theta)Nm##.

You can take the point of action of a force as anywhere along its line of action, so it is simpler to consider the force acting at the centre of the arc. The horizontal component then has no moment about O, and you can write the answer down immediately.

Btw, you put "momentum" in the title instead of "moment".
ok, but I still need to find the angle, is the statement I said correct to find it?
 
  • #4
Tapias5000 said:
ok, but I still need to find the angle, is the statement I said correct to find it?
Yes.
 
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1. How do I approach a physics exercise involving moments?

First, identify all the given information, including the values of the forces and the distances between them. Then, draw a clear diagram of the situation and label all the forces and distances. Next, choose a point to calculate the moment about and apply the formula M = F x d. Finally, solve for the unknown value.

2. What is the difference between a clockwise and counterclockwise moment?

A clockwise moment is a rotational force that causes an object to turn in a clockwise direction, while a counterclockwise moment causes an object to turn in a counterclockwise direction. This depends on the direction of the force in relation to the point of rotation.

3. How do I determine the direction of a moment?

The direction of a moment can be determined by the direction of the force and the direction of the distance from the point of rotation. If the force and distance are in the same direction, the moment will be positive (clockwise). If they are in opposite directions, the moment will be negative (counterclockwise).

4. What is the unit of measurement for moments?

Moments are typically measured in Newton-meters (Nm) or foot-pounds (ft-lb), depending on the unit system being used. This unit represents the amount of force (in Newtons or pounds) applied at a certain distance (in meters or feet) from the point of rotation.

5. How do I know if my answer for a moment exercise is correct?

To check if your answer is correct, you can use the principle of moments, which states that the sum of clockwise moments must be equal to the sum of counterclockwise moments for an object to be in equilibrium. If your calculated moments match this principle, then your answer is likely correct.

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