Equilibrium of forces acting at a point

[changd]

1. can an object be moving and still be in equilibrium?
2. consider a ring with a pin in the center that's not connected to the ring. three weights are attached to the ring at different angles and are hanging from the side of the apparatus where the ring lies. what criteria will decide when the forces on the ring are in equilibrium?
3. draw a set of three vectors whose sum is zero
4. how will you estimate the uncertainty of each force acting on the ring?
5. how will you estimate the uncertainty of each angle measurement?
6. how much error will be introduced if the table is not level? how could you test this empirically?
7. what are the units of sine and cosine? does your answer depend on the units of the angle (degrees or radians)?

 

[Defennder]

1. Yes, provided by "equilibrium", you mean no net force acting on it. Newton's 1st law covers this.

2. It's hard to visualise what you are describing here. But if a system is in equilibrium it either moves with a constant velocity or not at all. Rotational equilibrium means that there isn't any net torque about any chosen point.

3. That's pretty simple. Think of a closed shape consisting of three lines.

4. Uncertainty is related to measurement, so unless you tell us what instruments are used to measure the force and how you measure them, your question makes no sense.

5. Again it depends on the level of accuracy of your measuring instrument.

6. Don't know what you mean here. The apparatus is set up on the table, but what has this got to do with measurement errors? If the tilted table affects the results it would be a systematic error and not a random error. When someone asks "How much error/uncertainty is given in the results", they are usually referring to random errors, not systematic ones.

7. Certain trigo formulas work in radians but not degrees, but apart from that there is no difference between the two. The units of degrees are well, degrees and you should be able to determine the units of radian measurement by dimensional analysis.

 

[baba89]

1. Yes, an object can be moving and still be in equilibrium. Equilibrium refers to a state where all the forces acting on an object are balanced, resulting in a net force of zero. This means that the object will not accelerate or change its velocity, but it can still be in motion at a constant speed.

2. The forces on the ring will be in equilibrium when the vector sum of all the forces acting on the ring is zero. This means that the forces must be balanced in both magnitude and direction. The criteria for equilibrium will also depend on the specific situation and the forces involved.

3. A set of three vectors whose sum is zero can be drawn in various ways, depending on the specific scenario. One example could be three forces of equal magnitude but different directions, forming a triangle with the forces acting at the vertices.

4. The uncertainty of each force acting on the ring can be estimated by considering the accuracy and precision of the equipment used to measure the force. This could include the sensitivity of the force sensor or the accuracy of the weight measurements.

5. The uncertainty of each angle measurement can be estimated by considering the precision of the measuring instrument, such as a protractor or a digital angle gauge. The smaller the divisions on the instrument, the more precise the measurement can be.

6. If the table is not level, it can introduce an error in the angle measurements, which can affect the equilibrium of forces. This error can be tested empirically by using a level to check the table's horizontal position and comparing the results of the experiment when the table is level and when it is not.

7. The units of sine and cosine are dimensionless, as they are ratios of two sides of a right triangle. However, the angle measurement used in these trigonometric functions can be either in degrees or radians. The answer will depend on the units of the angle, as the conversion factor between degrees and radians is π/180.