Moments about a point (statics)

In summary, the conversation discusses how to solve a problem using moments and the confusion around determining the sign of the horizontal components. The solution is to focus on the tendency of the force to rotate the object rather than its direction.
  • #1
7
0

Homework Statement



qp254.jpg


Homework Equations



M = F*r

The Attempt at a Solution



I tried splitting each force into its xy components and solve but the answer is wrong. Here is my attempt:

For point A:

Horizontal moments:

(3 * cos 25) * 5.4
- (2 * cos 30) * 4

Vertical moments:
- 4 * 1.5
- (3 sin 25) * 4.5

Then add them to determine the final moment and I get -3.9513 kNm but it's not the same as the correct answer which is -19.46 kNm.

What am I missing?
 
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  • #2
OK... it turns out I have to reverse the sign for the horizontal components so it becomes like this:

-(3 * cos 25) * 5.4
+(2 * cos 30) * 4

But I don't understand why... the 3 kNm force is pulling to the right hence its horizontal component is positive.

Can someone explain?
 
  • #3
nonyabus said:
OK... it turns out I have to reverse the sign for the horizontal components so it becomes like this:

-(3 * cos 25) * 5.4
+(2 * cos 30) * 4

But I don't understand why... the 3 kNm force is pulling to the right hence its horizontal component is positive.

Can someone explain?
The direction of the force should not be used when determining the direction (sign) of the moment about a point. What is important in determing the sign of the moment is determining whether the tendency of the force to rotate the object is clockwise (cw) or counterclockwise (ccw). Arbitrarily (or by convention) choosing ccw as plus (+), then cw is minus (-). Look at all the forces again and see if the tendency of the force components is to rotate the object cw or ccw about the chosen point. Then try solving for the moment of the forces about B.

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1. What are moments about a point in statics?

Moments about a point refer to the turning effect of a force about a fixed point, also known as the moment of a force. It is a measure of the tendency of a force to cause an object to rotate about a specific point.

2. How do you calculate moments about a point?

Moments about a point can be calculated by multiplying the magnitude of the force by the perpendicular distance from the point to the line of action of the force. This distance is also known as the moment arm or lever arm.

3. What is the unit of measurement for moments about a point?

The unit of measurement for moments about a point is Newton-meters (Nm) in the SI system, and foot-pounds (ft-lb) in the English system. It represents the amount of torque or rotational force that is generated by a force acting on an object.

4. How do moments about a point affect the stability of an object?

Moments about a point can affect the stability of an object by causing it to rotate or topple over. The larger the moment, the greater the tendency for the object to rotate. Objects with a lower center of gravity and a larger base are more stable and less likely to be affected by moments about a point.

5. What are some real-life applications of moments about a point in statics?

Moments about a point are used in various fields such as engineering, architecture, and physics. They are essential in designing structures such as buildings, bridges, and machines to ensure their stability and safety. Moments about a point are also used in calculating the torque and rotational motion of objects, such as gears and pulleys.

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