As level mechanics unit 1 question on moments.

In summary, a non-uniform plank of wood with a length of 6m and a mass of 90kg is smoothly supported at its two ends A and B, with a woman of mass 60kg standing at point C, where AC=2m. The plank is in equilibrium with equal reaction forces at points A and B. The solution involves taking moments at point A and equating the total reaction force to the total downward force of the woman and plank. This allows for the calculation of the reaction force at point B and the distance of the center of mass of the plank from point A.
  • #1
Pagey
19
0

Homework Statement



A non-uniform plank of wood AB has length 6m and mass 90kg. The plank is smoothly supported at its two ends A and B, with A and B at the same horizontal level. A woman of mass 60kg stands on the plank at the point C, where AC=2m. The plank is in equilibrium and the magnitudes of the reactions at A and B are equal. the plank is modeled as a non-uniform rod and the woman as a particle. Find

(a) the magnitude of the reaction on the blank at B,

(b) the distance of the centre of mass of the plank from A.

Homework Equations



- general knowledge on moments.

The Attempt at a Solution



(a) i was going to take moments about the point A, therefore as the reaction force (R) at A acts through A its moment will = 0, therefore allowing me to find the reaction force (R) at B knowing the moment of the woman at A is (60g* x 2) *where g=9.8, but as the rod is non uniform i can't assume the rods mass (90kg) acts at the centre, i.e. 3m away from A (therfore the moment at A can't be 90g x 3), therefore i don't know how to take this into account without creating a distance X for the mass from A, which would only lead me onto part B anyway.

?

Thanks Mike.
 
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  • #2
Hint: What must the total reaction force from both supports equal?
 
  • #3
The total reaction force must equal the total downard force, i.e. 60g +90g for the woman and plank, even so i don't see how this can help me with the problem of not knowing the distance of the 90g when taking moments at A?
 
  • #4
O wait it can't be as simple as that the total reaction force must equal the total downard force, so as A and B are the same its just 90g+60g?
 
  • #5
Yes, it's that simple. :wink:
 

1. What is the definition of a moment in mechanics?

A moment in mechanics refers to the turning effect of a force around a pivot point. It is calculated by multiplying the magnitude of the force by the perpendicular distance from the pivot point to the line of action of the force.

2. How do you find the magnitude of a moment in a question on moments in AS level mechanics?

The magnitude of a moment can be found by multiplying the force applied by the perpendicular distance from the pivot point to the line of action of the force. This can be represented mathematically as M = F x d, where M is the moment, F is the force, and d is the distance.

3. Can you use moments to find the position of an object in equilibrium?

Yes, moments can be used to find the position of an object in equilibrium. This is done by setting the sum of the clockwise moments equal to the sum of the anticlockwise moments. This means that the object is balanced and not moving.

4. What is the difference between clockwise and anticlockwise moments?

Clockwise moments refer to moments that cause a rotation in the clockwise direction, while anticlockwise moments cause a rotation in the anticlockwise direction. This is determined by the direction of the force and the direction of the perpendicular distance from the pivot point.

5. How can moments be applied in real-world situations?

Moments are commonly used in engineering and construction to ensure that structures and machines are balanced and stable. They are also used in physics to understand the forces acting on objects and how they affect their motion. Additionally, moments are used in everyday life, such as in balancing a seesaw or tightening a bolt with a wrench.

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