Solve "Moments of Force" with Uniform Meter Rule & Pulley

In summary, the problem involves finding the position of a 50 g mass on a uniform meter rule that is balanced by a knife-edge and a string with a 20 g mass on the other end. Using the equation ΣF=0 and taking moments at the center of gravity, it is determined that the reaction force at the knife-edge is 0.8 and the position of the 50 g mass is 0.3125. However, further calculations are needed to find the exact position of the 50 g mass.
  • #1
look416
87
0

Homework Statement



A uniform metre rule of mass 100 g is supported by a knife-edge at the 40 cm mark and a string at the 100 cm mark. The string passes round a frictionless pulley and carries a mass of 20 g as shown in the diagram.

At which mark on the rule must a 50 g mass be suspended so that the rule balances?

Homework Equations





The Attempt at a Solution


using the [tex]\sum F[/tex]=0
therefore, R at the knife-edge + T at the 100 cm = W
R = 0.8
then take the moment at the c.g, which is at 0.5
therefore R(z)=T(50)
in the end,what i got is z=0.3125
where T=0.5N
wrong again...
 
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  • #2
Hi look416! :smile:

(have a sigma: ∑ :wink:)

I don't understand what you've done …

there should be moments of three forces …

and where does T = 0.5N come from? :confused:

(btw, no need to convert to N … they're all weights, so just use the masses :wink:)
 
  • #3
lolz
maybe I am not good in explaining XD
anyway
if i take the head of the ruler as the moment
which means
RX + 50(100) = 50(100)
which results in RX = 0
=.=
T = 0.5N is because the question demand for the X cm when the load is 50g
for 50g x 10 x 10^-3 = 0.5N
 
  • #4
look416 said:
RX + 50(100) = 50(100)

uhh? :redface: where's the 40cm? where's the 20g? and what's R? :confused:
 
  • #5
=.=
so, i have to find the value of R by taking moments as the head of the ruler
if so,
R(40)+20(100)=50(100)
R=75g
then??
 
  • #6
look416 said:
=.=
so, i have to find the value of R by taking moments as the head of the ruler

Is R the reaction force at the knife-edge?

If so, you don't find it by taking moments, you find it by adding the vertical components of force to zero …

which I thought you'd already done, and found it was 80g (weight) ??
R(40)+20(100)=50(100)

You haven't included the 50 g mass in this moments equation. :confused:

(btw, if you take moments about the knife-edge you won't need to find R anyway)
 
  • #7
but there said at which mark on the rule must a 50 g mass be suspended so that the rule balances?
so shouldn't i have to included the knife edge in my calculation?
not taking it as the moments ...
 
  • #8
look416 said:
but there said at which mark on the rule must a 50 g mass be suspended so that the rule balances?
so shouldn't i have to included the knife edge in my calculation?
not taking it as the moments ...

(i wish you wouldn't say "taking it as the moments" … you take moments of forces about a point :wink:)

Yes, the 50g mass, and its unknown position, must be included (unless you take moments about that position).

You can take moments about any point …

it can be either end of the ruler, or the knife-edge, or the point where the 50g is, or indeed anywhere else, either on or off the ruler.

But in this case it's easier to use the knife-edge, since that avoids working out the reaction force, R. :smile:
 

1. What is a "Moment of Force"?

A moment of force, also known as torque, is a measure of the tendency of a force to rotate an object around an axis or pivot point. It is calculated by multiplying the force by the distance from the pivot point to the line of action of the force.

2. How can a uniform meter rule and pulley be used to solve moments of force?

A uniform meter rule and pulley can be used to create a simple lever system, where the meter rule serves as the lever arm and the pulley acts as the pivot point. By applying a known force at a certain distance from the pivot point, the moment of force can be calculated using the equation M = Fd.

3. What is the difference between a uniform meter rule and a non-uniform meter rule?

A uniform meter rule is a meter rule that has a constant width and thickness along its entire length, while a non-uniform meter rule may have varying widths and thicknesses. This is important when calculating moments of force, as a uniform meter rule will provide more accurate results due to its consistent dimensions.

4. Can a uniform meter rule and pulley be used to solve moments of force for non-linear systems?

Yes, a uniform meter rule and pulley can be used to solve moments of force for both linear and non-linear systems. However, in non-linear systems, the distance from the pivot point to the line of action of the force may vary, making the calculation of the moment of force more complex.

5. What are some real-life applications of moments of force?

Moments of force are important in many fields, including engineering, physics, and biomechanics. They are used to design and analyze structures, machines, and equipment, as well as to understand the movement and stability of objects and organisms. Some specific applications include calculating the torque of engines and motors, determining the strength of materials, and studying the forces acting on the human body during physical activities.

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