M1 Progress Test: Calculate Mass 'm' of Rod AB Supported at Balance Point C

[ollistech]

Hi guys!

I've totally lost the plot with some questions I have for my progress test, please advise on a method for solution :)

A Uniform rod (AB) has a length of 1.5m and a mass of 8Kg. A particle of mass 'm'Kg is attached to the rod at B. The rod is supported at the point C (balance point).
Distance A-C = 0.9m and the system is in equilibrium, with the rod (AB) horizontal.

Show that mass 'm' = 2Kg.

Distances:
Rod AB = 1.5m
A-C (One end of rod to balance point) = 0.9m
C-B = 0.6m


I don't know if this is allowed but can someone who's feeling kind and knowledgeable add me on msn or skype?

MSN: rune_monkey@hotmail.co.uk
Skype: olliestech


Thanks in advance!

 

[jbsteele]

The answer to this problem can be found by using the principle of moments. This states that when a system is in equilibrium, then the sum of the clockwise moments is equal to the sum of the anticlockwise moments. This means that in your case, the moment of the 8kg mass at A (1.5m x 8kg x 9.81N/kg) needs to be equal to the moment of the unknown mass 'm' at B (0.6m x 'm' x 9.81N/kg). Rearranging this equation, we get m = (1.5m x 8kg x 9.81N/kg) / (0.6m x 9.81N/kg), which gives us a result of m = 2kg.

 

[nlightner]

Hello,

To calculate the mass 'm' of the particle attached to the rod, we can use the principle of moments. This states that for an object to be in equilibrium, the sum of the clockwise moments must equal the sum of the anticlockwise moments.

In this case, the clockwise moment is caused by the weight of the rod (8kg) acting at a distance of 0.9m from the balance point C. The anticlockwise moment is caused by the weight of the particle (mkg) acting at a distance of 0.6m from the balance point C.

So, we can set up the equation:

8kg x 0.9m = mkg x 0.6m

Solving for m, we get:

m = (8kg x 0.9m) / 0.6m
m = 12kg

However, since the system is in equilibrium, the mass of the particle must be equal to the mass of the rod at the balance point. So, we can set up another equation:

8kg = mkg

Solving for m, we get:

m = 8kg / 1.5m
m = 5.33kg

Since we know that the mass of the particle must be equal to the mass of the rod at the balance point, we can solve for m again using this new value:

m = 8kg / 1.5m
m = 2kg

Therefore, the mass 'm' of the particle attached to the rod is 2kg.

I hope this helps and good luck on your progress test! It is not recommended to share personal contact information on public forums, so I will not be able to add you on MSN or Skype, but I am more than happy to help with any other questions you may have.