A balanced diet of rods
Classical Mechanics
Level
2
If the rods are massles, can you determine which rods are balanced and which are unbalanced?
Rod A is unbalanced
Rod B is unbalanced
Rod C is unbalanced
Rod D is unbalanced
Rod E is unbalanced
Every rod is balanced
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1 solution
Let’s find out which rods are balanced:
The moment of force of an object is equal to the product of the Force and the arm of the force: F x bF=MF
Let’s start with Rod E:
The purple balloon has a weight of 6 units, and it’s 1 unit away from the wire, so the moment of force of the balloon is: 6 x 1= 6
The magenta balloon has a weight of 3 units and it’s 2 units away from the wire, so the moment of force of the balloon is: 3 x 2= 6
So rod E is balanced, since 6=6
Now let’s see if Rod D is balanced:
The yellow balloon has a weight of 2 and it’s 0.5 units away from the wire, so the moment of force of the balloon is: 2 x 0.5=1
The blue balloon has a weight of 1 and it’s 1 unit away from the wire, so the moment of force of the balloon is: 1 x 1=1
So rod D is balanced, since 1=1
Let’s see if rod C is balanced next:
The magenta balloon has a weight of 3 units and is 1 unit away from the wire, so the moment of the force of the balloon is: 3 x 1=3
The yellow balloon has a weight of 2 units and is 1.5 units away from, the wire, so the moment of the force of the balloon is: 2 x 1.5=3
So rod C is balanced, since 3=3
Rod B is next, and we’re almost done.
The red balloon has a weight of 5 units and is 1 unit away from the wire, so the moment of the force of the balloon is: 5 x 1=5
The blue balloon has a weight of 1 unit and is 1 unit away from the wire, so the moment of force of the balloon is: 1 x 1 = 1
Rod D has a weight of 3 units and is 2 units away from the wire, so the moment of force of the rod is: 3 x 2 = 6
Rod C has a weight of 5 units and is 2 units away from the wire so the moment of the force of the rod is: 5 x 2=10
Adding everything up, we can see that the part left of the wire is equal to 11 and so is the part right of the wire, this in turn meaning that rod B is balanced.
And now to finally finish this problem, rod A.
The yellow balloon has a weight of 2 units and is 1 unit away from the wire, so the moment of force of the balloon is: 2 x 1=2
The green balloon has a weight of 4 units and is 3 units away from the wire, so the moment of force of the balloon is: 4 x 3=12
Rod B has a weight of 14 units and is 2 units away from the wire, so the moment of force of the rod is: 14 x 2=28
Rod E has a weight of 9 units and is 2 units away from the wire, so the moment of force of the rod is: 9 x 2=18
Adding everything up, we can see that the part left of the wire weights 30 and that so does the part right of the wire, so rod A is balanced!
That means all of the rods are balanced, and the correct answear was: All of the rods are balanced.
Thank you for trying out my problem!