Two pans of a balance are 50cm apart. If the fulcrum is displaced by 1cm what percentage is the true weight marked up?
the answer i got was 1.3%,
please help if wrong (which it probably is).
To solve this problem, let's assume that the weight marked on one pan of the balance is W (in grams or any other unit). Since the pans are initially 50 cm apart, the fulcrum is at the midpoint of the balance.
When the fulcrum is displaced by 1 cm, the distance between the fulcrum and the weight marked on the pan becomes 49 cm.
According to the principle of moments, the clockwise moment (M_c) about the fulcrum is equal to the anticlockwise moment (M_a):
M_c = M_a
The moment (M) of a weight is calculated by multiplying its weight (W) by its distance from the fulcrum (L):
M_c = W * 50 cm (initial distance)
M_a = W * 49 cm
Therefore, we can set up the equation:
W * 50 = W * 49
50 = 49
However, this equation does not hold true. So, there must be an error in your calculation. Let's find the correct answer:
When the fulcrum is displaced by 1 cm, the percentage by which the true weight is marked up can be calculated using the formula:
Percentage = (Change in weight / True weight) * 100
In this case, the true weight marked up is the weight on the pan that was initially at 49 cm away from the fulcrum. So, let's calculate the change in weight:
Change in weight = (W * 49) - (W * 50)
Change in weight = W(49 - 50)
Change in weight = -W
Now, let's substitute the values in the formula:
Percentage = (Change in weight / True weight) * 100
Percentage = (-W / W) * 100
Percentage = -100
The negative sign indicates that the weight is marked down, not up. So, there must be an error in your initial calculation.
Therefore, the correct answer is that the true weight is marked down by 100%.
To calculate the percentage of the true weight marked up when the fulcrum is displaced, you can use the concept of leverage. The lever arm on one side of the fulcrum is 50cm, and when the fulcrum is displaced by 1cm, the lever arm on that side becomes 51cm.
Using the lever arm ratio, we can determine the change in leverage. The lever arm ratio is given by:
Lever arm ratio = (Lever arm with displacement) / (Original lever arm)
Lever arm ratio = 51cm / 50cm = 1.02
To find the percentage increase, subtract 1 from the lever arm ratio, and multiply by 100:
Percentage increase = (Lever arm ratio - 1) * 100
Percentage increase = (1.02 - 1) * 100 = 2%
Therefore, when the fulcrum is displaced by 1cm, the true weight marked up will increase by approximately 2%, not 1.3%.
It seems like you made a slight calculation error in your previous answer.
If the fulcrum is displaced 1 cm away from unknown mass M, the reference mass m that balances M satisfies the relation:
24m = 26 M
m = 13/12 M
If the fulcrum is in the correct place in the middle, M = m.
The person who is buying a mass M will be charged for a mass m, the balancing weight.
So M will be "marked up" 8.3%