to determine that force acting on each mass it was assumed that g=9.8m/s^2. The value of g at the place where the experiment is performed may be slightly different from that value. state what effect it would have on the percentage error calculated for the comparisons to test your answer to the question. leave g as a symbol in the calculation of percentage error
F = m g
dF/dg = m
dF = m dg
percent error in F =100 dF/F
= 100 m dg/(m g)
= 100 dg/g
1. To determine the force acting on each mass it was assumed that g = 9.80 m/s2. The
value of g at the place where the experiment is performed may be slightly different
from that value. State what effect (if any) it would have on the percentage error
calculated for the comparisons. To test your answer to the question, leave g as a
symbol in the calculation of the percentage error.
Well, if the value of g at the place where the experiment is performed is slightly different from 9.8m/s^2, it would definitely have an effect on the percentage error calculated for the comparisons. The percentage error is calculated by taking the difference between the measured value and the accepted value, dividing it by the accepted value, and then multiplying by 100.
Since g is a part of the accepted value, any discrepancy in its value would directly affect the accepted value. This, in turn, would alter the difference between the measured value and the accepted value, therefore impacting the percentage error calculated.
In order to leave g as a symbol in the calculation of the percentage error, you could express it as (g + Δg), where Δg represents the difference between the actual value of g and the assumed value of 9.8m/s^2. By including Δg in the calculation, you would account for the possible variation in g at the place of the experiment.
Just remember, when it comes to calculating percentage errors, it's always a good idea to account for any potential differences or uncertainties to get a more accurate understanding of the overall result.
The percentage error can be calculated using the formula:
% error = ( (measured value - actual value) / actual value ) x 100
In this case, the actual value of g is unknown and is represented by the symbol "g" in the calculation of the percentage error. Therefore, if the value of g at the place where the experiment is performed is slightly different from 9.8 m/s^2, it will not affect the percentage error calculation. The percentage error will remain the same as it is not dependent on the specific value of g, but rather on the difference between the measured value and the actual value.
To determine the effect of a slightly different value of acceleration due to gravity (g) on the percentage error calculated in the comparison, we need to understand how the percentage error is calculated.
The percentage error is typically calculated using the formula:
Percentage Error = (|experimental value - accepted value| / accepted value) * 100
In this case, since we are comparing the force acting on each mass, the experimental value and the accepted value would both depend on the value of acceleration due to gravity (g).
Let's assume the experimental value of force (F_experimental) and the accepted value of force (F_accepted). Since both of these values depend on g, we can write them as:
F_experimental = m * g_experimental
F_accepted = m * g_accepted
Here, m is the mass of the object under consideration, g_experimental is the experimental value of acceleration due to gravity, and g_accepted is the accepted value of acceleration due to gravity.
Now, let's calculate the percentage error using these formulas:
Percentage Error = (|F_experimental - F_accepted| / F_accepted) * 100
Substituting the values of F_experimental and F_accepted:
Percentage Error = (|m * g_experimental - m * g_accepted| / (m * g_accepted)) * 100
We can see that the mass (m) cancels out, leaving us with:
Percentage Error = (|g_experimental - g_accepted| / g_accepted) * 100
Here, g_experimental represents the experimental value of acceleration due to gravity, and g_accepted represents the accepted value of acceleration due to gravity.
If the value of g at the place where the experiment is performed is slightly different from the accepted value, it will directly impact the value of g_experimental. As a result, the difference |g_experimental - g_accepted| will be larger, leading to a higher percentage error.
In conclusion, if the value of g at the place where the experiment is performed is different from the accepted value, it will increase the percentage error calculated for the comparisons.