A worker drives a 0.500 kg spike into a rail tie with a 2.50 kg sledgeham-
1 answer:
Total internal energy increases by 1760 J
Step-by-step explanation:
The kinetic energy of an object is the energy possessed by the object due to its motion.
It is calculated as
where
m is the mass of the object
v is its speed
For the hammer in this problem:
m = 2.50 kg
v = 65.0 m/s
So its kinetic energy is
Then the problem says that 1/3 of the hammer's kinetic energy is converted into internal energy: therefore, the total internal energy increases by
Learn more about kinetic energy:
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Answer:
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis.
Step-by-step explanation:
Data given and notation
Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5
We can begin calculating the sample mean given by:
And the sample deviation given by:
And we got:
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a two sided test the p value would be:
Conclusion
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis.