Q2. A certain machine is used to lift a load of 500N when an effort of 50N is applied to the machine the load is raised by 10m a
2 answers:
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Answer:
a. μ 3 ± 1.8 = [1.2,4.8]
b. The correct answer is option D. No, because the sample size is large enough.
Explanation:
a. The population mean can be determined using a confidence interval which is made up of a point estimate from a given sample and the calculation error margin. Thus:
μ±(t*s)/sqrt(n)
where:
μ = is the 95% confidence interval estimate
x_ = mean of the sample = 3
s = standard deviation of the sample = 5.8
n = size of the sample = 41
t = the t statistic for 95% confidence and 40 (n-1) degrees of freedom = 2.021
substituting all the variable, we have:
μ 3 ± (2.021*5.8)/sqrt(41) = 3 ± 1.8 = [1.2,4.8]
b. The correct answer is option D. No, because the sample size is large enough.
Using the the Central Limit Theorem which states that regardless of the distribution shape of the underlying population, a sampling distribution of size which is ≥ 30 is normally distributed.
Answer:
a) The magnitude of the electric charge that a 60-kg human must have to overcome weight is 3.923 coulombs and its sign is negative.
b) The force of repulsion between two people is newtons. The use of the earth's electric field a feasible means of flight is not feasible since electric force of repulsion would destroy human body before taking advantage of any possible flight skill.
Explanation:
a) From Second Newton's Law, we form this equation of equilibrium:
(Eq. 1)
Where:
- Electrostatic force exerted on human, measured in Newton.
- Weight of the human, measured in Newton.
If we consider that human can be represented as a particle and make use of definitions of electric field and weight, the previous equation is expanded and electric charge is cleared afterwards:
(Eq. 2)
- Electric field, measured in Newtons per Coloumb.
- Mass, measured in kilograms.
- Gravity acceleration, measured in meters per square second.
- Electric charge, measured in Coulomb.
As electric field of the Earth is directed in toward the center of the planet, that is, in the same direction of gravity, electric field must be a negative value. If we know that ,
and
, the charge that a 60-kg human must have to overcome weight is:
The magnitude of the electric charge that a 60-kg human must have to overcome weight is 3.923 coulombs and its sign is negative.
b) The electric force of repulsion between two people with the same charge calculated in part (a) is determined by Coulomb's Law, whose definition we proceed to use:
(Eq. 3)
Where:
- Electrostatic constant, measured in Newton-square meter per square Coulomb.
- Electric charge, measured in Coulomb.
- Distance between two people, measured in meters.
If we know that ,
and
, then the force of repulsion between two people is:
The force of repulsion between two people is newtons. The use of the earth's electric field a feasible means of flight is not feasible since electric force of repulsion would destroy human body before taking advantage of any possible flight skill.