1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alchen [17]
3 years ago
14

A student measures the diameter of a small cylindrical object and gets the following readings: 4.32, 4.35, 4.31, 4.36, 4.37, 4.3

4 cm (a) What is the average diameter from these readings? (b) What is the standard deviation of these measurements? The student also measured the length of the object to be (0.126 ± 0.005) m and the mass to be object to be (1.66 ± 0.05) kg. Using the method from this week's lab, determine (c) the density and (d) the proportion of error in the density calculation.
Physics
1 answer:
Zinaida [17]3 years ago
3 0

Answer:

a. \bar{d}=4.34 cm

b. \sigma=0.023 cm

c. \rho=(0.0089\pm 0.00058) kg/cm^{3}

Explanation:

a) The average of this values is the sum each number divided by the total number of values.

\bar{d}=\frac{\Sigma_{i=1}^(N)x_{i}}{N}

  • x_{i} is values of each diameter
  • N is the total number of values. N=6

\bar{d}=\frac{4.32+4.35+4.31+4.36+4.37+4.34}{6}

\bar{d}=4.34 cm

b) The standard deviation equations is:

\sigma=\sqrt{\frac{1}{N}\Sigma^{N}_{i=1}(x_{i}-\bar{d})^{2}}

If we put all this values in that equation we will get:

\sigma=0.023 cm

Then the mean diameter will be:

\bar{d}=(4.34\pm 0.023)cm

c) We know that the density is the mass divided by the volume (ρ = m/V)

and we know that the volume of a cylinder is: V=\pi R^{2}h

Then:

\rho=\frac{m}{\pi R^{2}h}

Using the values that we have, we can calculate the value of density:

\rho=\frac{1.66}{3.14*(4.34/2)^{2}*12.6}=0.0089 kg/cm^{3}

We need to use propagation of error to find the error of the density.

\delta\rho=\sqrt{\left(\frac{\partial\rho}{\partial m}\right)^{2}\delta m^{2}+\left(\frac{\partial\rho}{\partial d}\right)^{2}\delta d^{2}+\left(\frac{\partial\rho}{\partial h}\right)^{2}\delta h^{2}}  

  • δm is the error of the mass value.
  • δd is the error of the diameter value.
  • δh is the error of the length value.

Let's find each partial derivative:

1. \frac{\partial\rho}{\partial m}=\frac{4m}{\pi d^{2}h}=\frac{4*1.66}{\pi 4.34^{2}*12.6}=0.0089

2.  \frac{\partial\rho}{\partial d}=-\frac{8m}{\pi d^{3}h}=-\frac{8*1.66}{\pi 4.34^{3}*12.6}=-0.004

3. \frac{\partial\rho}{\partial h}=-\frac{4m}{\pi d^{2}h^{2}}=-\frac{4*1.66}{\pi 4.34^{2}*12.6^{2}}=-0.00071

Therefore:

\delta\rho=\sqrt{\left(0.0089)^{2}*0.05^{2}+\left(-0.004)^{2}*0.023^{2}+\left(-0.00071)^{2}*0.5^{2}}

\delta\rho=0.00058

So the density is:

\rho=(0.0089\pm 0.00058) kg/cm^{3}

I hope it helps you!

You might be interested in
Which statement supports the giant-impact hypothesis of the moon’s formation
V125BC [204]

Answer:

the moon lacks a sizeable iron core

Explanation:

7 0
3 years ago
Read 2 more answers
The components of vector A are:
Korvikt [17]

here as it is given that x component of the vector is positive while y component of the vector is negative so we can say the vector must inclined in Fourth quadrant.

So angle must be more than 270 degree and less than 360 degree

Now in order to find the value we can say that

tan\theta = \frac{opposite\: side}{adjacent\: side}

tan\theta = \frac{8.6}{6.1}

\theta = tan^{-1}1.41

\theta = 54.65^0

so it is inclined at above angle with X axis in fourth quadrant

Now if angle is to be measured counterclockwise then its magnitude will be

\theta = 360 - 54.65 = 305.3^0

so the correct answer will be 305 degree

3 0
3 years ago
A spring on a horizontal surface can be stretched and held 0.5 m from its equilibrium position with a force of 60 N. a. How much
Lostsunrise [7]

Answer:

a)1815Joules b) 185Joules

Explanation:

Hooke's law states that the extension of a material is directly proportional to the applied force provided that the elastic limit is not exceeded. Mathematically;

F = ke where;

F is the applied force

k is the elastic constant

e is the extension of the material

From the formula, k = F/e

F1/e1 = F2/e2

If a force of 60N causes an extension of 0.5m of the string from its equilibrium position, the elastic constant of the spring will be ;

k = 60/0.5

k = 120N/m

a) To get the work done in stretching the spring 5.5m from its position,

Work done by the spring = 1/2ke²

Given k = 120N/m, e = 5.5m

Work done = 1/2×120×5.5²

Work done = 60× 5.5²

Work done = 1815Joules

b) work done in compressing the spring 1.5m from its equilibrium position will be gotten using the same formula;

Work done = 1/2ke²

Work done =1/2× 120×1.5²

Works done = 60×1.5²

Work done = 135Joules

8 0
3 years ago
Read 2 more answers
______ interference occurs when two waves overlap and the resulting wave has a larger amplitude.
ratelena [41]
Constructive is correct
8 0
3 years ago
Read 2 more answers
Astronauts need special tools to work in space. One specially designed tool that astronauts use is a screwdriver. Using Newton’s
Softa [21]
Due to the fact that for every action there is an equal reaction for every turn on the screw the screw will exert energy equal to the amount you gave
3 0
3 years ago
Other questions:
  • Alden, a passenger on a yacht moored 15 miles due north of a straight, east-west
    10·1 answer
  • the scientists tested a hypothesis on running in the rain performed only one controlled experiment that supported their hypothes
    5·1 answer
  • HELP PLZ HELPPPPPPPPPPPPPPPPPPPPPPP I need help
    5·1 answer
  • If a car can go from 0 to 60 mi/hr in 8.0 seconds, what would be its final speed after 5.0 seconds if its starting speed were 50
    15·2 answers
  • A net force of 10 N accelerates an object at 5.0 m/s^2. What is the mass of the object? A. 2 kg B. 10 kg C. 5 kg D. 20 kg
    13·1 answer
  • A typical reaction time to get your foot on the brake in your car is 0.2 second. If you are traveling at a speed of 60 mph (88 f
    8·2 answers
  • A car moved 40 km north and 90 km south. What is the displacement of the car?
    14·1 answer
  • TRUE OR FALSE
    12·1 answer
  • What do I need To do to get a moving object to stop moving ?
    10·1 answer
  • A sports car starts from rest it covers a distance of 900 m to attain a speed of 80m s determine the acceleration of the car and
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!