A stick of length 1 is broken into two pieces, at a uniformly random break point. (1) Find the CDF of the length of the smaller piece. (2) What is the average length of the smaller piece? Solve by hand and explain integration. Show calculations and derivatives.

A stick of length 1 is broken into two pieces, at a uniformly random break point. (1) Find the CDF of the length of the smaller piece. (2) What is the average length of the smaller piece? Solve by hand and explain integration. Show calculations and derivatives.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter9: Dynamics Of A System Of Particles

Section: Chapter Questions

Problem 9.17P

See similar textbooks

Related questions

Q: A long piece of wire with a mass of 0.1 kg and a total length of 4 m is used to make a square coil…

A: We know that the torque acting is the magnetic force and the other comes from the gravitational…

Q: 0 cm 10.0 cm 35.0 N 45.0 cm xcm 30.0 N 3. What is the value of the force at 40.0 cm in the diagram…

A: Please see the attached image for the solution.If there are queries, please do not hesitate to ask.…

Q: Exercise 3.23 A projectile is released horizontally from A and strikes the target at B as shown.…

Q: During a golf drive, the angular velocity of the driver is 2.9 revolutions/s just before impact with…

Q: 2.7. A water molecule is a permanent dipole with a dipole moment of 6.186 × 10-30 Cm. Treat the axis…

A: The objective of the question is to calculate the torque on a water molecule in an electric field.…

Q: 30 DENAKER What three properties of the nucleus can be deduced from the Rutherford scattering…

A: The objective of the question is to identify and explain the three properties of the atomic nucleus…

Q: A copper rod of length 0.77 m is lying on a frictionless table (see the drawing). Each end of the…

A: a) to the right (or counter-clockwise in the circuit)b) 0.0122 mExplanation:Step 1:Step 2:Step 3:

Q: The homogenous 79 kg disk supported by the rope AB rests against a rough vertical wall. Determine…

A: M=79 kg

Q: Don't provide hand writing solution

A: The equation of motion for a charged particle moving in a magnetic field and under the influence of…

Q: The uniform square steel plate has a mass of 7 kg and is resting on a smooth horizontal surface in…

Q: 2.5. Four equal point charges of 3.0 μC are held in place at the four corners of a square that is…

A: The objective of the question is to understand the behavior of electric fields created by point…

Q: NEW General HI Q Q ↓ Close 5. The figure shows a charged dielectric sphere centered at the origin…

A: The objective of the question is to find the magnitude of the electric field at a certain point in…

Q: How do you get dv/dx=(64.27-296.296t)

Q: The uniform solid block in the figure has mass 38.6 kg and edge lengths a = 0.780 m, b = 1.82 m, and…

A: 50.45 kg.m2Explanation:

Q: A stepladder of negligible weight is constructed as shown in the figure below, with AC = BC = { =…

Q: A patient is to be given a blood transfusion. The blood is to flow through a tube from a raised…

A: The inside diameter = 34 mm

Q: ་ Part A A 740 gram grinding wheel 26.5 cm in diameter is in the shape of a uniform solid disk. (We…

A: Please follow the steps below.Explanation:

Q: Problem 2: As shown in the figure, a rod completes a circuit as it slides with constant velocity, v,…

Q: A planet had a gravitational field at its surface if 7.6 m/s2 the mass of the planet us 4.5 x 10^24…

A: The objective of the question is to find the force of gravity on a 70 kg object on the surface of a…

Q: An atom in an excited state has a mass of 63.332 and then decays to a mass of 63.329 amu by emitting…

Q: A rugby player is pivoting about his longitudinal axis and his moment of inertia about this axis is…

Q: ← 11:45 HOLIDAY FIRST ASSIGNME... classroom.google.com Page 4 of 8 SUDAY FIRST R₁ 1002 10v V. ☐ Ra…

A: Step 1:Step 2:

Q: An electron is moving along the B field with speed v, to the right. What is the direction of the…

A: The electron is moving along the field B with a speed v, towards right.

Q: show all work, especially for 2.3

A: 2.1 To calculate the number of ions per second flowing through the channel, we can use Fick's…

Q: o Harry is designing the crumple zones in a new car. He decides to model the front end of the car as…

Q: These drawings illustrate various situations in which a magnetic field is directed out of the…

Q: Find the mass m of the counterweight needed to balance a truck with mass M = 1 360 kg truck on an…

A: The mass of the vehicle is The angle of inclination is Find:Mass of the object.

Q: (a) A cosmic-ray proton in interstellar space has an energy of 24.0 MeV and executes a circular…

A: a)The data is given as follows.Here, E is the radius, m is the mass of the proton, and q is the…

Q: S grune ni aoins) art ai jadw.. If M = 3.0 kg, and the tension in the string connecting M and 2M is…

A: The objective of the question is to find the force F acting on the mass of 2M. The given parameters…

Q: Suppose you want to set up a simple pendulum with a period of 9.02 s. How long should it be on a…

Q: (c) Someone has stolen an ATM card and knows that the first and last digits of the PIN are 8 and 3,…

A: Step 1:To solve this problem, we need to first determine the number of possible pin combinations…

Q: When boy is pulling his sister in a wagon, as shown in the future. He exerts a force of F = 43.5 N…

A: Write the given data.Here, F is the distance.

Q: A discus thrower exerts a torque of 4.5 Nm on a 1.9 kg discus. The discus has a radius of gyration…

Q: 8. The Achilles tendon, which connects the calf muscles to the heel, is the thickest and strongest…

A: Elasticity is the property by virtue of which the material tends to regain the original shape when…

Q: (a) A 1.00 cm-high object is placed 3.45 cm to the left of a converging lens of focal length 7.05…

Q: Brick with mass m that resting at the top of the inclined plane that has a height of 4.43 m and has…

A: Draw the free-body diagram of the brick when it is on an inclined plane.

Q: During a transcranial magnetic stimulation (TMS) treatment, a magnetic field, typically of magnitude…

A: The objective of this question is to calculate the magnitude of the average induced electromotive…

Q: Please help me answer the following question

Q: A conducting sphere of radius R has an amount of electric charge Q_0 and is brought into contact…

Q: A gymnast with a mass of 55 kg flipped in the air and achieved a maximum angular velocity of 445…

A: Approach to solving the question: Detailed explanation: Examples: Key references:

Q: 7. A tire has a radius of 0.330 m, and its center moves forward with a linear speed of 15.0 m/s. (a)…

A: Given values:R = 0.33 mv = 15 m/sr = 0.175 m a) Angular velocity of the wheel:We know, if a tire is…

Q: I need help finding U, K, and E in the table.

A: Approach to solving the question: Detailed explanation:Examples: Key references:

Q: A 1.60cm high object is situated 12.6 cm in front of a concave mirror that has a radius of curvature…

A: The objective of this question is to find the location and the height of the image formed by a…

Q: Three children are riding on the edge of a merry-go-round that has a mass of 105 kg and a radius of…

Q: OSM away You (who have a mass of 72 kg) are floating out in space holding an 11 kg ball. It also…

Q: Mass M is divided into two parts xM and (1-x)M. For a given separation, the value of x for which the…

A: The objective of the question is to find the value of x for which the gravitational attraction…

Q: 8. * Limits of human vision The wavelength limits of human vision are 400 nm to 700 nm. What range…

A: The visible range of wavelength is 400 nm–700 nm.Speed of light (c) = 3 × 108 m/s

Q: 2.5. Four equal point charges of 3.0 μC are held in place at the four corners of a square that is…

A: a)Draw the schematic diagram of the system of charges.

Q: A mass m is released from rest from the top of a frictionless ramp. The mass slides down and…

A: Step 1: Consider the conservation energy of the system Since the ramp is frictionless, there will be…

Q: 6. A particle with charge q = +e (where the value of e = 1.6 × 10-19 C) is at the center of a…

A: (a) The magnitude of electric field is E=3.84×10−7N/C (b) The direction of the electric field will…

Question

A stick of length 1 is broken into two pieces, at a uniformly random break point.

(1) Find the CDF of the length of the smaller piece.

(2) What is the average length of the smaller piece?

Solve by hand and explain integration. Show calculations and derivatives.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Problem

VIEW

Step 2: CDF of the length of the smaller piece

VIEW

Step 3: Average length of the smaller piece

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

The average life expectancy in Japan is 81 years. What is this time in SI units?
If , and , find the unknown constants a and b such that .
A popular unit of measure in the ancient world was the cubit (approximately the distance between a persons elbow and the end of the middle finger, when outstretched). Estimate the length of 1 cubit in centimeters. Given that there are about 1.609 103 m in 1 mile, how many cubits are there in 1 mile?
Take a 500-sheet ream of computer paper as it comes wrapped. Unwrap it and measure the height, width, and length of the stack. Determine the volume, measure the mass of the ream, and obtain the density. Determine how many reams come in a standard box. Estimate the total mass of the box. Discuss your assumptions and estimation procedure.
Please fill out the template with the work for this problem. Note that you need to have a picture, list of knowns and unknowns, the general equation/s you will use, the math steps to solve for the unknown, only plug in the numbers after you have solved for the unknown, and the answer with units included.
Please explain how to work out this problem. The correct answer is selected, I just don't understand how to get to that answer. I'm also confused by the unit conversions, so please emphasize that if you can. Thank you.
Explain the difference between a rate of change that is positive and one that is negative. Give an example of each. O Consider the ordered pair (x, y) where x is the independent variable and y is the dependent variable. If y increases with the increase in x, then the rate of change of y is positive. Whereas, if y decreases as x increases, then the rate of change is negative. For example, if you consider the speed of a car (y) over time (x), as the car accelerates, the speed increases with increasing time, and the rate of change of its speed is positive. When the car brakes, the rate of change of its speed is negative, because the speed decreases over time. Consider the ordered pair (x, y) where x is the independent variable and y is the dependent variable. If y increases with a decrease in x, then the rate of change of y is positive. Whereas, if y decreases as x decreases, then the rate of change is negative. For example, if you consider the speed of a car (y) over time (x), as the car…
Assume that you measure the dimensions of a hollow cube with vernier caliper many time and obtain the following average values in cm: Height: 4 Inner width: 2.23 Outer width: 7.02 Inner length: 1 Outer length: 1 Using these values, calculate the volume of the hollow cube in cm³. Express your result with 3 significant figures. Answer:
A uniform density sheet of metal is cut into the shape of an isosceles triangle, which is oriented with the base at the bottom and a corner at the top. It has a base B = 49 cm, height H = 15 cm, and area mass density σ. a) Consider a horizontal slice of the triangle that is a distance y from the top of the triangle and has a thickness dy. Write an equation for the area of this slice in terms of the distance y, and the base B and height H of the triangle. b) Set up an integral to calculate the vertical center of mass of the triangle, assuming it will have the form C ∫ f(y) where C has all the constants in it and f(y) is a function of y. What is f(y)? c)Integrate to find an equation for the location of the center of mass in the vertical direction. Use the coordinate system specified in the previous parts, with the origin at the top and positive downward. d)Find the numeric value for the distance between the top of the triangle and the center of mass in cm.
In this problem, I am suppose to manipulate the equation to find what r equals to. Thank you.
What is “Random and Systematic Error”? Give an example for each one. What is “Standard deviation” and its formula? What data percent of XAverage ± σ, or XAverage ± 2σ, or XAverage ± 3σ might be the most reliable one?
A. Compute for the average time of each free-fall distance. B. Compute for each average time squared for each free-fall distance. C. Compute for a slope. D. Compute for the percentage error. E. Give Conclusion and Analysis