H2. Suppose a particle of constant mass m with position x > 0, moves in one space dimensionunder the influence of the gravitational force of another point particle of constant mass Msitting at x = 0, i.e. the attracting force isF=(a) Using Newton's second law, show thatGmMx²i.1dr (2m²2² _ GimM)dt= 0.(i.e., the total energy, sum of kinetic and potential energy, is conserved).dx dt(b) Using the change of variables vdy = r, solve the equation of motion and determine thevelocity of the particle v(x) as a function of x assuming it starts with zero velocity at xo. Doesthe particle's speed in x = 0 depend on the initial position?

Given: F=-GmMx2i Solution: Let the velocity has the velocity ,v=vi From the Newton's second law of…

H2. Suppose a particle of constant mass m with position x > 0, moves in one space dimension under the influence of the gravitational force of another point particle of constant mass M sitting at x = 0, i.e. the attracting force is F (a) Using Newton's second law, show that d (2m²² -mx dt GmM x² = GmM = 0. (i.e., the total energy, sum of kinetic and potential energy, is conserved). (b) Using the change of variables vd dr, solve the equation of motion and determine the velocity of the particle v(x) as a function of x assuming it starts with zero velocity at xo. Does the particle's speed in x = 0 depend on the initial position? X

H2. Suppose a particle of constant mass m with position x > 0, moves in one space dimension under the influence of the gravitational force of another point particle of constant mass M sitting at x = 0, i.e. the attracting force is F (a) Using Newton's second law, show that d (2m²² -mx dt GmM x² = GmM = 0. (i.e., the total energy, sum of kinetic and potential energy, is conserved). (b) Using the change of variables vd dr, solve the equation of motion and determine the velocity of the particle v(x) as a function of x assuming it starts with zero velocity at xo. Does the particle's speed in x = 0 depend on the initial position? X

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

The ideal gas law, discovered experimentally, is an equation of state that relates the observable state variables of the gas--pressure, temperature, and density (or quantity per volume): PV = NkBT (or pV = nRT), Figure L₂ Lx 1 of 1 Part A Find the magnitude of the average force (F) in the x direction that the particle exerts on the right-hand wall of the container as it bounces back and forth. Assume that collisions between the wall and particle are elastic and that the position of the container is fixed. Be careful of the sign of your answer. Express the magnitude of the average force in terms of m, vr, and L₂. ► View Available Hint(s) Submit Part B IVE ΑΣΦ ? Imagine that the container from the problem introduction is now filled with N identical gas particles of mass m. The particles each have different x velocities. but their average x velocity squared. denoted
The small particle of mass (800 gm) spinning with angular velocity (w₁ = 2.3 rad/s, at r₁ = 400 mm), if we use force (F) to change the Angular velocity to (w₂, and r₂ = 250 mm) the value of F is: W1 Select one: A. None B. F = 5.63 N C. F = 9.47 N D. F = 3.52 N F
2- find the center of mass, the velocity of the center of mass, the momentum, and the kinetic energy of the following system: do f(xd) xaf] m₁ = 1 kg T₁=1+2j+3 k v₁ = 2î+3ĵ m₂ = 1 kg T₂ = 1-j+ k v₂ = 2) + 3k
Let's say that the semiempirical binding energy formula is Eb= aA-bA^2/3 - s(N-Z)^2/A -dZ^2/A^1/3 where a,b,s,d are constants. Imagine that you are in a different universe where there are 3 types of nucleons with spin equal to 1/2 and electric charges equal to +1, -1 and 0. Mass similar to that of a proton. Forces are similar to those of our universe. i) How do equations change for A and Z as a function of N+, N-, No and what is the semiempirical equation for the binding energy as a function of A, Z, and No? ii) At what Z and No do we have the maximum and minimum binding energy for every A? iii) When do we have stable nuclei under beta (β) decay? If "alpha particle" in this situation has N+ = N- = No = 2, what does apply for alpha (α) decay? iv) What does apply for nuclear fission and finally, how would life be in this situation?
2.3.16. [Level 21 A Republic laser weapon targets a Trade Federation battleship fleeing to space at a constant velocity of v = 25j m/s. If the length of the laser beam and its orientation with respect to the ground are described by r and 0, respectively, find what r, ř, ï, è, and 0 are when 0 = 50°. The horizontal distance between the laser weapon and battleship is 300 m. 6. 233j L. d --p- E2.3.16
Four masses A, B, C and D as shown below are to be completely balanced. Find the followings: v The axial distance between the planes of rotation of B and C(mm) v The magnitude and angular position of mass of Mp{Kg) v The angle between mass A and D (LAOD-7degree) A B. D 80 Mp Mass (kg) Radius 125 150 100 (mem) 50 60 200 120 A B 115mm
The particle in the box exercise 21 is in its ground state of nx=ny=nz=1. a) find the probability that the particle will be found in the volume defined by 0<x>L/4, 0<y>L/4, 0<z>L/4. b) Do the same for L/2 instead of L/4. ,
Physics 121 Spring 2021 - Document #11: Homework #04 & Reading Assignment page 4 of 8 Problem 1: Gnome Ride - This from a Previous Exam I. A Gnome of given mass M goes on the Gnome Ride as follows: He stands on a horizontal platform that is connected to a large piston so that the platform is driven vertically with a position as a function of time according to the following equation: y(t) = C cos(wt) Here w is a constant given angular frequency, C is a given constant (with appropriate physical units) and y represents the vertical position, positive upward as indicated. Part (a) - What is the velocity of the Gnome at time t = 0? Explain your work. Present your answer in terms of the given parameters Part (b) – What is the net force on the Gnome at time t = 0? Explain your work. Present your answer in terms of the given parameters Part (c) – What is the Normal Force on the Gnome at time t = 0? Explain your work. Present your answer in terms of the given parameters Some Possibly Useful…
FLUID STATICS. Only round off in the final answer. Use 3 decimal places. Thank you!Allison places her coffee mug on a spinner and rotates it around its axis. At rest, the mug is 10 cm deep and 6 cm in diameter, and it holds coffee 7 cm deep. What is the maximum angular rotation she can do in rad/s without spilling her coffee?
A net force F = 6t? along the x-direction acts on an object of mass m = seconds and F is in Newtons). The object is initially at rest and the force acts on the object during the 3kg (t is time in %3| time interval 0
Q2: As I navigate down the highway, my companion extends a digital kitchen scale from the window. The scale's surface is perpendicular to the incoming airflow, displaying a measurement of 4.0 kg. With the knowledge that the scale's surface area measures 0.06 m2, what is the velocity of the vehicle? Figure 2. Q2. It is generated by Bing Image Creator by requesting "please generate a picture that a digital kitchen scale is held out of the window of a moving car", powered by DALL.E (OpenAl)
(III) You are lying on a beach, your eyes 20 cm above the sand. Just as the Sun sets, fully disappearing over the horizon, you immediately jump up, your eyes now 150 cm above the sand, and you can again just see the top of the Sun. If you count the number of seconds(= t) until the Sun fully disappears again, you can estimate the Earth’s radius. But for this Problem, use the known radius of the Earth to calculate the time t.