A force F = −F0 e ^−x/λ (where F0 and λ are positive constants) acts on...

A force F = −F0 e ^−x/λ (where F0 and λ are positive constants) acts on a particle of mass m that is initially at x = x0 and moving with velocity v0 (> 0). Show that the velocity of the particle is given by

v(x)=(v0^2+(2F0λ /m)((e^-x/λ)-1))^1/2

where the upper (lower) sign corresponds to the motion in the positive (negative) x direction. Consider first the upper sign. For simplicity, define ve=(2F0 λ /m)^1/2 then show that the asymptotic velocity (limiting velocity as x → ∞) is given by v∞=(v0^2-ve^2)^1/2 Note that v∞ exists if v0 ≥ ve.Sketch the graph of v(x) in this case. Analyse the problem when v0 < ve by taking into account of the lower sign in the above solution. Sketch the graph of v(x) in this case. Show that the particle comes to rest (v(x) = 0) at a finite value of x given by xm=−λ ln(1-v0^2/ve^2)

Expert Solution

Colby Messinger answered 1 year ago

Given, op: (λ(n) (λ(f) (λ(x) (((n (λ(g) (λ(h) (h (g f))))) (λ(u) x)) (λ(u) u))))) zero:...

Given, op: (λ(n) (λ(f) (λ(x) (((n (λ(g) (λ(h) (h (g f))))) (λ(u) x)) (λ(u) u))))) zero: (λ(f) (λ(x) x)) one: (λ(f) (λ(x) (f x))) two: (λ(f) (λ(x) (f (f x)))) three: (λ(f) (λ(x) (f (f (f x))))) i. (4 pt) What is the result of (op one)? ii. (4 pt) What is the result of (op two)? iii. (4 pt)What is the result of (op three)? iv. (3 pt) What computation does op perform?

F is a position dependent force given by F(x) = -e^-x. Sketch the graphs showing F(t),...

F is a position dependent force given by F(x) = -e^-x. Sketch the graphs showing F(t), v(t), and x(t) for initial velocity of 10m/s, initial position of 100m, and mass = 1kg. Mention all salient points.

f(x)=e^x/(3+e^x) Find the first derivative of f. Use interval notation to indicate where f(x) is increasing....

f(x)=e^x/(3+e^x) Find the first derivative of f. Use interval notation to indicate where f(x) is increasing. List the x coordinates of all local minima of f. If there are no local maxima, enter 'NONE'. List the x coordinates of all local maxima of f. If there are no local maxima, enter 'NONE'. Find the second derivative of f: Use interval notation to indicate the interval(s) of upward concavity of f(x). Use interval notation to indicate the interval(s) of downward concavity...

Let X and Y have joint PDF f(x) = c(e^-(x/λ + y/μ)) 0 < x <...

Let X and Y have joint PDF f(x) = c(e^-(x/λ + y/μ)) 0 < x < infinity and 0 < y < infinity with parameters λ > 0 and μ > 0 a) Find c such that this is a PDF. b) Show that X and Y are Independent c) What is P(1 < X < 2, 0 < Y < 5) ? Leave in exponential form d) Find the marginal distribution of Y, f(y) e) Find E(Y)

A particle moves under constant external force F = F0 ˆi. It is also subjected to...

A particle moves under constant external force F = F0 ˆi. It is also subjected to a drag force, FD = −CDV. How will the particle move, qualitatively speaking? Describe in words before using equations. What will the particle's final velocity be? What is the sum of the external forces at the final velocity you found?

If X is a random variable with CDF F(x) = e-e(µ-x)/β, where β > 0 and...

If X is a random variable with CDF F(x) = e-e(µ-x)/β, where β > 0 and -∞ < µ, x < ∞; calculate the median of X. Also, obtain the PDF of X.

Let X be a random variable with CDF F(x) = e-e(µ-x)/β, where β > 0 and...

Let X be a random variable with CDF F(x) = e-e(µ-x)/β, where β > 0 and -∞ < µ, x < ∞. 1. What is the median of X? 2. Obtain the PDF of X. Use R to plot, in the range -10<x<30, the pdf for µ = 2, β = 5. 3. Draw a random sample of size 1000 from f(x) for µ = 2, β = 5 and draw a histogram of the values in the random sample...

A force, in the direction of increasing x, acts on an object moving along the x...

A force, in the direction of increasing x, acts on an object moving along the x axis. If the magnitude of the force is F = 10·eN, where x is in meters, find the work done by the force as the object moves from x = 0 to x = 2.0 m plz answer asap! thank you

The force acts on a particle F = 2xy ^ 2i + 2x ^ 2yj N...

The force acts on a particle F = 2xy ^ 2i + 2x ^ 2yj N Find the work done by force by moving the body from the point (0,0) to the point (2,4) following the following paths 1) (0,0) -----> (2,0) -----> (2,4) 2) (0,0) ----> (0,4) ----> (2,4) 3) Along the line that joins both points 4) Along the parabola y = x ^ 2 5) Is a conservative force? Please make the graphs and justify all your...

the force exerted by a spring is given by the equation where F is the force...

the force exerted by a spring is given by the equation where F is the force (in Newtons), xis the displacement of the spring from the equilibrium position (in centimeters), and k is a spring constant Create an Excel worksheet showing force as a function of displacement for two springs whose spring constants are 0.1 N/cm and 0.5 N/cm. Use displacements ranging from 0 to 20 cm (i.e. let x = 0, 1, 2 … 20 cm).

Question