The break mechanism used to reduce recoil in certain types of guns consists essentially of a piston attached to the barrel and moving in a fixed cylinder filled with oil. As the barrel recoils with an initial velocity vo , the piston moves and oil is forced through orifices in the piston, causing the piston and the barrel to decelerate at a rate proportional to their velocity, i.e.a=-kv. Express:a) v in terms of tb) x in terms of tc) v in terms of x

Question

quennnshyan1557 quennnshyan1557

05-02-2020
Engineering

contestada

The break mechanism used to reduce recoil in certain types of guns consists essentially of a piston attached to the barrel and moving in a fixed cylinder filled with oil. As the barrel recoils with an initial velocity vo , the piston moves and oil is forced through orifices in the piston, causing the piston and the barrel to decelerate at a rate proportional to their velocity, i.e.a=-kv. Express:a) v in terms of tb) x in terms of tc) v in terms of x

Respuesta :

Otras preguntas

correctly identify steps in the water cycle.

Draw and label an example of two parallel lines that are perpendicular to third line

What is a hemisphere?

Solve three and two fifths plus three and four sixths

When a country is able to invest more money in health infrastructure, how can you infer that would affect the population?

A tank in the shape of a hemisphere has a diameter of 26 feet. If the liquid that fills the tank has a density of 96.5 pounds per cubic foot, what is the total

Jeremy saves quarters and dimes. One night he counts his coins and finds that there are 30 coins with a total value of $4.50. How many of each kind of coin does

Hellllllppppp hurry

A restaurant manager figured that the food for nightly steak special actually cost $8.00. The restaurant will sell the special at an 80% markup. How much will a

HELP!!! Lots of Spanish questions incoming!

AyBaba7 AyBaba7 · Answer 1 · 2020-02-09T21:54:31+01:00

Answer:

a) v = v₀(e^-kt)

b) x = -v₀(e^-kt)/k

c) v = -kx

Explanation:

a) a = dv/dt

a = -kv = dv/dt

dv/v = -kdt

Integrating the left hand side from v₀ to v and the right hand side from 0 to t

In (v/v₀) = -kt

v/v₀ = e^(-kt)

v = v₀(e^-kt)

b) v = dx/dt

dx/dt = v = v₀(e^-kt)

dx/dt = v₀(e^-kt)

dx = v₀(e^-kt)dt

Integrating the right hand side from 0 to t and the left hand side from 0 to x,

x = -v₀(e^-kt)/k

c) Since v = v₀(e^-kt)

x = -v₀(e^-kt)/k

x = -v/k

v = -kx

Hope this helps!

AFOKE88 AFOKE88 · Answer 2 · 2022-03-29T17:00:00+02:00

The velocity (v) expressed in terms of t is; v = v₀(e^(-kt))

The distance expressed in terms of t is; x = -v₀(e^-kt)/k

The velocity expressed in terms of x is; v = -kx

What is the velocity in terms of other parameters?

a) We know that acceleration is simply change in speed with respect to time. Thus;

a = dv/dt

We are told that a = -kv. Thus;

a = dv/dt = -kv

dv/v = -kdt

Integrating both sides with respective boundary conditions gives;

v₀ to v∫dv/v = 0 to t∫-kdt

⇒ In (v/v₀) = -kt

v/v₀ = e^(-kt)

v = v₀(e^(-kt))

b) We know that velocity is change in distance with respect to time. Thus;

v = dx/dt

From a above, we saw that v = v₀(e^(-kt))

Thus;

dx/dt = v₀(e^(-kt))

dx = v₀(e^(-kt))dt

Integrating both sides with respective boundary conditions gives;

0 to x∫dx = 0 to t∫v₀(e^(-kt))dt

x = -v₀(e^-kt)/k

c) Earlier we saw that v = v₀(e^-kt)

Since x = -v₀(e^-kt)/k, then;

x = -v/k

Thus, velocity is;

v = -kx

Read more about velocity at; https://brainly.com/question/4931057