Physics, 31.10.2019 06:31 evapoliziani

Ablock with mass m = 0.450 kg is attached to one end of an ideal spring and moves on a horizontal frictionless surface. the other end of the spring is attached to a wall. when the block is at x = +0.240 m, its acceleration is ax = -14.0 m/s2 and its velocity is vx = +4.00 m/s. what is the spring's force constant k?

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Answer from: slycooper99

k = 26.25 N/m

Explanation:

given,

mass of the block= 0.450

distance of the block = + 0.240

acceleration = a_x = -14.0 m/s²

velocity = v_x = + 4 m/s

spring force constant (k) = ?

we know,

x = A cos (ωt - ∅).....(1)

v = - ω A cos (ωt - ∅)....(2)

a = ω²A cos (ωt - ∅).........(3)

$\omega = \sqrt{\dfrac{k}{m}}$

now from equation (3)

$a_x = \dfrac{k}{m}x$

$k = \dfrac{m a_x}{x}$

$k = \dfrac{0.45 \times (-14)}{0.24}$

k = 26.25 N/m

hence, spring force constant is equal to k = 26.25 N/m

Answer from: Killion2022

The spring's force constant is 26.25 N/m

$\texttt{ }$

Further explanation

Hooke's Law states that the length of a spring is directly proportional to the force acting on the spring.

$\boxed {F = k \times \Delta x}$

F = Force ( N )

k = Spring Constant ( N/m )

Δx = Extension ( m )

$\texttt{ }$

The formula for finding Young's Modulus is as follows:

$\boxed {E = \frac{F / A}{\Delta x / x_o}}$

E = Young's Modulus ( N/m² )

F = Force ( N )

A = Cross-Sectional Area ( m² )

Δx = Extension ( m )

x = Initial Length ( m )

Let us now tackle the problem !

$\texttt{ }$

Given:

mass of block = m = 0.450 kg

extension = x = +0.240 m

acceleration = a_x = -14.0 m/s²

velocity = v_x = +4.00 m/s

Asked:

spring's force constant = k = ?

Solution:

$k = m \omega^2$

$k = m \frac{-a_x}{x}$

$k = 0.450 \times \frac{ - ( -14.0 ) }{0.240}$

$\boxed{k = 26.25 \texttt{ N/m}}$

$\texttt{ }$

Learn moreYoung's modulus : Young's modulus for aluminum : Young's modulus of wire :

$\texttt{ }$

Answer details

Grade: College

Subject: Physics

Chapter: Elasticity

Ablock with mass m = 0.450 kg is attached to one end of an ideal spring and moves on a horizontal fr

Answer from: Quest

an obstruction

Answer from: Quest

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.

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Ablock with mass m = 0.450 kg is attached to one end of an ideal spring and moves on a horizontal fr...