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P6: An object of mass m sits on a spring of constant k in an elevator that is accelerating upwards with acceleration a. a) In terms of g, m, k, and a, how much is the spring compressed? b) If the compression is 2.5 times larger than it is when the mass sits in a still elevator, what is the acceleration? Please be sure to answer each of the questions in terms of the given variables and g.

Respuesta :

Answer:

(a). The spring compressed is [tex]\dfrac{ma+mg}{k}[/tex].

(b). The acceleration is 1.5 g.

Explanation:

Given that,

Acceleration = a

mass = m

spring constant = k

(a). We need to calculate the spring compressed

Using balance equation

[tex]kx-mg=ma[/tex]

[tex]x=\dfrac{ma+mg}{k}[/tex]....(I)

The spring compressed is [tex]\dfrac{ma+mg}{k}[/tex].

(b). If the compression is 2.5 times larger than it is when the mass sits in a still elevator,

The compression is given by

[tex]x=2.5\times x_{0}[/tex]

Here, acceleration is zero

So, [tex]x=2.5\times\dfrac{mg}{k}[/tex]

We need to calculate the acceleration

Put the value of x in equation (I)

[tex]2.5\times \dfrac{mg}{k}=\dfrac{ma+mg}{k}[/tex]

[tex]2.5\times\dfrac{mg}{k}=\dfrac{m}{k}(a+g)[/tex]

[tex]a=2.5g-g[/tex]

[tex]a=1.5g[/tex]

Hence, (a). The spring compressed is [tex]\dfrac{ma+mg}{k}[/tex].

(b). The acceleration is 1.5 g.