Question

Q.9) Consider a plot of the displacement (x) as a function of the applied force (F) for an ideal elastic spring as
shown, see figure. The slope of the curve would be
A) the acceleration due to gravity.
B) the reciprocal of the acceleration of gravity.
C) the mass of the object attached to the spring.
D) the reciprocal of the spring's constant.

Answer 1

Answer:

Option (D).

Explanation:

For an ideal spring, the force is given in terms of displacement as follows :

F=-kx

$x=\dfrac{-F}{k}\\\\\text{or}\\\\x=\dfrac{-1}{k}F$...(1)

Where,

x is displacement in spring i.e. compression or stretching

k is spring constant of the spring

-ve sign shows that the force exerted by the spring is in opposite direction of the spring's displacement.

The equation of a line is : y=mx+c, m is slope

From equation (1)

Slope = 1/k

or

Slope = reciprocal of the spring's constant.

It would mean that the slope of the curve represents the reciprocal of the spring's constant.

Answer 2

Using the spring constant and displacement relation, the slope of the curve would be the reciprocal of the spring's constant.

Using the Force constant relation :

• F = ke

F = Force ; k = spring constant ; e = extension

• F = kx

Making the x the subject of the formula :

• x = F/k

The slope, which is the spring constant can be expressed as ;

• x = 1/k × F

Hence, the slope is the reciprocal of the spring constant.

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