Question

Figure OQ7.10 shows a light extended spring exerting a force to the left on a block. (i) Does the block exert a force on the spring? Choose every correct answer. (a) No, it doesn’t. (b) Yes, it does, to the left. (c) Yes, it does, to the right. (d) Yes, it does, and its magnitude is larger than ${\mathbf{F}}_{\mathbf{s}}$. (e) Yes, it does, and its magnitude is equal to ${\mathbf{F}}_{\mathbf{s}}$. (ii) Does the spring exert a force on the wall? Choose your answers from the same list (a) through (e).

Short answer

(i) The correct options are (c) and (e):

(c) Yes, it does, to the right

(e) Yes, it does, and its magnitude is equal to ${\mathrm{F}}_{\mathrm{s}}$.

(ii) The correct options are (c) and (e):

(c) Yes, it does, to the right.

(e) Yes, it does, and its magnitude is equal to ${\mathrm{F}}_{\mathrm{s}}$.

Step-by-step solution

Given information

The force exerted by an extended light spring to the left on a block is ${\mathrm{F}}_{\mathrm{s}}$.

The displacement of the block is x.

The displacement of spring

An elastic spring is compressed to a certain distance when an external force acts on it, and the spring returns to its original position when the force is removed.

The displacement of the elastic spring is determined using the value of force exerted and the spring’s stiffness.

Force exerted by the block on the spring 

(i)

From the diagram, the force ${\mathrm{F}}_{\mathrm{s}}$acts toward the left on the block, and due to this force, the block moves to a distance of x.

At the equilibrium condition, theforce exerted by the block on the spring to the left is balanced by the force exerted by the spring on the block toward the right.

So, the force exerted by the spring on the block toward the right is equal to${\mathrm{F}}_{\mathrm{s}}$

Hence, the correct options are(c) and (e):

(c) Yes, it does, to the right

(e) Yes, it does, and its magnitude is equal to${\mathrm{F}}_{\mathrm{s}}$

Force exerted by the spring on the wall 

(ii)

The spring tension exerts equal-magnitude forces toward the center of the spring on objects at both ends.

The force acting from the block to the spring${\mathrm{F}}_{\mathrm{s}}$

toward the left is transferred to the left end connected to the wall. So, the spring tension exerts a force of equal magnitude on the objects at both ends.

The tension on the spring acts towards the center of the spring from both ends.

Hence, the correct options are (c) and (e).

(c) Yes, it does, to the right

(e) Yes, it does, and its magnitude is equal to${\mathrm{F}}_{\mathrm{s}}$