Hookes Law Quiz: Understanding Elastic Forces

1. Elasticity is the ability of a material to:

Conduct electricity

Return to its original shape after the force is removed

Increase mass when stretched

Become magnetic

Concept: elastic behavior. An elastic material deforms under force but recovers when the force is removed. If the deformation is permanent, it is no longer purely elastic.

Explanation

Concept: elastic behavior. An elastic material deforms under force but recovers when the force is removed. If the deformation is permanent, it is no longer purely elastic.

2. A deformation that disappears after unloading is called elastic deformation.

True

False

Concept: elastic vs permanent deformation. Elastic deformation is reversible. Permanent (plastic) deformation remains after the force is removed.

Explanation

Concept: elastic vs permanent deformation. Elastic deformation is reversible. Permanent (plastic) deformation remains after the force is removed.

3. Hooke’s law for a spring is often written as:

(f = k/x)

(f = kx)

(f = x/k)

(f = k + x)

Concept: Hooke’s law equation. In the Hooke’s law region, force is proportional to extension. The constant of proportionality is the spring constant (k).

Explanation

Concept: Hooke’s law equation. In the Hooke’s law region, force is proportional to extension. The constant of proportionality is the spring constant (k).

4. In (f = kx), (k) is the spring ______.

Concept: spring constant meaning. (k) measures stiffness: higher (k) means the spring is harder to stretch. Its unit is n/m.

Explanation

Concept: spring constant meaning. (k) measures stiffness: higher (k) means the spring is harder to stretch. Its unit is n/m.

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5. The SI unit of the spring constant (k) is n/m.

True

False

Concept: units from the formula. Since (k = f/x), units are newtons divided by meters. That gives n/m.

Explanation

Concept: units from the formula. Since (k = f/x), units are newtons divided by meters. That gives n/m.

6. A spring with k = 200 n/m is stretched by 0.10m. The force is:

2 n

10 n

20 n

2000 n

Concept: using Hooke’s law. Apply (f=kx): 200 * 0.10 = 20 n. This is valid only within the elastic (linear) region.

Explanation

Concept: using Hooke’s law. Apply (f=kx): 200 * 0.10 = 20 n. This is valid only within the elastic (linear) region.

7. If the extension doubles (still in the Hooke’s law region), the force doubles.

True

False

Concept: proportionality. Hooke’s law is linear: (f ∝ x). Doubling (x) doubles (f) as long as the spring remains elastic.

Explanation

Concept: proportionality. Hooke’s law is linear: (f ∝ x). Doubling (x) doubles (f) as long as the spring remains elastic.

8. The 'elastic limit' is the point beyond which:

The material becomes stronger

The material does not return fully to its original shape

The mass becomes zero

The object stops moving

Concept: elastic limit meaning. Beyond the elastic limit, the material begins plastic deformation. Removing the force leaves a permanent extension.

Explanation

Concept: elastic limit meaning. Beyond the elastic limit, the material begins plastic deformation. Removing the force leaves a permanent extension.

9. A rubber band always follows Hooke’s law perfectly.

True

False

Concept: non-hookean materials. Many materials (like rubber) have a non-linear force–extension relationship. Hooke’s law is an approximation that applies over a limited region.

Explanation

Concept: non-hookean materials. Many materials (like rubber) have a non-linear force–extension relationship. Hooke’s law is an approximation that applies over a limited region.

10. On a force–extension graph for a Hookean spring, the Hooke’s law region is:

Curved strongly

A straight line through the origin

A horizontal line

A vertical line

Concept: graph shape for Hooke’s law. If (f=kx), the plot of (f) vs (x) is linear. The slope of the line equals (k).

Explanation

Concept: graph shape for Hooke’s law. If (f=kx), the plot of (f) vs (x) is linear. The slope of the line equals (k).

11. The slope of an (f) vs (x) graph in the linear region equals the spring constant (k).

True

False

Concept: interpreting slope. From (f=kx), (k = Δ f/Δ x). A steeper slope means a stiffer spring.

Explanation

Concept: interpreting slope. From (f=kx), (k = Δ f/Δ x). A steeper slope means a stiffer spring.

12. Extension (x) is the change in length: (x = l - l_0), where (l_0) is the ______ length.

Concept: natural length. The natural length is the length with no load. Extension is measured relative to this baseline.

Explanation

Concept: natural length. The natural length is the length with no load. Extension is measured relative to this baseline.

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13. A spring has natural length 0.30 m and stretched length 0.38 m. Extension is:

0.08 m

0.68 m

0.30 m

Concept: finding extension. Extension is (0.38 - 0.30 = 0.08) m. Extension is what Hooke’s law uses.

Explanation

Concept: finding extension. Extension is (0.38 - 0.30 = 0.08) m. Extension is what Hooke’s law uses.

14. “Stiffer” springs have larger (k) values.

True

False

Concept: stiffness and (k). Larger (k) means more force is needed for the same extension. That’s the definition of being stiffer.

Explanation

Concept: stiffness and (k). Larger (k) means more force is needed for the same extension. That’s the definition of being stiffer.

15. If a spring is loaded beyond its elastic limit, then when unloaded it will:

Return exactly to its original length

Stay permanently stretched

Become shorter than before

Gain mass

Concept: plastic deformation. Past the elastic limit, the material structure changes. Some extension remains even after removing the force.

Explanation

Concept: plastic deformation. Past the elastic limit, the material structure changes. Some extension remains even after removing the force.

16. Elastic materials store energy when they are stretched or compressed.

True

False

Concept: elastic potential energy. Doing work to stretch a material stores energy. When released, that energy can be transferred back as kinetic energy.

Explanation

Concept: elastic potential energy. Doing work to stretch a material stores energy. When released, that energy can be transferred back as kinetic energy.

17. The region where force and extension are proportional is called the ______ region.

Concept: hookean region. In this region, (f) increases in direct proportion to (x). Outside it, the relationship may curve or fail.

Explanation

Concept: hookean region. In this region, (f) increases in direct proportion to (x). Outside it, the relationship may curve or fail.

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18. Which change would increase extension for the same applied force (within Hooke’s law)?

Increasing (k)

Decreasing (k)

Increasing mass of the spring

Painting the spring

Concept: rearranging Hooke’s law. Since (x=f/k), smaller (k) gives larger extension for the same force. A 'softer' spring stretches more.

Explanation

Concept: rearranging Hooke’s law. Since (x=f/k), smaller (k) gives larger extension for the same force. A 'softer' spring stretches more.

19. Hooke’s law can apply to compression as well as extension for many springs.

True

False

Concept: symmetry for ideal springs. Many springs resist both stretching and compressing. The same proportional rule can hold in both directions within the elastic range.

Explanation

Concept: symmetry for ideal springs. Many springs resist both stretching and compressing. The same proportional rule can hold in both directions within the elastic range.

20. The best overall summary is:

Elasticity means a material never changes shape

In the elastic region, many springs obey (f=kx); beyond the elastic limit, permanent deformation can occur

The spring constant has units of joules

A straight line graph means plastic behavior

Concept: elasticity recap. Elasticity is reversible deformation; Hooke’s law describes the linear part. The elastic limit marks the boundary before permanent changes appear.

Explanation

Concept: elasticity recap. Elasticity is reversible deformation; Hooke’s law describes the linear part. The elastic limit marks the boundary before permanent changes appear.