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Solved problems for the chapter:

Elasticity

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Introduction to Force

1. What is force?

2. How do we know that a force is acting on a body?

2.1. Effects of forces

3. Name, symbol and unit of force

4. Properties of force

5. Drawing forces

6. Contact force or field force

7. Surface and volume distributed forces

7.1. Area-distributed or surface forces

7.2. Volume-distributed or body forces

8. Measuring forces

9. Forum

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Deformation of Solids

1. Force pressure

2. Tensile stress

3. Extension of a material

4. Contraction of a material

5. Forum

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Measuring Forces with Springs

1. Hook's law

2. Spring balance

3. Forum

↓ Show theory [3] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:elasticity/5056/

Example 1.

We use a spring to assemble a spring balance. We suspend one, two, and three weights of 0.5 N each in succession on the spring and measure the extension of each spring compared to the load applied. The extension of each of the springs is shown in the figure.

Draw a graph of the relationship of force on extension.
What is the name of the law that describes this relationship?
Calculate the force if the extension is 14 cm.

Example 2.

The graph of the relationship between the force and the extension of two spring balances is given.

Answer the following questions:

Which spring balance can measure a greater force? What is this force and how much extension of the spring does it cause?
What forces cause an extension of 4 cm for both spring scales?
For both spring balances, determine to what limit the force is directly proportional to the extension.
The second spring balance has 10 divisions on the scale. What is the force represented by the gap between two divisions?
What can happen if we load the first spring balance with a force of 5 N?

With a force of 0.6 N, a spring balance is stretched by 4 cm. It stretches by 7 cm while measuring an unknown weight. What is the value of the weight?

We hang different weights on a spring balance and measure the extension. The results of the measurements are shown in the table below.

Force [N]	0.2	0.4	0.6	0.8	1.0	1.2	1.4	1.6
Extension [cm]	0.8	1.6	2.4	3.2	4	4.7	5.2	5.5

What is the maximum force we can measure with this spring balance?

The maximum force that can be measured with a spring balance is 9 N. At a force of 3 N, the spring stretches by 2 cm. Draw a graph of the force against the extension.

A spring balance has eight divisions on the scale. The distance between the divisions is 1 cm. The maximum force that can be measured with the balance is 4 N. Draw the graph of the force against the extension if the force and extension are considered to be directly proportional.

We have a spring 5 cm long. When a weight of 0.5 N is hung on it, the spring is 7.5 cm long. Calculate the value of an unknown weight that is hung on the spring if the spring is now 9 cm long.

We have two springs. If the first spring is loaded with a force of 5 N, it stretches by 2 cm. If a weight of 200 g is hung on the second spring, it stretches by 6 mm. Determine which spring is "stiffer" (stretches lesser under load).

We hang the masses in the table below on a spring balance and measure the extension produced by each mass. The results are shown in the table below.

Complete the table by entering the weight of each mass.
Draw the graph of the weight against the extension.
Determine to what limit the weight and extension are directly proportional.

Mass [g]	0	20	40	60	80	100	140
Weight [N]
Extension [mm]	0	8	16	24	32	40	48

10.

The maximum allowable force with which we can load a spring balance is 10 N. With this force, it stretches by 8 cm. If we hang an unknown mass on a spring balance, it stretches by 45 mm. What is this mass?

11.

If we load spring balance with a force of 4 N, the spring stretches by 6 cm, and if we load it with a force of 6 N, it stretches to three times its length. How long is the spring if no force acts on it?

12.

A graph of the relationship between the force and the extension for three spring balances is given.

Arrange all the three spring balances by hardness.
Can a weight of mass 120 g be hung on the first spring balance?
By how much does the second spring balance stretch if a 50 g weight is hung on it?

13.

Two spring balances are connected in series (one after the other) as shown in the figure. The graph of the relationship between the force and the extension for both spring balances is also given. What is the total extension of the arrangement if one is loaded with a force of 1.5 N?

14.

The graph of the relationship between the force and the extension for two spring balances is given. We tie the spring balances in parallel, side by side, as shown in the picture below on the right. When we hang a weight on the crossbar that connects the hooks, they stretch by 6 cm. What is the unknown weight?

15.

We want to measure the mass of an unknown weight with the help of a spring balance. The spring balance extends by 1 cm if a force of 0.1 N is applied to it. When we hang a weight with mass m on it, it stretches by 8 cm. What is the mass of the weight?

16.

A spring is extended by a force. The variation with extension of the force is shown in the figure below.

State the name of the law that relates the force and extension of the spring shown in the figure above.
Determine the spring constant, in , of the spring

17.

A spring has an unstretched length of . When a force of is applied to the spring, its length increases to . The limit of proportionality is not exceeded. What is the spring constant of the spring?

18.

A spring obeys Hooke’s law. Which graph is obtained by plotting the extension of the spring against the load applied?

19.

A student measures the length of a spring. She then attaches different weights to the spring. She measures the length of the spring for each weight. The table shows her results.

What is the extension of the spring with a weight of attached to it?

20.

A metal wire is loaded up to the limit of proportionality. Which statement is correct?

Hooke’s law is not obeyed when the load is increased from zero to this point.
When the load is increased beyond the limit of proportionality, the diameter of the wire will increase.
When the load is removed, the wire returns to its original length.
Up to the limit of proportionality, there is no change in the shape of the wire.

21.

The figure below shows part of the extension-load graph for a spring.

The spring obeys Hooke’s law between points A and B.

On the figure, complete the graph between A and B.
State the name of point B.

22.

A spring, which obeys Hooke’s law, has an unstretched length of . A load of is suspended from the spring. The new length of the spring is . What is the spring constant of the spring?

23.

Different weights are hung from a spring. The diagram shows the original length of the spring, and the lengths when different weights are added.

The extension of the spring is directly proportional to the weight hung from it. What is the weight of W?

24.

The extension–load graph for a spring is shown. The unstretched length of the spring is .

When an object is suspended from the spring, the length of the spring is . What is the weight of the object?

25.

The diagram shows the graph of the length of a spring against the load applied to it.

What is the spring constant of the spring?

26.

A load is hung from a steel wire. The load is increased and the length of the wire increases until the limit of proportionality is reached. The load is now increased slightly. What happens?

The extension of the wire increases and the wire no longer obeys Hooke’s law.
The extension of the wire decreases and the wire no longer obeys Hooke’s law.
The extension of the wire increases and it obeys Hooke’s law.
The extension of the wire decreases and it obeys Hooke’s law.

27.

The diagrams show a spring and a graph of the length of the spring against the load applied to it.

What is the extension of the spring when a load of is applied to it?

28.

The unstretched lengths and extension-load graphs are shown for each of four different springs. Which spring is the longest when a load of is hung from each spring?

29.

A student investigates a steel spring. He measures the length of the spring, then he hangs different weights from the spring. He measures the length of the spring for each different weight. The table shows his results.