Forces & Elasticity (OCR GCSE Physics A (Gateway))

A student investigates how a spring stretches.

She measures the original length of the spring, adds a 2.0 N weight, and then measures the extended length of the spring.

Look at her data in the table.

i) Calculate the spring constant for the spring.

 Use the equation: force = spring constant × extension

Spring constant = ............................................ N/cm [3]

ii) Suggest two ways that the student could improve and develop their method to find the spring constant.

[2]

The spring constant of a different spring is 40 N/m.

Calculate the energy stored in the spring when it is stretched 0.20 m.

Use an equation from the data sheet to help you.

Energy stored = ...................................................... J

The diagram shows an experiment a student set up to study moments.

The student:

• holds the metre rule so that it is horizontal

• adds weights to the metre rule at different distances from the pivot.

i) Calculate the moments of the 2 N weight and the 3 N weight about the pivot.

Use the equation: moment = force × distance from pivot

Moment of 2 N weight = .......................................................N cm Moment of 3 N weight = .......................................................N cm

ii) Which way will the metre rule rotate when it is released by the student?

The force–extension graphs for four different springs (A, B, C and D) are shown below.

Explain which of the springs (A, B, C or D) has the largest spring constant?

Explain why the line for spring B has a different shape from the other lines.

i) A spring has a spring constant of 27 N/m.

The spring is stretched to an extension of 25 cm.

The energy transferred can be calculated using the formula:

energy transferred = 0.5 × spring constant × extension²

Calculate the energy transferred in stretching.

Answer .......................... J [2]

ii) A student set up the apparatus shown in Fig. 20.1.

Fig. 20.1

The students want to plot a force-extension graph for this spring.

Describe how they could use this apparatus to collect data so that the graph could be plotted.

[4]

iii) The spring in Fig. 20.1 has a spring constant of 30 N/m.

This is replaced by a spring with a spring constant of 10 N/m.

What changes should the student make to this method to investigate this spring?

[2]

A student investigates the extension of a spring.

The student attaches 1.0 N weights to the spring gradually and records the extension using a ruler.

They plot a force-extension graph of their results.

The spring obeys Hooke’s law up to point A. 

Draw a line on the graph to show the relationship between force and extension up to point A.

When the weights are removed, the spring remains slightly extended.

The student writes some facts about the experiment.

State if each fact is correct or incorrect. Put a ring around the correct option.

Explain your answers.

i) Point A represents the elastic limit of the spring.

correct‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ incorrect

Reason: ..........................................................................................................

[1]

ii) The spring undergoes elastic deformation beyond point A.

correct‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ incorrect

Reason: ..........................................................................................................

[1]

iii) The relationship between force and extension is non-linear up to point A.

correct‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ incorrect

Reason: ..........................................................................................................

[1]

Use the graph to calculate the spring constant of the spring.

Use the equation: force exerted by a spring = extension × spring constant

‎ Spring constant = ................................................. N/m

Calculate the work done when the spring is stretched with a force of 12 N.

Use the Equation Sheet.

‎ Work done = ....................................................... J

A student investigates the compression of springs in a push-down bar.

Fig. 1.1 shows how the student applies force to the push-down bar.

Fig. 1.2 shows the construction of the push-down bar.

Fig. 1.1

Fig. 1.2

On Fig. 1.2 draw arrows to represent the forces that need to be applied in order to compress the springs.

The student compresses the push-down bar by increasing the force applied and measures the compression each time.

Fig. 1.3 shows the force-extension graph of their results.

Fig. 1.3

i) Use the graph in Fig. 1.3 to describe and explain the behaviour of the springs.

[2]

ii) Use data from Fig. 1.3 to calculate the spring constant for the springs.

Give your answer to 2 significant figures.

Use the equation: force exerted by a spring = extension × spring constant

‎ Spring constant = ................................................. N/m [4]

iii) Suggest why the spring constant of a single spring is lower than this.

[1]

The manufacturer claims using the push-down bar can help users 'burn calories'.

Use ideas about energy transfer to explain why the manufacturer is correct.

The manufacturer has a choice of three different springs to use in the push-down bar as shown in the table.

A user is looking to purchase a push-down bar which would 'burn the most calories'.

State and explain which spring the user should choose.