Two springs are used to make a catapult. The catapult is used to shoot a ball vertically upwards. The diagram shows the ball and catapult at different stages: At P the extension of each spring is 0.2m. The spring constant of each spring is 40N/m. Calculate the total elastic potential energy stored in the springs at P.

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Two springs are used to make a catapult - OCR Gateway - GCSE Physics - Question 21 - 2021 - Paper 1

Question 21

Two springs are used to make a catapult. The catapult is used to shoot a ball vertically upwards. The diagram shows the ball and catapult at different stages: At P... show full transcript

Worked Solution & Example Answer:Two springs are used to make a catapult - OCR Gateway - GCSE Physics - Question 21 - 2021 - Paper 1

Step 1

Calculate the elastic potential energy of one spring

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Answer

The formula for elastic potential energy (EPE) stored in a spring is given by:

$EPE = \frac{1}{2} k x^2$

where:

$k$ is the spring constant (40 N/m)
$x$ is the extension of the spring (0.2 m)

Substituting in the values:

$EPE = \frac{1}{2} \times 40 \times (0.2)^2$ $EPE = \frac{1}{2} \times 40 \times 0.04$ $EPE = \frac{1}{2} \times 1.6$ $EPE = 0.8 \, \text{J}$

Step 2

Calculate the total elastic potential energy stored in the two springs

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Answer

Since there are two identical springs, the total elastic potential energy (Total EPE) is:

$Total \, EPE = 2 \times EPE\n= 2 \times 0.8 \, \text{J} = 1.6 \, \text{J}$

Thus, the total elastic potential energy stored in the springs at P is 1.6 J.

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Two springs are used to make a catapult - OCR Gateway - GCSE Physics - Question 21 - 2021 - Paper 1

Worked Solution & Example Answer:Two springs are used to make a catapult - OCR Gateway - GCSE Physics - Question 21 - 2021 - Paper 1

Calculate the elastic potential energy of one spring

Calculate the total elastic potential energy stored in the two springs

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