Figure 7 shows an athlete using a fitness device. The athlete stretches the spring in the device by pulling the handles apart. The spring constant of the spring is 140 N/m. The athlete does 45 J of work to extend the spring. The athlete takes 0.6 s to expand the spring. (i) Calculate the useful power output of the athlete when stretching the spring. (ii) Calculate the extension of the spring. Use an equation selected from the list of equations at the end of this paper.

GCSE Edexcel Physics Combined Science Power: Figure 7 shows an athlete using

Figure 7 shows an athlete using a fitness device - Edexcel - GCSE Physics Combined Science - Question 5 - 2019 - Paper 1

Question 5

Figure 7 shows an athlete using a fitness device. The athlete stretches the spring in the device by pulling the handles apart. The spring constant of the spring is... show full transcript

Worked Solution & Example Answer:Figure 7 shows an athlete using a fitness device - Edexcel - GCSE Physics Combined Science - Question 5 - 2019 - Paper 1

Step 1

Calculate the useful power output of the athlete when stretching the spring.

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Answer

To calculate the useful power output, we use the formula:

$P = \frac{E}{t}$

where:

$P$ is the power,
$E$ is the work done (in joules),
$t$ is the time taken (in seconds).

Substituting the given values:

$P = \frac{45}{0.6} = 75 \text{ W}$

Thus, the useful power output of the athlete is 75 W.

Step 2

Calculate the extension of the spring.

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Answer

To find the extension of the spring, we use Hooke's Law, represented as:

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

where:

$E$ is the energy stored in the spring (45 J),
$k$ is the spring constant (140 N/m),
$x$ is the extension of the spring in meters.

Rearranging the equation to solve for $x$ :

$45 = \frac{1}{2} \times 140 \times x^2$

This simplifies to:

$x^2 = \frac{2 \times 45}{140} \Rightarrow x^2 = \frac{90}{140} \Rightarrow x^2 = 0.642857 \Rightarrow x = \sqrt{0.642857} \approx 0.8 \text{ m}$

Therefore, the extension of the spring is approximately 0.8 m.

Figure 7 shows an athlete using a fitness device - Edexcel - GCSE Physics Combined Science - Question 5 - 2019 - Paper 1

Worked Solution & Example Answer:Figure 7 shows an athlete using a fitness device - Edexcel - GCSE Physics Combined Science - Question 5 - 2019 - Paper 1

Calculate the useful power output of the athlete when stretching the spring.

Calculate the extension of the spring.

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