Figure 14 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 140N/m. The athlete does 45J of work to extend the spring. The athlete takes 0.6s to expand the spring. (i) Calculate the useful power output of the athlete when stretching the. (ii) Calculate the extension of the spring.

GCSE Edexcel Physics Forces & elasticity: Figure 14 shows an athlete using

Figure 14 shows an athlete using a fitness device - Edexcel - GCSE Physics - Question 8 - 2019 - Paper 1

Question 8

Figure 14 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 ... show full transcript

Worked Solution & Example Answer:Figure 14 shows an athlete using a fitness device - Edexcel - GCSE Physics - Question 8 - 2019 - Paper 1

Step 1

(i) Calculate the useful power output of the athlete when stretching the.

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Answer

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

$P = \frac{\text{work done}}{\text{time}}$

Given that the work done is 45 J and the time taken is 0.6 s, we can substitute the values into the equation:

$P = \frac{45 \text{ J}}{0.6 \text{ s}}$

Calculating this gives:

$P = 75 \text{ W}$

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

Step 2

(ii) Calculate the extension of the spring.

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Answer

To find the extension of the spring, we can use Hooke's Law, which states:

$F = k \cdot x$

Where:

$F$ is the force (in Newtons),
$k$ is the spring constant (in N/m), and
$x$ is the extension (in meters).

The work done on the spring can also be expressed as:

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

We can rearrange this formula to find $x$ :

Substitute $W = 45$ J and $k = 140$ N/m: $45 = \frac{1}{2} (140) x^2$
Rearranging gives: $x^2 = \frac{45 \times 2}{140}$
Calculating: $x^2 = \frac{90}{140} = \frac{9}{14}$
Finally, taking the square root to find $x$ : $x = \sqrt{\frac{9}{14}} \approx 0.75 \text{ m}$

Therefore, the extension of the spring is approximately 0.75 m.

Figure 14 shows an athlete using a fitness device - Edexcel - GCSE Physics - Question 8 - 2019 - Paper 1

Worked Solution & Example Answer:Figure 14 shows an athlete using a fitness device - Edexcel - GCSE Physics - Question 8 - 2019 - Paper 1

(i) Calculate the useful power output of the athlete when stretching the.

(ii) Calculate the extension of the spring.

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