Question

The elastic energy stored in your tendons can contribute up to 35% of your energy needs when running. Sports scientists find that (on average) the knee extensor tendons in sprinters stretch 45 mm while those of nonathletes stretch only 32 mm . The spring constant of the tendon is the same for both groups, 33 N/mm . Part A What is the difference in maximum stored energy between the sprinters and the nonathletes? Express your answer to two significant figures and include the appropriate units. View Available Hint(s)for Part A Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type ΔU =

Answer 1

Step-by-step explanation:

To calculate the difference in maximum stored energy between the sprinters and nonathletes, we can use the formula for elastic potential energy stored in a spring-like tendon:

Elastic Potential Energy

(

Δ

�

)

=

1

2

�

(

Δ

�

)

2

Elastic Potential Energy(ΔU)=

2

1

​

k(Δx)

2

where:

Δ

�

ΔU is the elastic potential energy stored in the tendon.

�

k is the spring constant of the tendon.

Δ

�

Δx is the amount of stretching or deformation in the tendon.

Given data:

Spring constant (

�

k) for both groups = 33 N/mm = 33 N / 1000 mm (converting to N/m)

Δ

�

Δx for sprinters = 45 mm = 45 mm (converting to meters)

Δ

�

Δx for nonathletes = 32 mm = 32 mm (converting to meters)

Now, we can calculate the elastic potential energy (

Δ

�

ΔU) for each group:

For sprinters:

Δ

�

sprinters

=

1

2

×

33

×

(

0.045

)

2

ΔU

sprinters

​

=

2

1

​

×33×(0.045)

2

For nonathletes:

Δ

�

nonathletes

=

1

2

×

33

×

(

0.032

)

2

ΔU

nonathletes

​

=

2

1

​

×33×(0.032)

2

Now, find the difference in maximum stored energy between the two groups:

Difference in maximum stored energy

=

Δ

�

sprinters

−

Δ

�

nonathletes

Difference in maximum stored energy=ΔU

sprinters

​

−ΔU

nonathletes

​

Calculate the values and subtract:

Δ

�

sprinters

=

1

2

×

33

×

(

0.045

)

2

=

0.033825

Nm

ΔU

sprinters

​

=

2

1

​

×33×(0.045)

2

=0.033825 Nm

Δ

�

nonathletes

=

1

2

×

33

×

(

0.032

)

2

=

0.02112

Nm

ΔU

nonathletes

​

=

2

1

​

×33×(0.032)

2

=0.02112 Nm

Difference in maximum stored energy

=

0.033825

−

0.02112

=

0.012705

Nm

Difference in maximum stored energy=0.033825−0.02112=0.012705 Nm

Rounded to two significant figures, the difference in maximum stored energy between the sprinters and nonathletes is approximately 0.013 Nm.