Question

A 97-kg sprinter wishes to accelerate from rest to a speed of 11 m/s in a distance of 21 m. What coefficient of static friction is required between the sprinter's shoes and the track?

Answer 1

coefficient of static friction required between the sprinter's shoes and the track is  u=0.293.

Explanation:-  

The frictional coefficient is found from newton’s second law

$\Sigma F=m u g \ldots \ldots \ldotseqn(1)$

We know that  

$F=m a \ldots \ldots \ldots{eqn}(2)$

Compare the Eqn (1) and eqn (2)  

$m u g=m a$

Mass (m) cancel each other both side

So

$u g=a$

Coefficient of static friction    

$u=\frac{a}{g} \ldots \ldots {eqn}(3)$

We know that  

Kinetics  $V^{2}=V_{0}^{2}+2 .a .\Delta s$  

$V=r e s t \text { of speed }=11 \mathrm{m} / \mathrm{s}$

$V_{0}=\text { initial speed}=0$

$\Delta s=d i s t a n c e=21 m$

$a=\text { acceleration }=\text { unknown }$

$a=\frac{\left(V^{2}-V_{0}^{2}\right)}{2 \Delta s}$

$a=\frac{\left(11^{2}-0\right)}{(2 \times 21)}$

$a=\frac{121}{42}$

$a=2.88 \mathrm{m} / \mathrm{s}^{2}$

Substitute the value of acceleration in eqn (3)

So that

Coefficient of static friction.

$u=\frac{\left(2.88 m / s^{2}\right)}{\left(9.8 m / s^{2}\right)}$

$g=9.8 \text { is earth gravity }$  

Coefficient of static friction     $u=0.293.$

Answer 2

the coefficient of static friction between the sprinter's shoes and the track is 0.294

To calculate the cofficient of static friction required between the sprinter's shoes and the track, we use the formula below.

Formula:

• μ = a/g............. Equation 1

Where:

• μ = Coefficient of static friction
• a = acceleration of the sprinter
• g = acceleration due to gravity

Given constat:

• g = 9.8 m/s²

To calculate the acceleration of the sprinter, we use

• v² = u²+2as.......... Equation 2

Make a the subject of the equation

• a = (v²-u²)/2s............... Equation 3

Where:

• v = Final velocity = 11 m/s
• u = initial velocity = 0 m/s (from rest)
• s = distance = 21 m

Substitute these values into equation 3

• a = (11²-0)/(2×21)
• a = 121/41
• a = 2.88 m/s²

Substitute these values of a into equation 1

• μ = 2.88/9.8
• μ = 0.294

Hence, the coefficient of static friction between the sprinter's shoes and the track is 0.294.

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