Answer:
The coefficient of static friction between the ground and the soles of a runner’s shoes is 0.98. What is the maximum speed in which the runner can accelerate without slipping if they have a mass of 73 kg?
Explanation:
The required value of distance covered by the child during sliding is of 6.08 m.
Given data:
The mass of child is, m = 48 kg.
The coefficient of friction between the child and floor is, [tex]\mu = 0.51[/tex].
The initial velocity of the child is, u = 7.8 m/s.
Applying the work-energy theorem, which says that the work done by the frictional force is equal to the kinetic energy change. Then,
[tex]W = \Delta KE \\\\f \times s = \dfrac{1}{2}mv^{2}- \dfrac{1}{2}mu^{2}[/tex]
Here, f is the frictional force and s is the stopping distance.
Solving as,
[tex]-(\mu \times mg) \times s = \dfrac{1}{2}mv^{2}- \dfrac{1}{2}mu^{2}\\\\-\mu \times g \times s = \dfrac{1}{2}(0)^{2}- \dfrac{1}{2}u^{2}\\\\-0.51 \times 9.8 \times s = - \dfrac{1}{2} \times 7.8^{2}\\\\s = 6.08 \;\rm m[/tex]
Thus, we can conclude that the required value of distance covered by the child during sliding is of 6.08 m.
Learn more about the Work-Energy theorem here:
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