Question

A child wearing socks is trying to see how far he can slide across his kitchen floor. If
he has a mass of 48 kg and the coefficient of friction between him and the floor is
0.51, how far can he slide with an initial velocity of 7.8 m/s?

Answer 1

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:

Answer 2

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, $\mu = 0.51$.

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,

$W = \Delta KE \\\\f \times s = \dfrac{1}{2}mv^{2}- \dfrac{1}{2}mu^{2}$

Here, f is the frictional force and s is the stopping distance.

Solving as,

$-(\mu \times mg) \times s = \dfrac{1}{2}mv^{2}- \dfrac{1}{2}mu^{2}\\\\-\mu \times g \times s = \dfrac{1}{2}(0)^{2}- \dfrac{1}{2}u^{2}\\\\-0.51 \times 9.8 \times s = - \dfrac{1}{2} \times 7.8^{2}\\\\s = 6.08 \;\rm m$

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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