Question

A child (mass Me) pulls a sled (mass Ms) holding a baby (mass m) across the snow (assume the snow is frictionless). When the child starts the sled moving the baby brother slips off the sled instead of moving with the sled. The child tries again with a slightly smaller force and the baby stays on the sled due to the friction between the baby and the sled. Write a symbolic solution for the coefficient offriction between the baby and the sled if the maximum acceleration ofthe sled for the baby to stay on the sled is a. The solution may include the variables MC: Ms, m: a and g but does not need to have all ofthem_ The computer Ivill not recognize any other variables. Do not include any numbers (or the in your answer). Fill in the blank

Answer 1

Answer:

symbolic solution for the coefficient of friction between the baby and the sled is  

   $\mu = \frac{m + M_s}{m} * \frac{a}{g}$

Explanation:

From the question we are told that

   The  mass of the boy is  $M_e =$

   The  mass of the shed is  $M_s$

    The mass of the baby is  $m$

    The  maximum acceleration for the baby to stay is  a

     

Generally the frictional  force between the baby and the shed is mathematically represented as

     $F_f = \mu N$

Here  N is the normal force acting on the baby which is mathematically represented as

     $N = m * g$

=>   $F_f = \mu * m * g$

Now for the baby not the slip off the shed the frictional  force between the baby and the shed must be equal to the the force applied by the child

The force applied by the child is mathematically represented as

    $F = [M_s+m] * a$

So

     $\mu * m * g = [M_s+m] * a$

=>    $\mu = \frac{m + M_s}{m} * \frac{a}{g}$